Sample records for gaussian beam model

  1. Improved Gaussian Beam-Scattering Algorithm

    NASA Technical Reports Server (NTRS)

    Lock, James A.

    1995-01-01

    The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

  2. Gaussian-Beam Laser-Resonator Program

    NASA Technical Reports Server (NTRS)

    Cross, Patricia L.; Bair, Clayton H.; Barnes, Norman

    1989-01-01

    Gaussian Beam Laser Resonator Program models laser resonators by use of Gaussian-beam-propagation techniques. Used to determine radii of beams as functions of position in laser resonators. Algorithm used in program has three major components. First, ray-transfer matrix for laser resonator must be calculated. Next, initial parameters of beam calculated. Finally, propagation of beam through optical elements computed. Written in Microsoft FORTRAN (Version 4.01).

  3. Hollow Gaussian Schell-model beam and its propagation

    NASA Astrophysics Data System (ADS)

    Wang, Li-Gang; Wang, Li-Qin

    2008-03-01

    In this paper, we present a new model, hollow Gaussian Schell-model beams (HGSMBs), to describe the practical dark hollow beams. An analytical propagation formula for HGSMBs passing through a paraxial first-order optical system is derived based on the theory of coherence. Based on the derived formula, an application example showing the influence of spatial coherence on the propagation of beams is illustrated. It is found that the beam propagating properties of HGSMBs will be greatly affected by their spatial coherence. Our model provides a very convenient way for analyzing the propagation properties of partially coherent dark hollow beams.

  4. Generalized Ince Gaussian beams

    NASA Astrophysics Data System (ADS)

    Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

    2006-08-01

    In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

  5. GAUSSIAN BEAM LASER RESONATOR PROGRAM

    NASA Technical Reports Server (NTRS)

    Cross, P. L.

    1994-01-01

    In designing a laser cavity, the laser engineer is frequently concerned with more than the stability of the resonator. Other considerations include the size of the beam at various optical surfaces within the resonator or the performance of intracavity line-narrowing or other optical elements. Laser resonators obey the laws of Gaussian beam propagation, not geometric optics. The Gaussian Beam Laser Resonator Program models laser resonators using Gaussian ray trace techniques. It can be used to determine the propagation of radiation through laser resonators. The algorithm used in the Gaussian Beam Resonator program has three major components. First, the ray transfer matrix for the laser resonator must be calculated. Next calculations of the initial beam parameters, specifically, the beam stability, the beam waist size and location for the resonator input element, and the wavefront curvature and beam radius at the input surface to the first resonator element are performed. Finally the propagation of the beam through the optical elements is computed. The optical elements can be modeled as parallel plates, lenses, mirrors, dummy surfaces, or Gradient Index (GRIN) lenses. A Gradient Index lens is a good approximation of a laser rod operating under a thermal load. The optical system may contain up to 50 elements. In addition to the internal beam elements the optical system may contain elements external to the resonator. The Gaussian Beam Resonator program was written in Microsoft FORTRAN (Version 4.01). It was developed for the IBM PS/2 80-071 microcomputer and has been implemented on an IBM PC compatible under MS DOS 3.21. The program was developed in 1988 and requires approximately 95K bytes to operate.

  6. Hollow vortex Gaussian beams

    NASA Astrophysics Data System (ADS)

    Zhou, GuoQuan; Cai, YangJian; Dai, ChaoQing

    2013-05-01

    A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular momentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respectively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter γ, and transfer matrix elements A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in optical micromanipulation.

  7. A Gaussian beam method for ultrasonic non-destructive evaluation modeling

    NASA Astrophysics Data System (ADS)

    Jacquet, O.; Leymarie, N.; Cassereau, D.

    2018-05-01

    The propagation of high-frequency ultrasonic body waves can be efficiently estimated with a semi-analytic Dynamic Ray Tracing approach using paraxial approximation. Although this asymptotic field estimation avoids the computational cost of numerical methods, it may encounter several limitations in reproducing identified highly interferential features. Nevertheless, some can be managed by allowing paraxial quantities to be complex-valued. This gives rise to localized solutions, known as paraxial Gaussian beams. Whereas their propagation and transmission/reflection laws are well-defined, the fact remains that the adopted complexification introduces additional initial conditions. While their choice is usually performed according to strategies specifically tailored to limited applications, a Gabor frame method has been implemented to indiscriminately initialize a reasonable number of paraxial Gaussian beams. Since this method can be applied for an usefully wide range of ultrasonic transducers, the typical case of the time-harmonic piston radiator is investigated. Compared to the commonly used Multi-Gaussian Beam model [1], a better agreement is obtained throughout the radiated field between the results of numerical integration (or analytical on-axis solution) and the resulting Gaussian beam superposition. Sparsity of the proposed solution is also discussed.

  8. TH-C-BRD-04: Beam Modeling and Validation with Triple and Double Gaussian Dose Kernel for Spot Scanning Proton Beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hirayama, S; Takayanagi, T; Fujii, Y

    2014-06-15

    Purpose: To present the validity of our beam modeling with double and triple Gaussian dose kernels for spot scanning proton beams in Nagoya Proton Therapy Center. This study investigates the conformance between the measurements and calculation results in absolute dose with two types of beam kernel. Methods: A dose kernel is one of the important input data required for the treatment planning software. The dose kernel is the 3D dose distribution of an infinitesimal pencil beam of protons in water and consists of integral depth doses and lateral distributions. We have adopted double and triple Gaussian model as lateral distributionmore » in order to take account of the large angle scattering due to nuclear reaction by fitting simulated inwater lateral dose profile for needle proton beam at various depths. The fitted parameters were interpolated as a function of depth in water and were stored as a separate look-up table for the each beam energy. The process of beam modeling is based on the method of MDACC [X.R.Zhu 2013]. Results: From the comparison results between the absolute doses calculated by double Gaussian model and those measured at the center of SOBP, the difference is increased up to 3.5% in the high-energy region because the large angle scattering due to nuclear reaction is not sufficiently considered at intermediate depths in the double Gaussian model. In case of employing triple Gaussian dose kernels, the measured absolute dose at the center of SOBP agrees with calculation within ±1% regardless of the SOBP width and maximum range. Conclusion: We have demonstrated the beam modeling results of dose distribution employing double and triple Gaussian dose kernel. Treatment planning system with the triple Gaussian dose kernel has been successfully verified and applied to the patient treatment with a spot scanning technique in Nagoya Proton Therapy Center.« less

  9. Experimental study of the focusing properties of a Gaussian Schell-model vortex beam

    NASA Astrophysics Data System (ADS)

    Wang, Fei; Zhu, Shijun; Cai, Yangjian

    2011-08-01

    We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results.

  10. Experimental study of the focusing properties of a Gaussian Schell-model vortex beam.

    PubMed

    Wang, Fei; Zhu, Shijun; Cai, Yangjian

    2011-08-15

    We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results. © 2011 Optical Society of America

  11. Ince Gaussian beams in strongly nonlocal nonlinear media

    NASA Astrophysics Data System (ADS)

    Deng, Dongmei; Guo, Qi

    2008-07-01

    Based on the Snyder-Mitchell model that describes the beam propagation in strongly nonlocal nonlinear media, the close forms of Ince-Gaussian (IG) beams have been found. The transverse structures of the IG beams are described by the product of the Ince polynomials and the Gaussian function. Depending on the input power of the beams, the IG beams can be either a soliton state or a breather state. The IG beams constitute the exact and continuous transition modes between Hermite-Gaussian beams and Laguerre-Gaussian beams. The IG vortex beams can be constructed by a linear combination of the even and odd IG beams. The transverse intensity pattern of IG vortex beams consists of elliptic rings, whose number and ellipticity can be controlled, and a phase displaying a number of in-line vortices, each with a unitary topological charge. The analytical solutions of the IG beams are confirmed by the numerical simulations of the nonlocal nonlinear Schr\\rm \\ddot{o} dinger equation.

  12. Diffraction of cosine-Gaussian-correlated Schell-model beams.

    PubMed

    Pan, Liuzhan; Ding, Chaoliang; Wang, Haixia

    2014-05-19

    The expression of spectral density of cosine-Gaussian-correlated Schell-model (CGSM) beams diffracted by an aperture is derived, and used to study the changes in the spectral density distribution of CGSM beams upon propagation, where the effect of aperture diffraction is emphasized. It is shown that, comparing with that of GSM beams, the spectral density distribution of CGSM beams diffracted by an aperture has dip and shows dark hollow intensity distribution when the order-parameter n is big enough. The central intensity increases with increasing truncation parameter of aperture. The comparative study of spectral density distributions of CGSM beams with aperture and that of without aperture is performed. Furthermore, the effect of order-parameter n and spatial coherence of CGSM beams on the spectral density distribution is discussed in detail. The results obtained may be useful in optical particulate manipulation.

  13. Generalized multi-Gaussian correlated Schell-model beam: from theory to experiment.

    PubMed

    Wang, Fei; Liang, Chunhao; Yuan, Yangsheng; Cai, Yangjian

    2014-09-22

    A new kind of partially coherent beam with non-conventional correlation function named generalized multi-Gaussian correlated Schell-model (GMGCSM) beam is proposed. The GMGCSM beam of the first or second kind is capable of producing dark hollow or flat-topped beam profile in the focal plane (or in the far field). Furthermore, we carry out experimental generation of a GMGCSM beam of the first or second kind, and measure its focused intensity. Our experimental results verify theoretical predictions. The GMGCSM beam will be useful for free-space optical communications, material thermal processing, particle or atom trapping.

  14. Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

    NASA Astrophysics Data System (ADS)

    Xiao, Zhiyu; Xia, Hui; Yu, Tao; Xie, Ding; Xie, Wenke

    2018-03-01

    The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω 0. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.

  15. Gyrator transform of Gaussian beams with phase difference and generation of hollow beam

    NASA Astrophysics Data System (ADS)

    Xiao, Zhiyu; Xia, Hui; Yu, Tao; Xie, Ding; Xie, Wenke

    2018-06-01

    The optical expression of Gaussian beams with phase difference, which is caused by gyrator transform (GT), has been obtained. The intensity and phase distribution of transform Gaussian beams are analyzed. It is found that the circular hollow vortex beam can be obtained by overlapping two GT Gaussian beams with π phase difference. The effect of parameters on the intensity and phase distributions of the hollow vortex beam are discussed. The results show that the shape of intensity distribution is significantly influenced by GT angle α and propagation distance z. The size of the hollow vortex beam can be adjusted by waist width ω 0. Compared with previously reported results, the work shows that the hollow vortex beam can be obtained without any model conversion of the light source.

  16. Hollow sinh-Gaussian beams and their paraxial properties.

    PubMed

    Sun, Qiongge; Zhou, Keya; Fang, Guangyu; Zhang, Guoqiang; Liu, Zhengjun; Liu, Shutian

    2012-04-23

    A new mathematical model of dark-hollow beams, described as hollow sinh-Gaussian (HsG) beams, has been introduced. The intensity distributions of HsG beams are characterized by a single bright ring along the propagation whose size is determined by the order of beams; the shape of the ring can be controlled by beam width and this leads to the elliptical HsG beams. Propagation characteristics of HsG beams through an ABCD optical system have been researched, they can be regarded as superposition of a series of Hypergeometric-Gaussian (HyGG) beams. As a numerical example, the propagation characteristics of HsG beams in free space have been demonstrated graphically. © 2012 Optical Society of America

  17. Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

    NASA Astrophysics Data System (ADS)

    Huang, Xingguo; Sun, Hui

    2018-05-01

    Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss-Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

  18. Elegant Gaussian beams for enhanced optical manipulation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Alpmann, Christina, E-mail: c.alpmann@uni-muenster.de; Schöler, Christoph; Denz, Cornelia

    2015-06-15

    Generation of micro- and nanostructured complex light beams attains increasing impact in photonics and laser applications. In this contribution, we demonstrate the implementation and experimental realization of the relatively unknown, but highly versatile class of complex-valued Elegant Hermite- and Laguerre-Gaussian beams. These beams create higher trapping forces compared to standard Gaussian light fields due to their propagation changing properties. We demonstrate optical trapping and alignment of complex functional particles as nanocontainers with standard and Elegant Gaussian light beams. Elegant Gaussian beams will inspire manifold applications in optical manipulation, direct laser writing, or microscopy, where the design of the point-spread functionmore » is relevant.« less

  19. Gaussian-Beam/Physical-Optics Design Of Beam Waveguide

    NASA Technical Reports Server (NTRS)

    Veruttipong, Watt; Chen, Jacqueline C.; Bathker, Dan A.

    1993-01-01

    In iterative method of designing wideband beam-waveguide feed for paraboloidal-reflector antenna, Gaussian-beam approximation alternated with more nearly exact physical-optics analysis of diffraction. Includes curved and straight reflectors guiding radiation from feed horn to subreflector. For iterative design calculations, curved mirrors mathematically modeled as thin lenses. Each distance Li is combined length of two straight-line segments intersecting at one of flat mirrors. Method useful for designing beam-waveguide reflectors or mirrors required to have diameters approximately less than 30 wavelengths at one or more intended operating frequencies.

  20. Propagation properties of cylindrical sinc Gaussian beam

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil T.; Bayraktar, Mert

    2016-09-01

    We investigate the propagation properties of cylindrical sinc Gaussian beam in turbulent atmosphere. Since an analytic solution is hardly derivable, the study is carried out with the aid of random phase screens. Evolutions of the beam intensity profile, beam size and kurtosis parameter are analysed. It is found that on the source plane, cylindrical sinc Gaussian beam has a dark hollow appearance, where the side lobes also start to emerge with increase in width parameter and Gaussian source size. During propagation, beams with small width and Gaussian source size exhibit off-axis behaviour, losing the dark hollow shape, accumulating the intensity asymmetrically on one side, whereas those with large width and Gaussian source size retain dark hollow appearance even at long propagation distances. It is seen that the beams with large widths expand more in beam size than the ones with small widths. The structure constant values chosen do not seem to alter this situation. The kurtosis parameters of the beams having small widths are seen to be larger than the ones with the small widths. Again the choice of the structure constant does not change this trend.

  1. Generation of singular optical beams from fundamental Gaussian beam using Sagnac interferometer

    NASA Astrophysics Data System (ADS)

    Naik, Dinesh N.; Viswanathan, Nirmal K.

    2016-09-01

    We propose a simple free-space optics recipe for the controlled generation of optical vortex beams with a vortex dipole or a single charge vortex, using an inherently stable Sagnac interferometer. We investigate the role played by the amplitude and phase differences in generating higher-order Gaussian beams from the fundamental Gaussian mode. Our simulation results reveal how important the control of both the amplitude and the phase difference between superposing beams is to achieving optical vortex beams. The creation of a vortex dipole from null interference is unveiled through the introduction of a lateral shear and a radial phase difference between two out-of-phase Gaussian beams. A stable and high quality optical vortex beam, equivalent to the first-order Laguerre-Gaussian beam, is synthesized by coupling lateral shear with linear phase difference, introduced orthogonal to the shear between two out-of-phase Gaussian beams.

  2. Propagation of elliptic-Gaussian beams in strongly nonlocal nonlinear media

    NASA Astrophysics Data System (ADS)

    Deng, Dongmei; Guo, Qi

    2011-10-01

    The propagation of the elliptic-Gaussian beams is studied in strongly nonlocal nonlinear media. The elliptic-Gaussian beams and elliptic-Gaussian vortex beams are obtained analytically and numerically. The patterns of the elegant Ince-Gaussian and the generalized Ince-Gaussian beams are varied periodically when the input power is equal to the critical power. The stability is verified by perturbing the initial beam by noise. By simulating the propagation of the elliptic-Gaussian beams in liquid crystal, we find that when the mode order is not big enough, there exists the quasi-elliptic-Gaussian soliton states.

  3. Hollow Gaussian beams and their propagation properties

    NASA Astrophysics Data System (ADS)

    Cai, Yangjian; Lu, Xuanhui; Lin, Qiang

    2003-07-01

    A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.

  4. Hollow Gaussian beams and their propagation properties.

    PubMed

    Cai, Yangjian; Lu, Xuanhui; Lin, Qiang

    2003-07-01

    A new mathematical model, described as hollow Gaussian beams (HGBs), is proposed to describe a dark hollow laser beam (DHB). The area of the dark region across the HGBs can easily be controlled by proper choice of the beam parameters. Based on the Collins integral, an analytical propagation formula for the HGBs through a paraxial optical system is derived. The HGBs also can be expressed as a superposition of a series of Lagurerre-Gaussian modes by use of a polynomial expansion. As a numerical example, the propagation properties of a DHB in free space are illustrated graphically. The HGBs provide a convenient and powerful way to describe and treat the propagation of DHBs and can be used conveniently to analyze atoms manipulated with a DHB.

  5. A 2D Gaussian-Beam-Based Method for Modeling the Dichroic Surfaces of Quasi-Optical Systems

    NASA Astrophysics Data System (ADS)

    Elis, Kevin; Chabory, Alexandre; Sokoloff, Jérôme; Bolioli, Sylvain

    2016-08-01

    In this article, we propose an approach in the spectral domain to treat the interaction of a field with a dichroic surface in two dimensions. For a Gaussian beam illumination of the surface, the reflected and transmitted fields are approximated by one reflected and one transmitted Gaussian beams. Their characteristics are determined by means of a matching in the spectral domain, which requires a second-order approximation of the dichroic surface response when excited by plane waves. This approximation is of the same order as the one used in Gaussian beam shooting algorithm to model curved interfaces associated with lenses, reflector, etc. The method uses general analytical formulations for the GBs that depend either on a paraxial or far-field approximation. Numerical experiments are led to test the efficiency of the method in terms of accuracy and computation time. They include a parametric study and a case for which the illumination is provided by a horn antenna. For the latter, the incident field is firstly expressed as a sum of Gaussian beams by means of Gabor frames.

  6. Elegant Ince-Gaussian beams in a quadratic-index medium

    NASA Astrophysics Data System (ADS)

    Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

    2011-09-01

    Elegant Ince—Gaussian beams, which are the exact solutions of the paraxial wave equation in a quadratic-index medium, are derived in elliptical coordinates. These kinds of beams are the alternative form of standard Ince—Gaussian beams and they display better symmetry between the Ince-polynomials and the Gaussian function in mathematics. The transverse intensity distribution and the phase of the elegant Ince—Gaussian beams are discussed.

  7. Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.

    PubMed

    Dennis, Mark R; Ring, James D

    2013-09-01

    We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.

  8. Full-wave generalizations of the fundamental Gaussian beam.

    PubMed

    Seshadri, S R

    2009-12-01

    The basic full wave corresponding to the fundamental Gaussian beam was discovered for the outwardly propagating wave in a half-space by the introduction of a source in the complex space. There is a class of extended full waves all of which reduce to the same fundamental Gaussian beam in the appropriate limit. For the extended full Gaussian waves that include the basic full Gaussian wave as a special case, the sources are in the complex space on different planes transverse to the propagation direction. The sources are cylindrically symmetric Gaussian distributions centered at the origin of the transverse planes, the axis of symmetry being the propagation direction. For the special case of the basic full Gaussian wave, the source is a point source. The radiation intensity of the extended full Gaussian waves is determined and their characteristics are discussed and compared with those of the fundamental Gaussian beam. The extended full Gaussian waves are also obtained for the oppositely propagating outwardly directed waves in the second half-space. The radiation intensity distributions in the two half-spaces have reflection symmetry about the midplane. The radiation intensity distributions of the various extended full Gaussian waves are not significantly different. The power carried by the extended full Gaussian waves is evaluated and compared with that of the fundamental Gaussian beam.

  9. Synthetic Incoherence via Scanned Gaussian Beams

    PubMed Central

    Levine, Zachary H.

    2006-01-01

    Tomography, in most formulations, requires an incoherent signal. For a conventional transmission electron microscope, the coherence of the beam often results in diffraction effects that limit the ability to perform a 3D reconstruction from a tilt series with conventional tomographic reconstruction algorithms. In this paper, an analytic solution is given to a scanned Gaussian beam, which reduces the beam coherence to be effectively incoherent for medium-size (of order 100 voxels thick) tomographic applications. The scanned Gaussian beam leads to more incoherence than hollow-cone illumination. PMID:27274945

  10. Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere.

    PubMed

    Chen, Rong; Liu, Lin; Zhu, Shijun; Wu, Gaofeng; Wang, Fei; Cai, Yangjian

    2014-01-27

    Laguerre-Gaussian Schell-model (LGSM) beam was proposed in theory [Opt. Lett.38, 91 (2013 Opt. Lett.38, 1814 (2013)] just recently. In this paper, we study the propagation of a LGSM beam in turbulent atmosphere. Analytical expressions for the cross-spectral density and the second-order moments of the Wigner distribution function of a LGSM beam in turbulent atmosphere are derived. The statistical properties, such as the degree of coherence and the propagation factor, of a LGSM beam in turbulent atmosphere are studied in detail. It is found that a LGSM beam with larger mode order n is less affected by turbulence than a LGSM beam with smaller mode order n or a GSM beam under certain condition, which will be useful in free-space optical communications.

  11. Gaussian beam and physical optics iteration technique for wideband beam waveguide feed design

    NASA Technical Reports Server (NTRS)

    Veruttipong, W.; Chen, J. C.; Bathker, D. A.

    1991-01-01

    The Gaussian beam technique has become increasingly popular for wideband beam waveguide (BWG) design. However, it is observed that the Gaussian solution is less accurate for smaller mirrors (approximately less than 30 lambda in diameter). Therefore, a high-performance wideband BWG design cannot be achieved by using the Gaussian beam technique alone. This article demonstrates a new design approach by iterating Gaussian beam and BWG parameters simultaneously at various frequencies to obtain a wideband BWG. The result is further improved by comparing it with physical optics results and repeating the iteration.

  12. Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wen, Wei; Chu, Xiuxiang, E-mail: xiuxiangchu@yahoo.com

    The self-healing ability during propagation process is one of the most important properties of non-diffracting beams. This ability has crucial advantages to light sheet-based microscopy to reduce scattering artefacts, increase the quality of the image and enhance the resolution of microscopy. Based on similarity between two infinite-dimensional complex vectors in Hilbert space, the ability to a Bessel–Gaussian beam and an Airy beam have been studied and compared. Comparing the evolution of the similarity of Bessel–Gaussian beam with Airy beam under the same conditions, we find that Bessel–Gaussian beam has stronger self-healing ability and is more stable than that of Airymore » beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.« less

  13. Time-domain least-squares migration using the Gaussian beam summation method

    NASA Astrophysics Data System (ADS)

    Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

    2018-04-01

    With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

  14. Time-domain least-squares migration using the Gaussian beam summation method

    NASA Astrophysics Data System (ADS)

    Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

    2018-07-01

    With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modelling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modelling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a pre-conditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

  15. Propagation of specular and anti-specular Gaussian Schell-model beams in oceanic turbulence

    NASA Astrophysics Data System (ADS)

    Zhou, Zhaotao; Guo, Mengwen; Zhao, Daomu

    2017-01-01

    On the basis of the extended Huygens-Fresnel principle and the unified theory of coherence and polarization of light, we investigate the propagation properties of the specular and anti-specular Gaussian Schell-model (GSM) beams through oceanic turbulence. It is shown that the specularity of specular GSM beams and the anti-specularity of anti-specular GSM beams are destroyed on propagation in oceanic turbulence. The spectral density and the spectral degree of coherence are also studied in detail. The results may be helpful for underwater communication.

  16. Beam wander characteristics of flat-topped, dark hollow, cos and cosh-Gaussian, J0- and I0- Bessel Gaussian beams propagating in turbulent atmosphere: a review

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil T.; Baykal, Yahya; Çil, Celal Z.; Korotkova, Olga; Cai, Yangjian

    2010-02-01

    In this paper we review our work done in the evaluations of the root mean square (rms) beam wander characteristics of the flat-topped, dark hollow, cos-and cosh Gaussian, J0-Bessel Gaussian and the I0-Bessel Gaussian beams in atmospheric turbulence. Our formulation is based on the wave-treatment approach, where not only the beam sizes but the source beam profiles are taken into account as well. In this approach the first and the second statistical moments are obtained from the Rytov series under weak atmospheric turbulence conditions and the beam size are determined as a function of the propagation distance. It is found that after propagating in atmospheric turbulence, under certain conditions, the collimated flat-topped, dark hollow, cos- and cosh Gaussian, J0-Bessel Gaussian and the I0-Bessel Gaussian beams have smaller rms beam wander compared to that of the Gaussian beam. The beam wander of these beams are analyzed against the propagation distance, source spot sizes, and against specific beam parameters related to the individual beam such as the relative amplitude factors of the constituent beams, the flatness parameters, the beam orders, the displacement parameters, the width parameters, and are compared against the corresponding Gaussian beam.

  17. Spatiotemporal behaviour of isodiffracting hollow Gaussian pulsed beams

    NASA Astrophysics Data System (ADS)

    Xu, Yanbing; Lü, Baida

    2007-05-01

    A model of isodiffracting hollow Gaussian pulsed beams (HGPBs) is presented. Based on the Fourier transform method, an analytical formula for the HGPBs propagating in free space is derived, which enables us to study the spatiotemporal behaviour of the ultrashort pulsed beams. Some interesting phenomena of ultrashort pulsed beams, such as the symmetrical temporal profiles, the dark rings, etc, are discussed in detail and illustrated numerically.

  18. Hermite-Gaussian beams with self-forming spiral phase distribution

    NASA Astrophysics Data System (ADS)

    Zinchik, Alexander A.; Muzychenko, Yana B.

    2014-05-01

    Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).

  19. Modified hollow Gaussian beam and its paraxial propagation

    NASA Astrophysics Data System (ADS)

    Cai, Yangjian; Chen, Chiyi; Wang, Fei

    2007-10-01

    A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.

  20. Aberration analysis and calculation in system of Gaussian beam illuminates lenslet array

    NASA Astrophysics Data System (ADS)

    Zhao, Zhu; Hui, Mei; Zhou, Ping; Su, Tianquan; Feng, Yun; Zhao, Yuejin

    2014-09-01

    Low order aberration was founded when focused Gaussian beam imaging at Kodak KAI -16000 image detector, which is integrated with lenslet array. Effect of focused Gaussian beam and numerical simulation calculation of the aberration were presented in this paper. First, we set up a model of optical imaging system based on previous experiment. Focused Gaussian beam passed through a pinhole and was received by Kodak KAI -16000 image detector whose microlenses of lenslet array were exactly focused on sensor surface. Then, we illustrated the characteristics of focused Gaussian beam and the effect of relative space position relations between waist of Gaussian beam and front spherical surface of microlenses to the aberration. Finally, we analyzed the main element of low order aberration and calculated the spherical aberration caused by lenslet array according to the results of above two steps. Our theoretical calculations shown that , the numerical simulation had a good agreement with the experimental result. Our research results proved that spherical aberration was the main element and made up about 93.44% of the 48 nm error, which was demonstrated in previous experiment. The spherical aberration is inversely proportional to the value of divergence distance between microlens and waist, and directly proportional to the value of the Gaussian beam waist radius.

  1. Propagation of Ince-Gaussian beams in a thermal lens medium

    NASA Astrophysics Data System (ADS)

    Xu, Ting; Wang, Shaomin

    2006-09-01

    The propagation of Ince-Gaussian beams in a thermal lens medium is studied in this paper. Based on the ABCD matrix for Gaussian beams passing through a thermal lens medium, distinct expressions for the beam transverse intensity distributions and the longitudinal phase shift are deduced and discussed. Similar to Laguerre and Hermite-Gaussian beams, Ince-Gaussian beams, which constitute the third complete family of exact and orthogonal solutions of the paraxial wave equation, can also be used in other inhomogeneous media such as lenslike media and saturated absorption media.

  2. Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Lukin, Igor P.

    2017-11-01

    In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.

  3. Evolution of the frequency chirp of Gaussian pulses and beams when passing through a pulse compressor.

    PubMed

    Li, Derong; Lv, Xiaohua; Bowlan, Pamela; Du, Rui; Zeng, Shaoqun; Luo, Qingming

    2009-09-14

    The evolution of the frequency chirp of a laser pulse inside a classical pulse compressor is very different for plane waves and Gaussian beams, although after propagating through the last (4th) dispersive element, the two models give the same results. In this paper, we have analyzed the evolution of the frequency chirp of Gaussian pulses and beams using a method which directly obtains the spectral phase acquired by the compressor. We found the spatiotemporal couplings in the phase to be the fundamental reason for the difference in the frequency chirp acquired by a Gaussian beam and a plane wave. When the Gaussian beam propagates, an additional frequency chirp will be introduced if any spatiotemporal couplings (i.e. angular dispersion, spatial chirp or pulse front tilt) are present. However, if there are no couplings present, the chirp of the Gaussian beam is the same as that of a plane wave. When the Gaussian beam is well collimated, the introduced frequency chirp predicted by the plane wave and Gaussian beam models are in closer agreement. This work improves our understanding of pulse compressors and should be helpful for optimizing dispersion compensation schemes in many applications of femtosecond laser pulses.

  4. Generation of hollow Gaussian beams by spatial filtering

    NASA Astrophysics Data System (ADS)

    Liu, Zhengjun; Zhao, Haifa; Liu, Jianlong; Lin, Jie; Ashfaq Ahmad, Muhammad; Liu, Shutian

    2007-08-01

    We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

  5. Generation of hollow Gaussian beams by spatial filtering.

    PubMed

    Liu, Zhengjun; Zhao, Haifa; Liu, Jianlong; Lin, Jie; Ahmad, Muhammad Ashfaq; Liu, Shutian

    2007-08-01

    We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

  6. Gaussian entanglement generation from coherence using beam-splitters

    PubMed Central

    Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan

    2016-01-01

    The generation and quantification of quantum entanglement is crucial for quantum information processing. Here we study the transition of Gaussian correlation under the effect of linear optical beam-splitters. We find the single-mode Gaussian coherence acts as the resource in generating Gaussian entanglement for two squeezed states as the input states. With the help of consecutive beam-splitters, single-mode coherence and quantum entanglement can be converted to each other. Our results reveal that by using finite number of beam-splitters, it is possible to extract all the entanglement from the single-mode coherence even if the entanglement is wiped out before each beam-splitter. PMID:27892537

  7. Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.

    PubMed

    Lukin, Igor P

    2016-04-20

    The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.

  8. Hypergeometric Gaussian beam and its propagation in turbulence

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil Tanyer; Cai, Yangjian

    2012-10-01

    We study propagation characteristics of hypergeometric Gaussian beam in turbulence. In this context, we formulate the receiver plane intensity using extended Huygens-Fresnel integral. From the graphical results, it is seen that, after propagation, hypergeometric Gaussian will in general assume the shape of a dark hollow beam at topological charges other than zero. Increasing values of topological charge will make the beam broader with steeper walls. On the other hand, higher values of hollowness parameter will contract into a narrower shape. Raising the topological charge or the hollowness parameter individually will cause outer rings to appear. Both increased levels of turbulence and longer propagation distances will accelerate the beam evolution and help reach the final Gaussian shape sooner. At lower wavelengths, there will be less beam spreading.

  9. Generation of helical Ince-Gaussian beams: beam-shaping with a liquid crystal display

    NASA Astrophysics Data System (ADS)

    Davis, Jeffrey A.; Bentley, Joel B.; Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

    2006-08-01

    We review the three types of laser beams - Hermite-Gaussian (HG), Laguerre-Gaussian (LG) and the newly discovered Ince-Gaussian (IG) beams. We discuss the helical forms of the LG and IG beams that consist of linear combinations of the even and odd solutions and form a number of vortices that are useful for optical trapping applications. We discuss how to generate these beams by encoding the desired amplitude and phase onto a single parallel-aligned liquid crystal display (LCD). We introduce a novel interference technique where we generate both the object and reference beams using a single LCD and show the vortex interference patterns.

  10. The tight focusing properties of Laguerre-Gaussian-correlated Schell-model beams

    NASA Astrophysics Data System (ADS)

    Xu, Hua-Feng; Zhang, Zhou; Qu, Jun; Huang, Wei

    2016-08-01

    Based on the Richards-Wolf vectorial diffraction theory, the tight focusing properties, including the intensity distribution, the degree of polarization and the degree of coherence, of the Laguerre-Gaussian-correlated Schell-model (LGSM) beams through a high-numerical-aperture (NA) focusing system are investigated in detail. It is found that the LGSM beam exhibits some extraordinary focusing properties, which is quite different from that of the GSM beam, and the tight focusing properties are closely related to the initial spatial coherence ? and the mode order n. The LGSM beam can form an elliptical focal spot, a circular focal spot or a doughnut-shaped dark hollow beam at the focal plane by choosing a suitable value of the initial spatial coherence ?, and the central dark size of the dark hollow beam increases with the increase of the mode order n. In addition, the influences of the initial spatial coherence ? and the mode order n on the degree of polarization and the degree of coherence are also analysed in detail, respectively. Our results may find applications in optical trapping.

  11. Laguerre-Gaussian, Hermite-Gaussian, Bessel-Gaussian, and Finite-Energy Airy Beams Carrying Orbital Angular Momentum in Strongly Nonlocal Nonlinear Media

    NASA Astrophysics Data System (ADS)

    Wu, Zhenkun; Gu, Yuzong

    2016-12-01

    The propagation of two-dimensional beams is analytically and numerically investigated in strongly nonlocal nonlinear media (SNNM) based on the ABCD matrix. The two-dimensional beams reported in this paper are described by the product of the superposition of generalized Laguerre-Gaussian (LG), Hermite-Gaussian (HG), Bessel-Gaussian (BG), and circular Airy (CA) beams, carrying an orbital angular momentum (OAM). Owing to OAM and the modulation of SNNM, we find that the propagation of these two-dimensional beams exhibits complete rotation and periodic inversion: the spatial intensity profile first extends and then diminishes, and during the propagation the process repeats to form a breath-like phenomenon.

  12. Trapping two types of particles with a focused generalized Multi-Gaussian Schell model beam

    NASA Astrophysics Data System (ADS)

    Liu, Xiayin; Zhao, Daomu

    2015-11-01

    We numerically investigate the trapping effect of the focused generalized Multi-Gaussian Schell model (GMGSM) beam of the first kind which produces dark hollow beam profile at the focal plane. By calculating the radiation forces on the Rayleigh dielectric sphere in the focused GMGSM beam, we show that such beam can trap low-refractive-index particles at the focus, and simultaneously capture high-index particles at different positions of the focal plane. The trapping range and stability depend on the values of the beam index N and the coherence width. Under the same conditions, the low limits of the radius of low-index and high-index particles for stable trapping are indicated to be different.

  13. Apertured averaged scintillation of fully and partially coherent Gaussian, annular Gaussian, flat toped and dark hollow beams

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil T.

    2015-03-01

    Apertured averaged scintillation requires the evaluation of rather complicated irradiance covariance function. Here we develop a much simpler numerical method based on our earlier introduced semi-analytic approach. Using this method, we calculate aperture averaged scintillation of fully and partially coherent Gaussian, annular Gaussian flat topped and dark hollow beams. For comparison, the principles of equal source beam power and normalizing the aperture averaged scintillation with respect to received power are applied. Our results indicate that for fully coherent beams, upon adjusting the aperture sizes to capture 10 and 20% of the equal source power, Gaussian beam needs the largest aperture opening, yielding the lowest aperture average scintillation, whilst the opposite occurs for annular Gaussian and dark hollow beams. When assessed on the basis of received power normalized aperture averaged scintillation, fixed propagation distance and aperture size, annular Gaussian and dark hollow beams seem to have the lowest scintillation. Just like the case of point-like scintillation, partially coherent beams will offer less aperture averaged scintillation in comparison to fully coherent beams. But this performance improvement relies on larger aperture openings. Upon normalizing the aperture averaged scintillation with respect to received power, fully coherent beams become more advantageous than partially coherent ones.

  14. Mean intensity of the vortex Bessel-Gaussian beam in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Lukin, Igor P.

    2017-11-01

    In this work the question of stability of the vortex Bessel-Gaussian optical beams formed in turbulent atmosphere is theoretically considered. The detailed analysis of features of spatial structure of distribution of mean intensity of vortex Bessel-Gaussian optical beams in turbulent atmosphere are analyzed. The quantitative criterion of possibility of formation of vortex Bessel-Gaussian optical beams in turbulent atmosphere is derived. It is shown that stability of the form of a vortex Bessel-Gaussian optical beam during propagation in turbulent atmosphere increases with increase of value of a topological charge of this optical beam.

  15. Propagation of Ince-Gaussian beams in uniaxial crystals orthogonal to the optical axis

    NASA Astrophysics Data System (ADS)

    Xu, Y. Q.; Zhou, G. Q.

    2012-03-01

    An analytical propagation expression of an Ince-Gaussian beam in uniaxial crystals orthogonal to the optical axis is derived. The uniaxial crystal considered here has the property of the extraordinary refractive index being larger than the ordinary refractive index. The Ince-Gaussian beam in the transversal direction along the optical axis spreads more rapidly than that in the other transversal direction. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the spreading of the Ince-Gaussian beam in the transversal direction along the optical axis increases and the spreading of the Ince-Gaussian beam in the other transversal direction decreases. The effective beam size in the transversal direction along the optical axis is always larger than that in the other transversal direction. When the even and odd modes of Ince-Gaussian beams exist simultaneously, the effective beam size in the direction along the optical axis of the odd Ince-Gaussian beam is smaller than that of the even Ince-Gaussian beam in the corresponding direction, and the effective beam size in the transversal direction orthogonal to the optical axis of the odd Ince-Gaussian beam is larger than that of the even Ince-Gaussian beam in the corresponding direction.

  16. Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Lukin, Igor P.

    2017-11-01

    In the given article mean intensity of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is studied. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian beam of optical radiation. Distributions of mean intensity of a fundamental Bessel- Gaussian beam optical beam in longitudinal and transverse to a direction of propagation of optical radiation are investigated in detail. Influence of atmospheric turbulence on change of radius of the central part of a Bessel optical beam is estimated. Values of parameters at which it is possible to generate in turbulent atmosphere a nondiffracting pseudo-Bessel optical beam by means of a fundamental Bessel-Gaussian optical beam are established.

  17. Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Lukin, Igor P.

    2017-11-01

    In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.

  18. Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere.

    PubMed

    Chu, Xiuxiang

    2007-12-24

    The propagation of a cosh-Gaussian beam through an arbitrary ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity at any receiver plane are obtained. As an elementary example, the average intensity and its radius at the image plane of a cosh-Gaussian beam through a thin lens are studied. To show the effects of a lens on the average intensity and the intensity radius of the laser beam in turbulent atmosphere, the properties of a collimated cosh-Gaussian beam and a focused cosh-Gaussian beam for direct propagation in turbulent atmosphere are studied and numerically calculated. The average intensity profiles of a cosh-Gaussian beam through a lens can have a shape similar to that of the initial beam for a longer propagation distance than that of a collimated cosh-Gaussian beam for direct propagation. With the increment in the propagation distance, the average intensity radius at the image plane of a cosh-Gaussian beam through a thin lens will be smaller than that at the focal plane of a focused cosh-Gaussian beam for direct propagation. Meanwhile, the intensity distributions at the image plane of a cosh-Gaussian beam through a lens with different w(0) and Omega(0) are also studied.

  19. Generally astigmatic Gaussian beam representation and optimization using skew rays

    NASA Astrophysics Data System (ADS)

    Colbourne, Paul D.

    2014-12-01

    Methods are presented of using skew rays to optimize a generally astigmatic optical system to obtain the desired Gaussian beam focus and minimize aberrations, and to calculate the propagating generally astigmatic Gaussian beam parameters at any point. The optimization method requires very little computation beyond that of a conventional ray optimization, and requires no explicit calculation of the properties of the propagating Gaussian beam. Unlike previous methods, the calculation of beam parameters does not require matrix calculations or the introduction of non-physical concepts such as imaginary rays.

  20. Radiation pressure acceleration of corrugated thin foils by Gaussian and super-Gaussian beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Adusumilli, K.; Goyal, D.; Tripathi, V. K.

    Rayleigh-Taylor instability of radiation pressure accelerated ultrathin foils by laser having Gaussian and super-Gaussian intensity distribution is investigated using a single fluid code. The foil is allowed to have ring shaped surface ripples. The radiation pressure force on such a foil is non-uniform with finite transverse component F{sub r}; F{sub r} varies periodically with r. Subsequently, the ripple grows as the foil moves ahead along z. With a Gaussian beam, the foil acquires an overall curvature due to non-uniformity in radiation pressure and gets thinner. In the process, the ripple perturbation is considerably washed off. With super-Gaussian beam, the ripplemore » is found to be more strongly washed out. In order to avoid transmission of the laser through the thinning foil, a criterion on the foil thickness is obtained.« less

  1. Reversible wavefront shaping between Gaussian and Airy beams by mimicking gravitational field

    NASA Astrophysics Data System (ADS)

    Wang, Xiangyang; Liu, Hui; Sheng, Chong; Zhu, Shining

    2018-02-01

    In this paper, we experimentally demonstrate reversible wavefront shaping through mimicking gravitational field. A gradient-index micro-structured optical waveguide with special refractive index profile was constructed whose effective index satisfying a gravitational field profile. Inside the waveguide, an incident broad Gaussian beam is firstly transformed into an accelerating beam, and the generated accelerating beam is gradually changed back to a Gaussian beam afterwards. To validate our experiment, we performed full-wave continuum simulations that agree with the experimental results. Furthermore, a theoretical model was established to describe the evolution of the laser beam based on Landau’s method, showing that the accelerating beam behaves like the Airy beam in the small range in which the linear potential approaches zero. To our knowledge, such a reversible wavefront shaping technique has not been reported before.

  2. Integral transformation solution of free-space cylindrical vector beams and prediction of modified Bessel-Gaussian vector beams.

    PubMed

    Li, Chun-Fang

    2007-12-15

    A unified description of free-space cylindrical vector beams is presented that is an integral transformation solution to the vector Helmholtz equation and the transversality condition. In the paraxial condition, this solution not only includes the known J(1) Bessel-Gaussian vector beam and the axisymmetric Laguerre-Gaussian vector beam that were obtained by solving the paraxial wave equations but also predicts two kinds of vector beam, called a modified Bessel-Gaussian vector beam.

  3. Extension of filament propagation in water with Bessel-Gaussian beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kaya, G.; Sayrac, M.; Boran, Y.

    We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.

  4. Nonexistence of exact solutions agreeing with the Gaussian beam on the beam axis or in the focal plane

    NASA Astrophysics Data System (ADS)

    Lekner, John; Andrejic, Petar

    2018-01-01

    Solutions of the Helmholtz equation which describe electromagnetic beams (and also acoustic or particle beams) are discussed. We show that an exact solution which reproduces the Gaussian beam waveform on the beam axis does not exist. This is surprising, since the Gaussian beam is a solution of the paraxial equation, and thus supposedly accurate on and near the beam axis. Likewise, a solution of the Helmholtz equation which exactly reproduces the Gaussian beam in the focal plane does not exist. We show that the last statement also holds for Bessel-Gauss beams. However, solutions of the Helmholtz equation (one of which is discussed in detail) can approximate the Gaussian waveform within the central focal region.

  5. Accurately modeling Gaussian beam propagation in the context of Monte Carlo techniques

    NASA Astrophysics Data System (ADS)

    Hokr, Brett H.; Winblad, Aidan; Bixler, Joel N.; Elpers, Gabriel; Zollars, Byron; Scully, Marlan O.; Yakovlev, Vladislav V.; Thomas, Robert J.

    2016-03-01

    Monte Carlo simulations are widely considered to be the gold standard for studying the propagation of light in turbid media. However, traditional Monte Carlo methods fail to account for diffraction because they treat light as a particle. This results in converging beams focusing to a point instead of a diffraction limited spot, greatly effecting the accuracy of Monte Carlo simulations near the focal plane. Here, we present a technique capable of simulating a focusing beam in accordance to the rules of Gaussian optics, resulting in a diffraction limited focal spot. This technique can be easily implemented into any traditional Monte Carlo simulation allowing existing models to be converted to include accurate focusing geometries with minimal effort. We will present results for a focusing beam in a layered tissue model, demonstrating that for different scenarios the region of highest intensity, thus the greatest heating, can change from the surface to the focus. The ability to simulate accurate focusing geometries will greatly enhance the usefulness of Monte Carlo for countless applications, including studying laser tissue interactions in medical applications and light propagation through turbid media.

  6. Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam

    PubMed Central

    Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu

    2016-01-01

    We introduce a method for modulating the Gaussian beam by means of sine-azimuthal wavefront and carry out the experimental generation. The analytical propagation formula of such a beam passing through a paraxial ABCD optical system is derived, by which the intensity properties of the sine-azimuthal wavefront modulated Gaussian (SWMG) beam are examined both theoretically and experimentally. Both of the experimental and theoretical results show that the SWMG beam goes through the process from beam splitting to a Gaussian-like profile, which is closely determined by the phase factor and the propagation distance. Appropriate phase factor and short distance are helpful for the splitting of beam. However, in the cases of large phase factor and focal plane, the intensity distributions tend to take a Gaussian form. Such unique features may be of importance in particle trapping and medical applications. PMID:27443798

  7. An optical tweezer in asymmetrical vortex Bessel-Gaussian beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P.

    We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.

  8. Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures.

    PubMed

    Gao, Yanqi; Zhu, Baoqiang; Liu, Daizhong; Lin, Zunqi

    2009-07-20

    A general model for different apertures and flat-topped laser beams based on the multi-Gaussian function is developed. The general analytical expression for the propagation of a flat-topped beam through a general double-lens system with apertures is derived using the above model. Then, the propagation characteristics of the flat-topped beam through a spatial filter are investigated by using a simplified analytical expression. Based on the Fluence beam contrast and the Fill factor, the influences of a pinhole size on the propagation of the flat-topped multi-Gaussian beam (FMGB) through the spatial filter are illustrated. An analytical expression for the propagation of the FMGB through the spatial filter with a misaligned pinhole is presented, and the influences of the pinhole offset are evaluated.

  9. Vector spherical quasi-Gaussian vortex beams

    NASA Astrophysics Data System (ADS)

    Mitri, F. G.

    2014-02-01

    Model equations for describing and efficiently computing the radiation profiles of tightly spherically focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave fields without the need of either the higher-order corrections or the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist.

  10. Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere.

    PubMed

    Eyyuboğlu, Halil Tanyer

    2005-08-01

    Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.

  11. Gaussian content as a laser beam quality parameter.

    PubMed

    Ruschin, Shlomo; Yaakobi, Elad; Shekel, Eyal

    2011-08-01

    We propose the Gaussian content (GC) as an optional quality parameter for the characterization of laser beams. It is defined as the overlap integral of a given field with an optimally defined Gaussian. The definition is especially suited for applications where coherence properties are targeted. Mathematical definitions and basic calculation procedures are given along with results for basic beam profiles. The coherent combination of an array of laser beams and the optimal coupling between a diode laser and a single-mode fiber are elaborated as application examples. The measurement of the GC and its conservation upon propagation are experimentally confirmed.

  12. Effect of polarization on the evolution of electromagnetic hollow Gaussian Schell-model beam

    NASA Astrophysics Data System (ADS)

    Long, Xuewen; Lu, Keqing; Zhang, Yuhong; Guo, Jianbang; Li, Kehao

    2011-02-01

    Based on the theory of coherence, an analytical propagation formula for partially polarized and partially coherent hollow Gaussian Schell-model beams (HGSMBs) passing through a paraxial optical system is derived. Furthermore, we show that the degree of polarization of source may affect the evolution of HGSMBs and a tunable dark region may exist. For two special cases of fully coherent and partially coherent δxx = δyy, normalized intensity distributions are independent of the polarization of source.

  13. Non-gaussian statistics of pencil beam surveys

    NASA Technical Reports Server (NTRS)

    Amendola, Luca

    1994-01-01

    We study the effect of the non-Gaussian clustering of galaxies on the statistics of pencil beam surveys. We derive the probability from the power spectrum peaks by means of Edgeworth expansion and find that the higher order moments of the galaxy distribution play a dominant role. The probability of obtaining the 128 Mpc/h periodicity found in pencil beam surveys is raised by more than one order of magnitude, up to 1%. Further data are needed to decide if non-Gaussian distribution alone is sufficient to explain the 128 Mpc/h periodicity, or if extra large-scale power is necessary.

  14. Hollow Gaussian beam generated by beam shaping with phase-only liquid crystal spatial light modulator

    NASA Astrophysics Data System (ADS)

    Nie, Yongming; Li, Xiujian; Qi, Junli; Ma, Haotong; Liao, Jiali; Yang, Jiankun; Hu, Wenhua

    2012-03-01

    Based on the refractive beam shaping system, the transformation of a quasi-Gaussian beam into a dark hollow Gaussian beam by a phase-only liquid crystal spatial light modulator (LC-SLM) is proposed. According to the energy conservation and constant optical path principle, the phase distribution of the aspheric lens and the phase-only LC-SLM can modulate the wave-front properly to generate the hollow beam. The numerical simulation results indicate that, the dark hollow intensity distribution of the output shaped beam can be maintained well for a certain propagation distance during which the dark region will not decrease whereas the ideal hollow Gaussian beam will do. By designing the phase modulation profile, which loaded into the LC-SLM carefully, the experimental results indicate that the dark hollow intensity distribution of the output shaped beam can be maintained well even at a distance much more than 550 mm from the LC-SLM, which agree with the numerical simulation results.

  15. The variance of angle-of-arrival fluctuation of partially coherent Gaussian-Schell Model beam propagations in slant atmospheric turbulence

    NASA Astrophysics Data System (ADS)

    Tan, Zhenkun; Ke, Xizheng

    2017-10-01

    The variance of angle-of-arrival fluctuation of the partially coherent Gaussian-Schell Model (GSM) beam propagations in the slant path, based on the extended Huygens-Fresnel principle and the model of atmospheric refraction index structural constant proposed by the international telecommunication union-radio (ITU-R), has been investigated under the modified Hill turbulence model. The expression of that has been obtained. Firstly, the effects of optical wavelength, the inner-and-outer scale of the turbulence and turbulence intensity on the variance of angle-of-arrival fluctuation have been analyzed by comparing with the partially coherent GSM beam and the completely coherent Gaussian beam. Secondly, the variance of angle-of-arrival fluctuation has been compared with the von Karman spectrum and the modified Hill spectrum under the partially coherent GSM beam. Finally, the effects of beam waist radius and partial coherence length on the variance of angle-of-arrival of the collimated (focused) beam have been analyzed under the modified Hill turbulence model. The results show that the influence of the variance of angle-of-arrival fluctuation for the inner scale effect is larger than that of the outer scale effect. The variance of angle-of-arrival fluctuation under the modified Hill spectrum is larger than that of the von Karman spectrum. The influence of the waist radius on the variance of angle-of-arrival for the collimated beam is less than focused the beam. This study will provide a necessary theoretical basis for the experiments of partially coherent GSM beam propagation through atmosphere turbulence.

  16. Gyrator transform of generalized sine-Gaussian beams and conversion an edge-dislocation into a vortex

    NASA Astrophysics Data System (ADS)

    Zhu, Kaicheng; Tang, Huiqin; Tang, Ying; Xia, Hui

    2014-12-01

    We proposed a scheme that converts a sine-Gaussian beam with an edge dislocation into a dark hollow beam with a vortex. Based on the gyrator transform (GT) relation, the closed-form field distribution of generalized sine-Gaussian beams passing through a GT system is derived; the intensity distribution and the corresponding phase distribution associated with the transforming generalized sine-Gaussian beams are analyzed. According to the numerical method, the distributions are graphically demonstrated and found that, for appropriate beam parameters and the GT angle, dark hollow vortex beams with topological charge 1 can be achieved using sine-Gaussian beams carrying an edge dislocation. Moreover, the orbital angular momentum content of a GT sine-Gaussian beam is analyzed. It is proved that the GT retains the odd- or even-order spiral harmonics structures of generalized sine-Gaussian beams in the transform process. In particular, it is wholly possible to convert an edge dislocation embedded in sine-Gaussian beams into a vortex with GT. The study also reveals that to obtain a dark hollow beam making use of GT of cos-Gaussian beams is impossible.

  17. Diffraction of a Gaussian Beam by a Spherical Obstacle

    NASA Technical Reports Server (NTRS)

    Lock, James A.; Hovenac, Edward A.

    1993-01-01

    The Kirchhoff integral for diffraction in the near-forward direction is derived from the exact solution of the electromagnetic boundary value problem of a focused Gaussian laser beam incident on a spherical particle. The diffracted intensity in the vicinity of the particle is computed and the way in which the features of the diffraction pattern depend on the width of the Gaussian beam is commented on.

  18. Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

    NASA Technical Reports Server (NTRS)

    Steely, Sidney L.

    1993-01-01

    The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

  19. Nonparaxial Dark-Hollow Gaussian Beams

    NASA Astrophysics Data System (ADS)

    Gao, Zeng-Hui; Lü, Bai-Da

    2006-01-01

    The concept of nonparaxial dark-hollow Gaussian beams (DHGBs) is introduced. By using the Rayleigh-Sommerfeld diffraction integral, the analytical propagation equation of DHGBs in free space is derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that the parameter f = 1/kw0 with k being the wave number and w0 being the waist width determines the nonparaxiality of DHGBs. However, the parameter range, within which the paraxial approach is valid, depends on the propagation distance. The beam order affects the beam profile and position of maximum on-axis intensity.

  20. Propagation properties of hollow sinh-Gaussian beams through fractional Fourier transform optical systems

    NASA Astrophysics Data System (ADS)

    Tang, Bin; Jiang, ShengBao; Jiang, Chun; Zhu, Haibin

    2014-07-01

    A hollow sinh-Gaussian beam (HsG) is an appropriate model to describe the dark-hollow beam. Based on Collins integral formula and the fact that a hard-edged-aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of a HsG beam passing through fractional Fourier transform (FRFT) optical systems with and without apertures have been studied in detail by some typical numerical examples. The results obtained using the approximate analytical formula are in good agreement with those obtained using numerical integral calculation. Further, the studies indicate that the normalized intensity distribution of the HsG beam in FRFT plane is closely related with not only the fractional order but also the beam order and the truncation parameter. The FRFT optical systems provide a convenient way for laser beam shaping.

  1. Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

    NASA Astrophysics Data System (ADS)

    Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

    2011-03-01

    The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

  2. Irradiance tailoring by fractional Fourier transform of a radial Gaussian beam array

    NASA Astrophysics Data System (ADS)

    Zhou, Pu; Wang, Xiaolin; Ma, Yanxing; Ma, Haotong; Liu, Zejin

    2010-07-01

    The fractional Fourier transform (FRFT) is applied to a radial Gaussian beam array. Analytical formula is derived for the irradiance distribution of coherent and incoherent radial Gaussian beam array in FRFT domain using Collins integral formula. It is revealed that the irradiance pattern can be tailored to be controllable dark-hollow, flat-topped and Gaussian beam pattern by changing of the fractional order of FRFT and the coherent state of the laser array.

  3. Optical assembly of microparticles into highly ordered structures using Ince-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Woerdemann, Mike; Alpmann, Christina; Denz, Cornelia

    2011-03-01

    Ince-Gaussian (IG) beams are a third complete family of solutions of the paraxial Helmholtz equation. While many applications of Hermite-Gaussian and Laguerre-Gaussian beams have been demonstrated for manipulation of microparticles, the potential of the more general class of IG beams has not yet been exploited at all. We describe the unique properties of IG beams with respect to optical trapping applications, demonstrate a flexible experimental realization of arbitrary IG beams and prove the concept by creating two- and three-dimensional, highly ordered assemblies of typical microparticles. The concept is universal and can easily be integrated into existing holographic optical tweezers setups.

  4. Focusing of concentric piecewise vector Bessel-Gaussian beam

    NASA Astrophysics Data System (ADS)

    Li, Jinsong; Fang, Ying; Zhou, Shenghua; Ye, Youxiang

    2010-12-01

    The focusing properties of a concentric piecewise vector Bessel-Gaussian beam are investigated in this paper. The beam consists of three portions: the center circular portion and outer annular portion are radially polarized, while the inner annular portion is generalized polarized with tunable polarized angle. Numerical simulations show that the evolution of focal pattern is altered considerably with different Bessel parameters in the Bessel term of the vector Bessel-Gaussian beam. The polarized angle also affects the focal pattern remarkably. Some interesting focal patterns may appear, such as two-peak, dark hollow focus; ring focus; spherical shell focus; cylindrical shell focus; and multi-ring-peak focus, and transverse focal switch occurs with increasing polarized angle of the inner annular portion, which may be used in optical manipulation.

  5. Matching optics for Gaussian beams

    NASA Technical Reports Server (NTRS)

    Gunter, William D. (Inventor)

    1991-01-01

    A system of matching optics for Gaussian beams is described. The matching optics system is positioned between a light beam emitter (such as a laser) and the input optics of a second optics system whereby the output from the light beam emitter is converted into an optimum input for the succeeding parts of the second optical system. The matching optics arrangement includes the combination of a light beam emitter, such as a laser with a movable afocal lens pair (telescope) and a single movable lens placed in the laser's output beam. The single movable lens serves as an input to the telescope. If desired, a second lens, which may be fixed, is positioned in the beam before the adjustable lens to serve as an input processor to the movable lens. The system provides the ability to choose waist diameter and position independently and achieve the desired values with two simple adjustments not requiring iteration.

  6. A closed form of a kurtosis parameter of a hypergeometric-Gaussian type-II beam

    NASA Astrophysics Data System (ADS)

    F, Khannous; A, A. A. Ebrahim; A, Belafhal

    2016-04-01

    Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric-Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.

  7. Sparse decomposition of seismic data and migration using Gaussian beams with nonzero initial curvature

    NASA Astrophysics Data System (ADS)

    Liu, Peng; Wang, Yanfei

    2018-04-01

    We study problems associated with seismic data decomposition and migration imaging. We first represent the seismic data utilizing Gaussian beam basis functions, which have nonzero curvature, and then consider the sparse decomposition technique. The sparse decomposition problem is an l0-norm constrained minimization problem. In solving the l0-norm minimization, a polynomial Radon transform is performed to achieve sparsity, and a fast gradient descent method is used to calculate the waveform functions. The waveform functions can subsequently be used for sparse Gaussian beam migration. Compared with traditional sparse Gaussian beam methods, the seismic data can be properly reconstructed employing fewer Gaussian beams with nonzero initial curvature. The migration approach described in this paper is more efficient than the traditional sparse Gaussian beam migration.

  8. Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen.

    PubMed

    Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng

    2011-09-12

    In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.

  9. Dynamic splitting of Gaussian pencil beams in heterogeneity-correction algorithms for radiotherapy with heavy charged particles.

    PubMed

    Kanematsu, Nobuyuki; Komori, Masataka; Yonai, Shunsuke; Ishizaki, Azusa

    2009-04-07

    The pencil-beam algorithm is valid only when elementary Gaussian beams are small enough compared to the lateral heterogeneity of a medium, which is not always true in actual radiotherapy with protons and ions. This work addresses a solution for the problem. We found approximate self-similarity of Gaussian distributions, with which Gaussian beams can split into narrower and deflecting daughter beams when their sizes have overreached lateral heterogeneity in the beam-transport calculation. The effectiveness was assessed in a carbon-ion beam experiment in the presence of steep range compensation, where the splitting calculation reproduced a detour effect amounting to about 10% in dose or as large as the lateral particle disequilibrium effect. The efficiency was analyzed in calculations for carbon-ion and proton radiations with a heterogeneous phantom model, where the beam splitting increased computing times by factors of 4.7 and 3.2. The present method generally improves the accuracy of the pencil-beam algorithm without severe inefficiency. It will therefore be useful for treatment planning and potentially other demanding applications.

  10. Photoexcitation of atoms by Laguerre-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Peshkov, A. A.; Seipt, D.; Surzhykov, A.; Fritzsche, S.

    2017-08-01

    In a recent experiment, Schmiegelow et al. [Nat. Commun. 7, 12998 (2016), 10.1038/ncomms12998] investigated the magnetic sublevel population of Ca+ ions in a Laguerre-Gaussian light beam if the target atoms were just centered along the beam axis. They demonstrated in this experiment that the sublevel population of the excited atoms is uniquely defined by the projection of the orbital angular momentum of the incident light. However, little attention has been paid so far to the question of how the magnetic sublevels are populated when atoms are displaced from the beam axis by some impact parameter b . Here, we analyze this sublevel population for different atomic impact parameters in first-order perturbation theory and by making use of the density-matrix formalism. Detailed calculations are performed especially for the 4 s 1/2 2S →3 d 5/2 2 transition in Ca+ ions and for the vector potential of a Laguerre-Gaussian beam in Coulomb gauge. It is shown that the magnetic sublevel population of the excited 5/2 2D level varies significantly with the impact parameter and is sensitive to the polarization, the radial index, as well as the orbital angular momentum of the incident light beam.

  11. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

    PubMed

    Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

    2016-06-27

    We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

  12. Novel theory for propagation of tilted Gaussian beam through aligned optical system

    NASA Astrophysics Data System (ADS)

    Xia, Lei; Gao, Yunguo; Han, Xudong

    2017-03-01

    A novel theory for tilted beam propagation is established in this paper. By setting the propagation direction of the tilted beam as the new optical axis, we establish a virtual optical system that is aligned with the new optical axis. Within the first order approximation of the tilt and off-axis, the propagation of the tilted beam is studied in the virtual system instead of the actual system. To achieve more accurate optical field distributions of tilted Gaussian beams, a complete diffraction integral for a misaligned optical system is derived by using the matrix theory with angular momentums. The theory demonstrates that a tilted TEM00 Gaussian beam passing through an aligned optical element transforms into a decentered Gaussian beam along the propagation direction. The deviations between the peak intensity axis of the decentered Gaussian beam and the new optical axis have linear relationships with the misalignments in the virtual system. ZEMAX simulation of a tilted beam through a thick lens exposed to air shows that the errors between the simulation results and theoretical calculations of the position deviations are less than 2‰ when the misalignments εx, εy, εx', εy' are in the range of [-0.5, 0.5] mm and [-0.5, 0.5]°.

  13. A new method for generating a hollow Gaussian beam

    NASA Astrophysics Data System (ADS)

    Wei, Cun; Lu, Xingyuan; Wu, Gaofeng; Wang, Fei; Cai, Yangjian

    2014-04-01

    Hollow Gaussian beam (HGB) was introduced 10 years ago (Cai et al. in Opt Lett 28:1084, 2003). In this paper, we introduce a new method for generating a HGB through transforming a Laguerre-Gaussian beam with radial index 0 and azimuthal index l into a HGB with mode n = l/2. Furthermore, we report experimental generation of a HGB based on the proposed method, and we carry out experimental study of the focusing properties of the generated HGB. Our experimental results agree well with the theoretical predictions.

  14. Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

    NASA Astrophysics Data System (ADS)

    Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

    2018-01-01

    Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

  15. Propagation of radially polarized multi-cosine Gaussian Schell-model beams in non-Kolmogorov turbulence

    NASA Astrophysics Data System (ADS)

    Tang, Miaomiao; Zhao, Daomu; Li, Xinzhong; Wang, Jingge

    2018-01-01

    Recently, we introduced a new class of radially polarized beams with multi-cosine Gaussian Schell-model(MCGSM) correlation function based on the partially coherent theory (Tang et al., 2017). In this manuscript, we extend the work to study the statistical properties such as the spectral density, the degree of coherence, the degree of polarization, and the state of polarization of the beam propagating in isotropic turbulence with a non-Kolmogorov power spectrum. Analytical formulas for the cross-spectral density matrix elements of a radially polarized MCGSM beam in non-Kolmogorov turbulence are derived. Numerical results show that lattice-like intensity pattern of the beam, which keeps propagation-invariant in free space, is destroyed by the turbulence when it passes at sufficiently large distances from the source. It is also shown that the polarization properties are mainly affected by the source correlation functions, and change in the turbulent statistics plays a relatively small effect. In addition, the polarization state exhibits self-splitting property and each beamlet evolves into radially polarized structure upon propagation.

  16. Beam width evolution of astigmatic hollow Gaussian beams in highly nonlocal nonlinear media

    NASA Astrophysics Data System (ADS)

    Yang, Zhen-Feng; Jiang, Xue-Song; Yang, Zhen-Jun; Li, Jian-Xing; Zhang, Shu-Min

    We investigate the beam width evolution of astigmatic hollow Gaussian beams propagating in highly nonlocal nonlinear media. The input-power-induced different evolutions of the beam width are illustrated: (i) the beam widths in two transverse directions are compressed or broadened at the same time; (ii) the beam width in one transverse direction keeps invariant, and the other is compressed or broadened; (iii) furthermore, the beam width in one transverse direction is compressed, whereas it in the other transverse direction is broadened.

  17. Stable donutlike vortex beam generation from lasers with controlled Ince-Gaussian modes

    NASA Astrophysics Data System (ADS)

    Chu, Shu-Chun; Otsuka, Kenju

    2007-11-01

    This study proposes a three-lens configuration for generating a stable donutlike vortex laser beam with controlled Ince-Gaussian mode (IGM) operation in the model of laser-diode (LD)-pumped solid-state lasers. Simply controlling the lateral off-axis position of the pump beam's focus on the laser crystal can generate a desired donutlike vortex beam from the proposed simple and easily made three-lens configuration, a proposed astigmatic mode converter assembled into one body with a concave-convex laser cavity.

  18. Application of partially coherent modes for studying generation of a Gaussian partially coherent laser beam

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Suvorov, A A

    2010-10-15

    The problem of steady-state generation of a Gaussian partially coherent beam in a stable-cavity laser is considered within the framework of the method of expansion of the radiation coherence function in partially coherent modes. We discuss the conditions whose fulfilment makes it possible to neglect the intermode beatings of the radiation field and the effect of the gain dispersion on the steady-state generation of multimode partially coherent radiation. Based on the simplified model, we solve the self-consistent problem of generation of a Gaussian partially coherent beam for the given laser pump conditions and the resonator parameters. The dependence of themore » beam characteristics (power, radius, etc.) on the active medium properties and the resonator parameters is obtained. (laser beams)« less

  19. The robustness of truncated Airy beam in PT Gaussian potentials media

    NASA Astrophysics Data System (ADS)

    Wang, Xianni; Fu, Xiquan; Huang, Xianwei; Yang, Yijun; Bai, Yanfeng

    2018-03-01

    The robustness of truncated Airy beam in parity-time (PT) symmetric Gaussian potentials media is numerically investigated. A high-peak power beam sheds from the Airy beam due to the media modulation while the Airy wavefront still retain its self-bending and non-diffraction characteristics under the influence of modulation parameters. Increasing the modulation factor results in the smaller value of maximum power of the center beam, and the opposite trend occurs with the increment of the modulation depth. However, the parabolic trajectory of the Airy wavefront does not be influenced. By utilizing the unique features, the Airy beam can be used as a long distance transmission source under the PT symmetric Gaussian potentials medium.

  20. On the exploration of effect of critical beam power on the propagation of Gaussian laser beam in collisionless magnetized plasma

    NASA Astrophysics Data System (ADS)

    Urunkar, T. U.; Valkunde, A. T.; Vhanmore, B. D.; Gavade, K. M.; Patil, S. D.; Takale, M. V.

    2018-05-01

    It is quite known that critical power of the laser plays vital role in the propagation of Gaussian laser beam in collisionless plasma. The nonlinearity in dielectric constant considered herein is due to the ponderomotive force. In the present analysis, the interval of critical beam power has been explored to sustain the competition between diffraction and self-focusing of Gaussian laser beam during propagation in collisionless magnetized plasma. Differential equation for beam-width parameter has been established by using WKB and paraxial approximations under parabolic equation approach. The effect of critical power on the propagation of Gaussian laser beam has been presented graphically and discussed.

  1. Tilt angle measurement with a Gaussian-shaped laser beam tracking

    NASA Astrophysics Data System (ADS)

    Šarbort, Martin; Řeřucha, Šimon; Jedlička, Petr; Lazar, Josef; Číp, Ondrej

    2014-05-01

    We have addressed the challenge to carry out the angular tilt stabilization of a laser guiding mirror which is intended to route a laser beam with a high energy density. Such an application requires good angular accuracy as well as large operating range, long term stability and absolute positioning. We have designed an instrument for such a high precision angular tilt measurement based on a triangulation method where a laser beam with Gaussian profile is reflected off the stabilized mirror and detected by an image sensor. As the angular deflection of the mirror causes a change of the beam spot position, the principal task is to measure the position on the image chip surface. We have employed a numerical analysis of the Gaussian intensity pattern which uses the nonlinear regression algorithm. The feasibility and performance of the method were tested by numeric modeling as well as experimentally. The experimental results indicate that the assembled instrument achieves a measurement error of 0.13 microradian in the range +/-0.65 degrees over the period of one hour. This corresponds to the dynamic range of 1:170 000.

  2. Investigations into phase effects from diffracted Gaussian beams for high-precision interferometry

    NASA Astrophysics Data System (ADS)

    Lodhia, Deepali

    Gravitational wave detectors are a new class of observatories aiming to detect gravitational waves from cosmic sources. All-reflective interferometer configurations have been proposed for future detectors, replacing transmissive optics with diffractive elements, thereby reducing thermal issues associated with power absorption. However, diffraction gratings introduce additional phase noise, creating more stringent conditions for alignment stability, and further investigations are required into all-reflective interferometers. A suitable mathematical framework using Gaussian modes is required for analysing the alignment stability using diffraction gratings. Such a framework was created, whereby small beam displacements are modelled using a modal technique. It was confirmed that the original modal-based model does not contain the phase changes associated with grating displacements. Experimental tests verified that the phase of a diffracted Gaussian beam is independent of the beam shape. Phase effects were further examined using a rigorous time-domain simulation tool. These findings show that the perceived phase difference is based on an intrinsic change of coordinate system within the modal-based model, and that the extra phase can be added manually to the modal expansion. This thesis provides a well-tested and detailed mathematical framework that can be used to develop simulation codes to model more complex layouts of all-reflective interferometers.

  3. Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems.

    PubMed

    Cai, Yangjian; Lin, Qiang

    2004-06-01

    A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite-Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.

  4. Hollow elliptical Gaussian beam and its propagation through aligned and misaligned paraxial optical systems

    NASA Astrophysics Data System (ADS)

    Cai, Yangjian; Lin, Qiang

    2004-06-01

    A new mathematical model called hollow elliptical Gaussian beam (HEGB) is proposed to describe a dark-hollow laser beam with noncircular symmetry in terms of a tensor method. The HEGB can be expressed as a superposition of a series of elliptical Hermite-Gaussian modes. By using the generalized diffraction integral formulas for light passing through paraxial optical systems, analytical propagation formulas for HEGBs passing through paraxial aligned and misaligned optical systems are obtained through vector integration. As examples of applications, evolution properties of the intensity distribution of HEGBs in free-space propagation were studied. Propagation properties of HEGBs through a misaligned thin lens were also studied. The HEGB provides a convenient way to describe elliptical dark-hollow laser beams and can be used conveniently to study the motion of atoms in a dark-hollow laser beam.

  5. Launching and controlling Gaussian beams from point sources via planar transformation media

    NASA Astrophysics Data System (ADS)

    Odabasi, Hayrettin; Sainath, Kamalesh; Teixeira, Fernando L.

    2018-02-01

    Based on operations prescribed under the paradigm of complex transformation optics (CTO) [F. Teixeira and W. Chew, J. Electromagn. Waves Appl. 13, 665 (1999), 10.1163/156939399X01104; F. L. Teixeira and W. C. Chew, Int. J. Numer. Model. 13, 441 (2000), 10.1002/1099-1204(200009/10)13:5%3C441::AID-JNM376%3E3.0.CO;2-J; H. Odabasi, F. L. Teixeira, and W. C. Chew, J. Opt. Soc. Am. B 28, 1317 (2011), 10.1364/JOSAB.28.001317; B.-I. Popa and S. A. Cummer, Phys. Rev. A 84, 063837 (2011), 10.1103/PhysRevA.84.063837], it was recently shown in [G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, Phys. Rev. Lett. 110, 173901 (2013), 10.1103/PhysRevLett.110.173901] that a complex source point (CSP) can be mimicked by parity-time (PT ) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such a metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to nonsymmetric complex coordinate transformations as put forth in [S. Savoia, G. Castaldi, and V. Galdi, J. Opt. 18, 044027 (2016), 10.1088/2040-8978/18/4/044027] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed outside the slab as well. By making use of the extra degrees of freedom (the real and imaginary parts of the coordinate transformation) provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization of Gaussian-like beams. We illustrate how beam properties such as peak amplitude and waist location can be controlled by a proper choice of (complex-valued) CTO Jacobian elements. In particular, the beam waist

  6. The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Leung Shingyu, E-mail: masyleung@ust.h; Qian Jianliang, E-mail: qian@math.msu.ed

    2010-11-20

    We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying themore » FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.« less

  7. The effects of induced heat loads on the propagation of Ince-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Nadgaran, H.; Servatkhah, M.

    2011-10-01

    Thermal effects are very much influential in high power beam generators. Their impacts on special types of beams such as Helmholtz-Gauss beams have attracted special attentions. This work reports thermal effects on the generation and propagation of Ince-Gaussian beams. The results show considerable beam spot size variations for near fields under various induced heat loads. As Ince-Gaussian beams are directly related to cavity symmetry breaking, the results can greatly help system designers for circumventing these types of symmetry breaks usually encountered in high power lasers.

  8. Numerical modeling on carbon fiber composite material in Gaussian beam laser based on ANSYS

    NASA Astrophysics Data System (ADS)

    Luo, Ji-jun; Hou, Su-xia; Xu, Jun; Yang, Wei-jun; Zhao, Yun-fang

    2014-02-01

    Based on the heat transfer theory and finite element method, the macroscopic ablation model of Gaussian beam laser irradiated surface is built and the value of temperature field and thermal ablation development is calculated and analyzed rationally by using finite element software of ANSYS. Calculation results show that the ablating form of the materials in different irritation is of diversity. The laser irradiated surface is a camber surface rather than a flat surface, which is on the lowest point and owns the highest power density. Research shows that the higher laser power density absorbed by material surface, the faster the irritation surface regressed.

  9. Interpretation of Extinction in Gaussian-Beam Scattering

    NASA Technical Reports Server (NTRS)

    Lock, James A.

    1995-01-01

    The extinction efficiency for the interaction of a plane wave with a large nonabsorbing spherical particle is approximately 2.0. When a Gaussian beam of half-width w(sub 0) is incident upon a spherical particle of radius a with w(sub 0)/a less than 1, the extinction efficiency attains unexpectedly high or low values, contrary to intuitive expectations. The reason for this is associated with the so-called compensating term in the scattered field, which cancels the field of the Gaussian beam behind the particle, thereby producing the particle's shadow. I introduce a decomposition of the total exterior field into incoming and outgoing portions that are free of compensating terms. It is then shown that a suitably defined interaction efficiency has the intuitively expected asymptotic values of 2.0 for w(sub 0)/a much greater than 1 and 1.0 for w(sub 0)/a much less than 1.

  10. Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media

    NASA Astrophysics Data System (ADS)

    Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Zhou, Meiling; Zhang, Liping; Li, Dongdong; Deng, Dongmei

    2016-12-01

    The propagation of a Pearcey-Gaussian-vortex beam (PGVB) has been investigated numerically in free space and Kerr media. In addition, we have done a numerical experiment for the beam in free space. A PGVB maintains the characteristics of auto-focusing, self-healing and form-invariance which are possessed by a Pearcey beam and a Pearcey-Gaussian beam. Due to the influence of the optical vortex, a bright speck occurs in front of the main lobe. Compared with a Pearcey beam and a Pearcey-Gaussian beam, a PGVB has the most remarkable intensity singularity and the phase singularity. It is worth noting that the impact of the vortex at the coordinate origins means that a PGVB in the vicinity carries no angular momentum or transverse energy flow. We have investigated and numerically simulated the transverse intensity of a PGVB in Kerr media. We find that the auto-focusing of a PGVB in a Kerr medium becomes stronger with increasing power.

  11. Coherent and incoherent off-axis Hermite-Gaussian beam combinations.

    PubMed

    Lü, B; Ma, H

    2000-03-10

    A detailed study of the coherent and the incoherent combinations of two-dimensional off-axis Hermite-Gaussian beams with rectangular symmetry is made. The closed-form propagation formulas of the resulting beam are derived, and the resulting beam quality in terms of the M(2) factor and power in the bucket is discussed and compared for the coherent and the incoherent combinations. In addition, it is shown that the resulting astigmatic beam can be symmetrized in the sense of the second-moment definition of beam width. However, the symmetrizing transformation of the resulting astigmatic beams is incomplete, because there exist different irradiance profiles.

  12. Structured Laguerre-Gaussian beams for mitigation of spherical aberration in tightly focused regimes

    NASA Astrophysics Data System (ADS)

    Haddadi, S.; Bouzid, O.; Fromager, M.; Hasnaoui, A.; Harfouche, A.; Cagniot, E.; Forbes, A.; Aït-Ameur, K.

    2018-04-01

    Many laser applications utilise a focused laser beam having a single-lobed intensity profile in the focal plane, ideally with the highest possible on-axis intensity. Conventionally, this is achieved with the lowest-order Laguerre-Gaussian mode (LG00), the Gaussian beam, in a tight focusing configuration. However, tight focusing often involves significant spherical aberration due to the high numerical aperture of the systems involved, thus degrading the focal quality. Here, we demonstrate that a high-order radial LG p0 mode can be tailored to meet and in some instances exceed the performance of the Gaussian. We achieve this by phase rectification of the mode using a simple binary diffractive optic. By way of example, we show that the focusing of a rectified LG50 beam is almost insensitive to a spherical aberration coefficient of over three wavelengths, in contrast with the usual Gaussian beam for which the intensity of the focal spot is reduced by a factor of two. This work paves the way towards enhanced focal spots using structured light.

  13. Cosine-Gaussian Schell-model sources.

    PubMed

    Mei, Zhangrong; Korotkova, Olga

    2013-07-15

    We introduce a new class of partially coherent sources of Schell type with cosine-Gaussian spectral degree of coherence and confirm that such sources are physically genuine. Further, we derive the expression for the cross-spectral density function of a beam generated by the novel source propagating in free space and analyze the evolution of the spectral density and the spectral degree of coherence. It is shown that at sufficiently large distances from the source the degree of coherence of the propagating beam assumes Gaussian shape while the spectral density takes on the dark-hollow profile.

  14. Fractional Fourier transform of truncated elliptical Gaussian beams.

    PubMed

    Du, Xinyue; Zhao, Daomu

    2006-12-20

    Based on the fact that a hard-edged elliptical aperture can be expanded approximately as a finite sum of complex Gaussian functions in tensor form, an analytical expression for an elliptical Gaussian beam (EGB) truncated by an elliptical aperture and passing through a fractional Fourier transform system is derived by use of vector integration. The approximate analytical results provide more convenience for studying the propagation and transformation of truncated EGBs than the usual way by using the integral formula directly, and the efficiency of numerical calculation is significantly improved.

  15. Stability of Ince-Gaussian beams in elliptical core few-mode fibers.

    PubMed

    Sakpal, Sahil; Milione, Giovanni; Li, Min-Jun; Nouri, Mehdi; Shahoei, Hiva; LaFave, Tim; Ashrafi, Solyman; MacFarlane, Duncan

    2018-06-01

    A comparative stability analysis of Ince-Gaussian and Hermite-Gaussian modes in elliptical core few-mode fibers is provided to inform the design of spatial division multiplexing systems. The correlation method is used to construct crosstalk matrices that characterize the spatial modes of the fiber. Up to six low-order modes are shown to exhibit about -20  dB crosstalk. The crosstalk performance of each mode set is found to be similar. However, a direct comparison between modes of equal Gouy phase shift, a parameter that ensures identical beam quality, and phase at the detector, demonstrates better relative power transmission for Ince-Gaussian beams. This result is consistent with the natural modes supported by a 100 m elliptical core fiber for which a mode ellipticity of ϵ=2 was found to be optimal. The relative power difference is expected to be magnified over longer fiber lengths in favor of Ince-Gaussian modes.

  16. Propagation of Airy Gaussian vortex beams in uniaxial crystals

    NASA Astrophysics Data System (ADS)

    Weihao, Yu; Ruihuang, Zhao; Fu, Deng; Jiayao, Huang; Chidao, Chen; Xiangbo, Yang; Yanping, Zhao; Dongmei, Deng

    2016-04-01

    The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108, 11374107, 10904041, and 11547212), the Foundation of Cultivating Outstanding Young Scholars of Guangdong Province, China, the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, the National Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 2015093), and the Science and Technology Projects of Guangdong Province, China (Grant No. 2013B031800011).

  17. Generation of dark hollow beam by focusing a sine-Gaussian beam using a cylindrical lens and a focusing lens

    NASA Astrophysics Data System (ADS)

    Tang, Huiqin; Zhu, Kaicheng

    2013-12-01

    Based on the generalized Huygens-Fresnel diffraction integral, a closed-form propagation equation related to sine-Gaussian beams through a cylindrical lens and a focusing lens is derived and illustrated with numerical methods. It is found that a sine-Gaussian beam through such a system may be converted into a dark hollow beam (DHB) with topological charge index one and its bright enclosure is approximately an elongated ellipse with very high ellipticity. Moreover, the parameter values at which the DHBs have perfect intensity patterns are designed. The optimal relative orientation between the dislocation line of the input sine-Gaussian beam and the axial orientation of the cylindrical lens is specified. And the ellipticity of the elliptical DHBs is mainly defined by the focal length of the cylindrical lens and the Fresnel number of the optical system.

  18. Log-amplitude variance and wave structure function: A new perspective for Gaussian beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Miller, W.B.; Ricklin, J.C.; Andrews, L.C.

    1993-04-01

    Two naturally linked pairs of nondimensional parameters are identified such that either pair, together with wavelength and path length, completely specifies the diffractive propagation environment for a lowest-order paraxial Gaussian beam. Both parameter pairs are intuitive, and within the context of locally homogeneous and isotropic turbulence they reflect the long-recognized importance of the Fresnel zone size in the behavior of Rytov propagation statistics. These parameter pairs, called, respectively, the transmitter and receiver parameters, also provide a change in perspective in the analysis of optical turbulence effects on Gaussian beams by unifying a number of behavioral traits previously observed or predicted,more » and they create an environment in which the determination of limiting interrelationships between beam forms is especially simple. The fundamental nature of the parameter pairs becomes apparent in the derived analytical expressions for the log-amplitude variance and the wave structure function. These expressions verify general optical turbulence-related characteristics predicted for Gaussian beams, provide additional insights into beam-wave behavior, and are convenient tools for beam-wave analysis. 22 refs., 10 figs., 2 tabs.« less

  19. Scattering of Gaussian Beams by Disordered Particulate Media

    NASA Technical Reports Server (NTRS)

    Mishchenko, Michael I.; Dlugach, Janna M.

    2016-01-01

    A frequently observed characteristic of electromagnetic scattering by a disordered particulate medium is the absence of pronounced speckles in angular patterns of the scattered light. It is known that such diffuse speckle-free scattering patterns can be caused by averaging over randomly changing particle positions and/or over a finite spectral range. To get further insight into the possible physical causes of the absence of speckles, we use the numerically exact superposition T-matrix solver of the Maxwell equations and analyze the scattering of plane-wave and Gaussian beams by representative multi-sphere groups. We show that phase and amplitude variations across an incident Gaussian beam do not serve to extinguish the pronounced speckle pattern typical of plane-wave illumination of a fixed multi-particle group. Averaging over random particle positions and/or over a finite spectral range is still required to generate the classical diffuse speckle-free regime.

  20. Spot size characterization of focused non-Gaussian X-ray laser beams.

    PubMed

    Chalupský, J; Krzywinski, J; Juha, L; Hájková, V; Cihelka, J; Burian, T; Vysín, L; Gaudin, J; Gleeson, A; Jurek, M; Khorsand, A R; Klinger, D; Wabnitz, H; Sobierajski, R; Störmer, M; Tiedtke, K; Toleikis, S

    2010-12-20

    We present a new technique for the characterization of non-Gaussian laser beams which cannot be described by an analytical formula. As a generalization of the beam spot area we apply and refine the definition of so called effective area (A(eff)) [1] in order to avoid using the full-width at half maximum (FWHM) parameter which is inappropriate for non-Gaussian beams. Furthermore, we demonstrate a practical utilization of our technique for a femtosecond soft X-ray free-electron laser. The ablative imprints in poly(methyl methacrylate) - PMMA and amorphous carbon (a-C) are used to characterize the spatial beam profile and to determine the effective area. Two procedures of the effective area determination are presented in this work. An F-scan method, newly developed in this paper, appears to be a good candidate for the spatial beam diagnostics applicable to lasers of various kinds.

  1. An alternative theoretical model for an anomalous hollow beam.

    PubMed

    Cai, Yangjian; Wang, Zhaoying; Lin, Qiang

    2008-09-15

    An alternative and convenient theoretical model is proposed to describe a flexible anomalous hollow beam of elliptical symmetry with an elliptical solid core, which was observed in experiment recently (Phys. Rev. Lett, 94 (2005) 134802). In this model, the electric field of anomalous hollow beam is expressed as a finite sum of elliptical Gaussian modes. Flattopped beams, dark hollow beams and Gaussian beams are special cases of our model. Analytical propagation formulae for coherent and partially coherent anomalous hollow beams passing through astigmatic ABCD optical systems are derived. Some numerical examples are calculated to show the propagation and focusing properties of coherent and partially coherent anomalous hollow beams.

  2. High power infrared super-Gaussian beams: generation, propagation, and application

    NASA Astrophysics Data System (ADS)

    du Preez, Neil C.; Forbes, Andrew; Botha, Lourens R.

    2008-10-01

    In this paper we present the design of a CO2 laser resonator that produces as the stable transverse mode a super-Gaussian laser beam. The resonator makes use of an intra-cavity diffractive mirror and a flat output coupler, generating the desired intensity profile at the output coupler with a flat wavefront. We consider the modal build-up in such a resonator and show that such a resonator mode has the ability to extract more energy from the cavity that a standard cavity single mode beam (e.g., Gaussian mode cavity). We demonstrate the design experimentally on a high average power TEA CO2 laser for paint stripping applications.

  3. Device and method for creating Gaussian aberration-corrected electron beams

    DOEpatents

    McMorran, Benjamin; Linck, Martin

    2016-01-19

    Electron beam phase gratings have phase profiles that produce a diffracted beam having a Gaussian or other selected intensity profile. Phase profiles can also be selected to correct or compensate electron lens aberrations. Typically, a low diffraction order produces a suitable phase profile, and other orders are discarded.

  4. Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region

    NASA Astrophysics Data System (ADS)

    Liu, Pusheng; Lü, Baida

    2007-04-01

    By using the vectorial Debye diffraction theory, phase singularities of high numerical aperture (NA) dark-hollow Gaussian beams in the focal region are studied. The dependence of phase singularities on the truncation parameter δ and semi-aperture angle α (or equally, NA) is illustrated numerically. A comparison of phase singularities of high NA dark-hollow Gaussian beams with those of scalar paraxial Gaussian beams and high NA Gaussian beams is made. For high NA dark-hollow Gaussian beams the beam order n additionally affects the spatial distribution of phase singularities, and there exist phase singularities outside the focal plane, which may be created or annihilated by variation of the semi-aperture angle in a certain region.

  5. The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Leung, Shingyu; Qian, Jianliang

    2010-11-01

    We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.

  6. Reshaping a multimode laser beam into a constructed Gaussian beam for generating a thin light sheet.

    PubMed

    Saghafi, Saiedeh; Haghi-Danaloo, Nikoo; Becker, Klaus; Sabdyusheva, Inna; Foroughipour, Massih; Hahn, Christian; Pende, Marko; Wanis, Martina; Bergmann, Michael; Stift, Judith; Hegedus, Balazs; Dome, Balazs; Dodt, Hans-Ulrich

    2018-06-01

    Based on the modal analysis method, we developed a model that describes the output beam of a diode-pumped solid state (DPSS) laser emitting a multimode beam. Measuring the output beam profile in the near field and at the constructed far field the individual modes, their respective contributions, and their optical parameters are determined. Using this information, the beam is optically reshaped into a quasi-Gaussian beam by the interference and superposition of the various modes. This process is controlled by a mode modulator unit that includes different meso-aspheric elements and a soft-aperture. The converted beam is guided into a second optical unit comprising achromatic-aspheric elements to produce a thin light sheet for ultramicroscopy. We found that this light sheet is markedly thinner and exhibits less side shoulders compared with a light sheet directly generated from the output of a DPSS multimode laser. © 2018 The Authors. Journal of Biophotonics published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  7. Gaussian versus flat-top spatial beam profiles for optical stimulation of the prostate nerves

    NASA Astrophysics Data System (ADS)

    Tozburun, Serhat; Lagoda, Gwen A.; Burnett, Arthur L.; Fried, Nathaniel M.

    2010-02-01

    The cavernous nerves (CN) course along the prostate surface and are responsible for erectile function. Improved identification and preservation of the CN's is critical to maintaining sexual potency after prostate cancer surgery. Noncontact optical nerve stimulation (ONS) of the CN's was recently demonstrated in a rat model, in vivo, as a potential alternative to electrical nerve stimulation (ENS) for identification of the CN's during prostate surgery. However, the therapeutic window for ONS is narrow, so optimal design of the fiber optic delivery system is critical for safe, reproducible stimulation. This study describes modeling, assembly, and testing of an ONS probe for delivering a small, collimated, flat-top laser beam for uniform CN stimulation. A direct comparison of the magnitude and response time of the intracavernosal pressure (ICP) for both Gaussian and flat-top spatial beam profiles was performed. Thulium fiber laser radiation (λ=1870 nm) was delivered through a 200-μm fiber, with distal fiber tip chemically etched to convert a Gaussian to flat-top beam profile. The laser beam was collimated to a 1-mm-diameter spot using an aspheric lens. Computer simulations of light propagation were used to optimize the probe design. The 10-Fr (3.4-mm-OD) laparoscopic probe provided a constant radiant exposure at the CN surface. The probe was tested in four rats, in vivo. ONS of the CN's was performed with a 1-mm-diameter spot, 5-ms pulse duration, and pulse rate of 20 Hz for a duration of 15-30 s. The flat-top laser beam profile consistently produced a faster and higher ICP response at a lower radiant exposure than the Gaussian beam profile due, in part, to easier alignment of the more uniform beam with nerve. The threshold for ONS was approximately 0.14 J/cm2, corresponding to a temperature increase of 6-8°C at the CN surface after a stimulation time of 15 s. With further development, ONS may be used as a diagnostic tool for identification of CN's during prostate

  8. Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean.

    PubMed

    Li, Ye; Yu, Lin; Zhang, Yixin

    2017-05-29

    Applying the angular spectrum theory, we derive the expression of a new Hermite-Gaussian (HG) vortex beam. Based on the new Hermite-Gaussian (HG) vortex beam, we establish the model of the received probability density of orbital angular momentum (OAM) modes of this beam propagating through a turbulent ocean of anisotropy. By numerical simulation, we investigate the influence of oceanic turbulence and beam parameters on the received probability density of signal OAM modes and crosstalk OAM modes of the HG vortex beam. The results show that the influence of oceanic turbulence of anisotropy on the received probability of signal OAM modes is smaller than isotropic oceanic turbulence under the same condition, and the effect of salinity fluctuation on the received probability of the signal OAM modes is larger than the effect of temperature fluctuation. In the strong dissipation of kinetic energy per unit mass of fluid and the weak dissipation rate of temperature variance, we can decrease the effects of turbulence on the received probability of signal OAM modes by selecting a long wavelength and a larger transverse size of the HG vortex beam in the source's plane. In long distance propagation, the HG vortex beam is superior to the Laguerre-Gaussian beam for resisting the destruction of oceanic turbulence.

  9. Numerical investigations of non-collinear optical parametric chirped pulse amplification for Laguerre-Gaussian vortex beam

    NASA Astrophysics Data System (ADS)

    Xu, Lu; Yu, Lianghong; Liang, Xiaoyan

    2016-04-01

    We present for the first time a scheme to amplify a Laguerre-Gaussian vortex beam based on non-collinear optical parametric chirped pulse amplification (OPCPA). In addition, a three-dimensional numerical model of non-collinear optical parametric amplification was deduced in the frequency domain, in which the effects of non-collinear configuration, temporal and spatial walk-off, group-velocity dispersion and diffraction were also taken into account, to trace the dynamics of the Laguerre-Gaussian vortex beam and investigate its critical parameters in the non-collinear OPCPA process. Based on the numerical simulation results, the scheme shows promise for implementation in a relativistic twisted laser pulse system, which will diversify the light-matter interaction field.

  10. Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

    NASA Astrophysics Data System (ADS)

    Dennis, M. R.; Alonso, M. A.

    2017-02-01

    The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization. This article is part of the themed issue 'Optical orbital angular momentum'.

  11. Correction factor for ablation algorithms used in corneal refractive surgery with gaussian-profile beams

    NASA Astrophysics Data System (ADS)

    Jimenez, Jose Ramón; González Anera, Rosario; Jiménez del Barco, Luis; Hita, Enrique; Pérez-Ocón, Francisco

    2005-01-01

    We provide a correction factor to be added in ablation algorithms when a Gaussian beam is used in photorefractive laser surgery. This factor, which quantifies the effect of pulse overlapping, depends on beam radius and spot size. We also deduce the expected post-surgical corneal radius and asphericity when considering this factor. Data on 141 eyes operated on LASIK (laser in situ keratomileusis) with a Gaussian profile show that the discrepancy between experimental and expected data on corneal power is significantly lower when using the correction factor. For an effective improvement of post-surgical visual quality, this factor should be applied in ablation algorithms that do not consider the effects of pulse overlapping with a Gaussian beam.

  12. Gaussian beam in two-photon fluorescence imaging of rat brain microvessel

    NASA Astrophysics Data System (ADS)

    Shi, Lingyan; Rodríguez-Contreras, Adrián; Alfano, Robert R.

    2014-12-01

    The critical optical properties of a Gaussian laser beam in two-photon or multiphoton fluorescence imaging, including the beam spot size, depth of focus, and intensity profile, are investigated for spatially locating nanoscale solutes in and surrounding the microvessels of rat brain.

  13. Ultrasound beam transmission using a discretely orthogonal Gaussian aperture basis

    NASA Astrophysics Data System (ADS)

    Roberts, R. A.

    2018-04-01

    Work is reported on development of a computational model for ultrasound beam transmission at an arbitrary geometry transmission interface for generally anisotropic materials. The work addresses problems encountered when the fundamental assumptions of ray theory do not hold, thereby introducing errors into ray-theory-based transmission models. Specifically, problems occur when the asymptotic integral analysis underlying ray theory encounters multiple stationary phase points in close proximity, due to focusing caused by concavity on either the entry surface or a material slowness surface. The approach presented here projects integrands over both the transducer aperture and the entry surface beam footprint onto a Gaussian-derived basis set, thereby distributing the integral over a summation of second-order phase integrals which are amenable to single stationary phase point analysis. Significantly, convergence is assured provided a sufficiently fine distribution of basis functions is used.

  14. Dipole saturated absorption modeling in gas phase: Dealing with a Gaussian beam

    NASA Astrophysics Data System (ADS)

    Dupré, Patrick

    2018-01-01

    With the advent of new accurate and sensitive spectrometers, cf. combining optical cavities (for absorption enhancement), the requirement for reliable molecular transition modeling is becoming more pressing. Unfortunately, there is no trivial approach which can provide a definitive formalism allowing us to solve the coupled systems of equations associated with nonlinear absorption. Here, we propose a general approach to deal with any spectral shape of the electromagnetic field interacting with a molecular species under saturation conditions. The development is specifically applied to Gaussian-shaped beams. To make the analytical expressions tractable, approximations are proposed. Finally, two or three numerical integrations are required for describing the Lamb-dip profile. The implemented model allows us to describe the saturated absorption under low pressure conditions where the broadening by the transit-time may dominate the collision rates. The model is applied to two specific overtone transitions of the molecular acetylene. The simulated line shapes are discussed versus the collision and the transit-time rates. The specific collisional and collision-free regimes are illustrated, while the Rabi frequency controls the intermediate regime. We illustrate how to recover the input parameters by fitting the simulated profiles.

  15. Channel capacity of OAM based FSO communication systems with partially coherent Bessel-Gaussian beams in anisotropic turbulence

    NASA Astrophysics Data System (ADS)

    Peng, Juan; Zhang, Li; Zhang, Kecheng; Ma, Junxian

    2018-07-01

    Based on the Rytov approximation theory, the transmission model of an orbital angular momentum (OAM)-carrying partially coherent Bessel-Gaussian (BG) beams propagating in weak anisotropic turbulence is established. The corresponding analytical expression of channel capacity is presented. Influences of anisotropic turbulence parameters and beam parameters on channel capacity of OAM-based free-space optical (FSO) communication systems are discussed in detail. The results indicate channel capacity increases with increasing of almost all of the parameters except for transmission distance. Raising the values of some parameters such as wavelength, propagation altitude and non-Kolmogorov power spectrum index, would markedly improve the channel capacity. In addition, we evaluate the channel capacity of Laguerre-Gaussian (LG) beams and partially coherent BG beams in anisotropic turbulence. It indicates that partially coherent BG beams are better light sources candidates for mitigating the influences of anisotropic turbulence on channel capacity of OAM-based FSO communication systems.

  16. Determination of Cross-Sectional Area of Focused Picosecond Gaussian Laser Beam

    NASA Technical Reports Server (NTRS)

    Ledesma, Rodolfo; Fitz-Gerald, James; Palmieri, Frank; Connell, John

    2018-01-01

    Measurement of the waist diameter of a focused Gaussian-beam at the 1/e(sup 2) intensity, also referred to as spot size, is key to determining the fluence in laser processing experiments. Spot size measurements are also helpful to calculate the threshold energy and threshold fluence of a given material. This work reports an application of a conventional method, by analyzing single laser ablated spots for different laser pulse energies, to determine the cross-sectional area of a focused Gaussian-beam, which has a nominal pulse width of approx. 10 ps. Polished tungsten was used as the target material, due to its low surface roughness and low ablation threshold, to measure the beam waist diameter. From the ablative spot measurements, the ablation threshold fluence of the tungsten substrate was also calculated.

  17. Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Karbstein, Felix; Mosman, Elena A.

    2017-12-01

    In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.

  18. Paint stripping with high power flattened Gaussian beams

    NASA Astrophysics Data System (ADS)

    Forbes, Andrew; du Preez, Neil C.; Belyi, Vladimir; Botha, Lourens R.

    2009-08-01

    In this paper we present results on improved paint stripping performance with an intra-cavity generated Flattened Gaussian Beam (FGB). A resonator with suitable diffractive optical elements was designed in order to produce a single mode flat-top like laser beam as the output. The design was implemented in a TEA CO2 laser outputting more than 5 J per pulse in the desired mode. The FGB showed improved performance in a paint stripping application due to its uniformity of intensity, and high energy extraction from the cavity.

  19. Propagation of a Gaussian-beam wave in general anisotropic turbulence

    NASA Astrophysics Data System (ADS)

    Andrews, L. C.; Phillips, R. L.; Crabbs, R.

    2014-10-01

    Mathematical models for a Gaussian-beam wave propagating through anisotropic non-Kolmogorov turbulence have been developed in the past by several researchers. In previous publications, the anisotropic spatial power spectrum model was based on the assumption that propagation was in the z direction with circular symmetry maintained in the orthogonal xy-plane throughout the path. In the present analysis, however, the anisotropic spectrum model is no longer based on a single anisotropy parameter—instead, two such parameters are introduced in the orthogonal xyplane so that circular symmetry in this plane is no longer required. In addition, deviations from the 11/3 power-law behavior in the spectrum model are allowed by assuming power-law index variations 3 < α < 4 . In the current study we develop theoretical models for beam spot size, spatial coherence, and scintillation index that are valid in weak irradiance fluctuation regimes as well as in deep turbulence, or strong irradiance fluctuation regimes. These new results are compared with those derived from the more specialized anisotropic spectrum used in previous analyses.

  20. Experimental Profiling of a Non-truncated Focused Gaussian Beam and Fine-tuning of the Quadratic Phase in the Fresnel Gaussian Shape Invariant

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    S., Juan Manuel Franco; Cywiak, Moises; Cywiak, David

    2015-06-24

    A homodyne profiler is used for recording the intensity distribution of focused non-truncated Gaussian beams. The spatial distributions are obtained at planes in the vicinity of the back-focal plane of a focusing lens placed at different distances from a He–Ne laser beam with a Gaussian intensity profile. Comparisons of the experimental data with those obtained from the analytical equations for an ideal focusing lens allow us to propose formulae to fine-tune the quadratic term in the Fresnel Gaussian shape invariant at each interface of the propagated field. Furthermore, we give analytical expressions to calculate adequately the propagation of the fieldmore » through an optical system.« less

  1. Propagation of hollow Gaussian beam through a misaligned first-order optical system and its propagation properties

    NASA Astrophysics Data System (ADS)

    Zhao, Cheng Liang; Lu, Xuan Hui

    2007-06-01

    Propagation properties of hollow Gaussian beam through a misaligned first-order ABCD system is studied using the generalized Huygens-Fresnel diffraction integral, augmented matrix. It is shown that, as a hollow Gaussian beam passes through the misaligned first-order ABCD system, the beam shape is not preserved, the out-put beams have differences when passing different misaligned optical systems. We can adjust the size of dark region through adjusting the misaligned transverse vector E.

  2. Scattering of aerosol particles by a Hermite-Gaussian beam in marine atmosphere.

    PubMed

    Huang, Qingqing; Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Yan, Xu; Liu, Songhua

    2017-07-01

    Based on the complex-source-point method and the generalized Lorenz-Mie theory, the scattering properties and polarization of aerosol particles by a Hermite-Gaussian (HG) beam in marine atmosphere is investigated. The influences of beam mode, beam width, and humidity on the scattered field are analyzed numerically. Results indicate that when the number of HG beam modes u (v) increase, the radar cross section of aerosol particles alternating appears at maximum and minimum values in the forward and backward scattering, respectively, because of the special petal-shaped distribution of the HG beam. The forward and backward scattering of aerosol particles decreases with the increase in beam waist. When beam waist is less than the radius of the aerosol particle, a minimum value is observed in the forward direction. The scattering properties of aerosol particles by the HG beam are more sensitive to the change in relative humidity compared with those by the plane wave and the Gaussian beam (GB). The HG beam shows superiority over the plane wave and the GB in detecting changes in the relative humidity of marine atmosphere aerosol. The effects of relative humidity on the polarization of the HG beam have been numerically analyzed in detail.

  3. Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma

    NASA Astrophysics Data System (ADS)

    Valkunde, Amol T.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Patil, Sandip D.; Takale, Mansing V.

    2018-05-01

    In this work, nonlinear aspects of a high intensity q-Gaussian laser beam propagating in collisionless plasma having upward density ramp of exponential profiles is studied. We have employed the nonlinearity in dielectric function of plasma by considering ponderomotive nonlinearity. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing of q-Gaussian laser beam for various values of q is systematically carried out and compared with results Gaussian laser beam propagating in collisionless plasma having uniform density. It is found that exponential plasma density ramp causes the laser beam to become more focused and gives reasonably interesting results.

  4. Generalized M-factor of hollow Gaussian beams through a hard-edge circular aperture

    NASA Astrophysics Data System (ADS)

    Deng, Dongmei

    2005-06-01

    Based on the generalized truncated second-order moments, the generalized M-factor (MG2-factor) of three-dimensional hollow Gaussian beams (HGBs) through a hard-edge circular aperture is studied in cylindrical coordinate system analytically and numerically. The closed-form expression for the MG2-factor of the truncated HGBs, which is dependent on the truncation parameter β and the beam order n, can be simplified to that of the truncated, the untruncated Gaussian beams and the untruncated HGBs. Also, the power fraction is demonstrated analytically and numerically, which shows that the area of the dark region across the HGBs increases as n increasing.

  5. Modeling of a VMJ PV array under Gaussian high intensity laser power beam condition

    NASA Astrophysics Data System (ADS)

    Eom, Jeongsook; Kim, Gunzung; Park, Yongwan

    2018-02-01

    The high intensity laser power beaming (HILPB) system is one of the most promising systems in the long-rang wireless power transfer field. The vertical multi-junction photovoltaic (VMJ PV) array converts the HILPB into electricity to power the load or charges a battery. The output power of a VMJ PV array depends mainly on irradiance values of each VMJ PV cells. For simulating an entire VMJ PV array, the irradiance profile of the Gaussian HILPB and the irradiance level of the VMJ PV cell are mathematically modeled first. The VMJ PV array is modeled as a network with dimension m*n, where m represents the number of VMJ PV cells in a column, and n represents the number of VMJ PV cells in a row. In order to validate the results obtained in modeling and simulation, a laboratory setup was developed using 55 VMJ PV array. By using the output power model of VMJ PV array, we can establish an optimal power transmission path by the receiver based on the received signal strength. When the laser beam from multiple transmitters aimed at a VMJ PV array at the same time, the received power is the sum of all energy at a VMJ PV array. The transmitter sends its power characteristics as optically coded laser pulses and powers as HILPB. Using the attenuated power model and output power model of VMJ PV array, the receiver can estimate the maximum receivable powers from the transmitters and select optimal transmitters.

  6. Propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere.

    PubMed

    Zhou, Guoquan; Cai, Yangjian; Chu, Xiuxiang

    2012-04-23

    The propagation of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity and the degree of the polarization of a partially coherent hollow vortex Gaussian beam through a paraxial ABCD optical system are derived in turbulent atmosphere, respectively. The average intensity distribution and the degree of the polarization of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters, the topological charge, the transverse coherent lengths, and the structure constant of the atmospheric turbulence on the propagation of a partially coherent hollow vortex Gaussian beam in turbulent atmosphere are also examined in detail. This research is beneficial to the practical applications in free-space optical communications and the remote sensing of the dark hollow beams. © 2012 Optical Society of America

  7. The propagation of a flattened circular Gaussian beam through an optical system in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Chu, X. X.; Liu, Z. J.; Wu, Y.

    2008-07-01

    Based on the Huygens-Fresnel integral, the properties of a circular flattened Gaussian beam through a stigmatic optical system in turbulent atmosphere are investigated. Analytical formulas for the average intensity are derived. As elementary examples, the average intensity distributions of a collimated circular flattened Gaussian beam and a focused circular flattened Gaussian beam through a simple optical system are studied. To see the effects of the optical system on the propagation, the average intensity distributions of the beam for direct propagation are also studied. From the analysis, comparison and numerical calculation we can see that there are many differences between the two propagations. These differences are due to the geometrical magnification of the optical system, different diffraction and different turbulence-induced spreading. Namely, an optical system not only affects the diffraction but also affects the turbulence-induced spreading.

  8. Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam

    NASA Astrophysics Data System (ADS)

    Romero, J.; Giovannini, D.; McLaren, M. G.; Galvez, E. J.; Forbes, A.; Padgett, M. J.

    2012-08-01

    We report orbital angular momentum (OAM) and angle correlations between signal and idler photons observed when the nonlinear crystal used in spontaneous parametric down-conversion is illuminated by a non-fundamental Gaussian pump beam. We introduce a π-phase step to the transverse profile of the pump, before it impinges on the crystal to create a phase-flipped Gaussian mode, which is a close approximation to an HG10 Hermite-Gaussian-like beam. The correlations in OAM and angular position are then measured holographically using two separate spatial light modulators in the signal and idler arms. We show the transfer of the OAM spectrum of the pump to the down-converted fields, manifested as a redistribution in the OAM correlations consistent with OAM conservation. This corresponds to a modulation of the angular position correlations consistent with the Fourier relationship between the OAM and angle.

  9. A Comparison of Propagation Between Apertured Bessel and Gaussian beams

    NASA Astrophysics Data System (ADS)

    Lin, Mei; Yu, Yanzhong

    2009-04-01

    A true Bessel beam is a family of diffraction-free beams. Thus the most interesting and attractive characteristic of such beam is non-diffracting propagation. In optics, the comparisons of maximum propagation distance had been done between Bessel and Gaussian beams by Durnin and Sprangle, respectively. However, the results obtained by them are conflict due to the difference between their criteria. Because Bessel beams have many potential applications in millimeter wave bands, therefore, it is necessary and significant that the comparison is carried out at these bands. A new contrast criterion at millimeter wavelengths is proposed in our paper. Under this criterion, the numerical results are presented and a new conclusion is drawn.

  10. Generation of Multiple Vortex Beams with Specified Vortex Number from Lasers with Controlled Ince-Gaussian Modes

    NASA Astrophysics Data System (ADS)

    Chu, Shu-Chun

    2008-07-01

    This study proposes a systematic method of selecting excitations of part of Ince-Gaussian modes (IGMs) and a three-lens configuration for generating multiple vortex beams with forced IGMs in the model of laser-diode (LD)-pumped solid-state lasers. Simply changing the lateral off-axis position of the tight pump beam focus on the laser crystal can produce the desired multiple optical vortex beam from the laser in a well-controlled manner using a proposed astigmatic mode converter assembled into one body with the laser cavity.

  11. The effect of optically active turbulence on Gaussian laser beams in the ocean

    NASA Astrophysics Data System (ADS)

    Nootz, G.; Matt, S.; Jarosz, E.; Hou, W.

    2016-02-01

    Motivated by the high resolution and data transfer potential, optical imaging and communication methods are intensely investigated for marine applications. The majority of research focuses on overcoming the strong scattering of light by particles present in the ocean. However when operating in very clear water the limiting factor for such applications can be the strongly forward biased scattering from optically active turbulent layers. For this presentation the effect of optically active turbulence on focused Gaussian beams has been studied in the field, in a controlled laboratory test tank, and by numerical simulations. For the field experiments a telescoping rigid underwater sensor structure (TRUSS) was deployed in the Bahamas equipped with a diffractive optics element projecting a matrix of beams towards a fast beam profiler. Image processing techniques are used to extract the beam wander and beam breathing. The results are compared to theoretical values for the optical turbulence strength derived from the measured temperature microstructure at the test side. Laboratory and simulated experiments are carried out in a physical and numerical Rayleigh-Benard convection turbulence tank of the same geometry. A focused Gaussian laser beam is propagated through the test tank and recorded with a camera from the back side of a diffuser. Similarly, a focused Gaussian beam is propagated numerically by means of split-step Fourier method through the simulated turbulence environment. Results will be presented for weak to moderate turbulence as they are most typical for oceanic conditions. Conclusions about the effect on optical imaging and communication applications will be discussed.

  12. Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum

    PubMed Central

    Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.

    2016-01-01

    Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625

  13. Application of Gaussian beam ray-equivalent model and back-propagation artificial neural network in laser diode fast axis collimator assembly.

    PubMed

    Yu, Hao; Rossi, Giammarco; Braglia, Andrea; Perrone, Guido

    2016-08-10

    The paper presents the development of a tool based on a back-propagation artificial neural network to assist in the accurate positioning of the lenses used to collimate the beam from semiconductor laser diodes along the so-called fast axis. After training using a Gaussian beam ray-equivalent model, the network is capable of indicating the tilt, decenter, and defocus of such lenses from the measured field distribution, so the operator can determine the errors with respect to the actual lens position and optimize the diode assembly procedure. An experimental validation using a typical configuration exploited in multi-emitter diode module assembly and fast axis collimating lenses with different focal lengths and numerical apertures is reported.

  14. Scattering and propagation of a Laguerre-Gaussian vortex beam by uniaxial anisotropic bispheres

    NASA Astrophysics Data System (ADS)

    Qu, Tan; Wu, Zhensen; Shang, Qingchao; Li, Zhengjun; Wu, Jiaji; Li, Haiying

    2018-04-01

    Within the framework of the generalized multi-particle Mie (GMM) theory, analytical solution to electromagnetic scattering of two interacting homogeneous uniaxial anisotropic spheres by a Laguerre-Gaussian (LG) vortex beam is investigated. The particles with different size and dielectric parameter tensor elements are arbitrarily configured. Based on the continuous boundary conditions at each sphere surface, the interactive scattering coefficients are derived. The internal and near-surface field is investigated to describe the propagation of LG vortex beam through the NaCl crystal. In addition, the far fields of some typical anisotropic medium such as LiNbO3, TiO2 bispheres illuminated by an LG vortex beam are numerically presented in detail to analyze the influence of the anisotropic parameters, sphere positions, separation distance and topological charge etc. The results show that LG vortex beam has a better recovery after interacting with a spherical particle compared with Gaussian beam. The study in the paper are useful for the further research on the scattering and propagation characteristics of arbitrary vortex beam in anisotropic chains and periodic structure.

  15. Experimental generation of Laguerre-Gaussian beam using digital micromirror device.

    PubMed

    Ren, Yu-Xuan; Li, Ming; Huang, Kun; Wu, Jian-Guang; Gao, Hong-Fang; Wang, Zi-Qiang; Li, Yin-Mei

    2010-04-01

    A digital micromirror device (DMD) modulates laser intensity through computer control of the device. We experimentally investigate the performance of the modulation property of a DMD and optimize the modulation procedure through image correction. Furthermore, Laguerre-Gaussian (LG) beams with different topological charges are generated by projecting a series of forklike gratings onto the DMD. We measure the field distribution with and without correction, the energy of LG beams with different topological charges, and the polarization property in sequence. Experimental results demonstrate that it is possible to generate LG beams with a DMD that allows the use of a high-intensity laser with proper correction to the input images, and that the polarization state of the LG beam differs from that of the input beam.

  16. Goos-Hänchen and Imbert-Fedorov shifts for astigmatic Gaussian beams

    NASA Astrophysics Data System (ADS)

    Ornigotti, Marco; Aiello, Andrea

    2015-06-01

    In this work we investigate the role of the beam astigmatism in the Goos-Hänchen and Imbert-Fedorov shift. As a case study, we consider a Gaussian beam focused by an astigmatic lens and we calculate explicitly the corrections to the standard formulas for beam shifts due to the astigmatism induced by the lens. Our results show that the different focusing in the longitudinal and transverse direction introduced by an astigmatic lens may enhance the angular part of the shift.

  17. Propagation properties of hollow sinh-Gaussian beams in quadratic-index medium

    NASA Astrophysics Data System (ADS)

    Zou, Defeng; Li, Xiaohui; Pang, Xingxing; Zheng, Hairong; Ge, Yanqi

    2017-10-01

    Based on the Collins integral formula, the analytical expression for a hollow sinh-Gaussian (HsG) beam propagating through the quadratic-index medium is derived. The propagation properties of a single HsG beam and their interactions have been studied in detail with numerical examples. The results show that inhomogeneity can support self-repeating intensity distributions of HsG beams. With high-ordered beam order n, HsG beams could maintain their initial dark hollow distributions for a longer distance. In addition, interference fringes appear at the interactional region. The central intensity is a prominent peak for two in-phase beams, which is zero for two out-of phase beams. By tuning the initial beam phase shift, the distribution of the fringes can be controlled.

  18. Negative refraction and backward wave in pseudochiral mediums: illustrations of Gaussian beams.

    PubMed

    Chern, Ruey-Lin; Chang, Po-Han

    2013-02-11

    We investigate the phenomena of negative refraction and backward wave in pseudochiral mediums, with illustrations of Gaussian beams. Due to symmetry breaking intrinsic in pseudochiral mediums, there exist two elliptically polarized eigenwaves with different wave vectors. As the chirality parameter increases from zero, the two waves begin to split from each other. For a wave incident from vacuum onto a pseudochiral medium, negative refraction may occur for the right-handed wave, whereas backward wave may appear for the left-handed wave. These features are illustrated with Gaussian beams based on Fourier integral formulations for the incident, reflected, and transmitted waves. Negative refraction and backward wave are manifest, respectively, on the energy flow in space and wavefront movement in time.

  19. Generation of helical Ince-Gaussian beams with a liquid-crystal display.

    PubMed

    Bentley, Joel B; Davis, Jeffrey A; Bandres, Miguel A; Gutiérrez-Vega, Julio C

    2006-03-01

    We generate helical Ince-Gaussian (HIG) beams by using complex amplitude and phase masks encoded onto a liquid-crystal display (LCD). These beams display an intensity pattern consisting of elliptic rings, whose number and ellipticity can be controlled, and a phase exhibiting a number of in-line vortices, each with a unitary topological charge. We show experimental results that display the properties of these elliptic dark hollow beams. We introduce a novel interference technique for generating the object and reference beams by using a single LCD and show the vortex interference patterns. We expect that these HIG beams will be useful in optical trapping applications.

  20. Generation of helical Ince-Gaussian beams with a liquid-crystal display

    NASA Astrophysics Data System (ADS)

    Bentley, Joel B.; Davis, Jeffrey A.; Bandres, Miguel A.; Gutiérrez-Vega, Julio C.

    2006-03-01

    We generate helical Ince-Gaussian (HIG) beams by using complex amplitude and phase masks encoded onto a liquid-crystal display (LCD). These beams display an intensity pattern consisting of elliptic rings, whose number and ellipticity can be controlled, and a phase exhibiting a number of in-line vortices, each with a unitary topological charge. We show experimental results that display the properties of these elliptic dark hollow beams. We introduce a novel interference technique for generating the object and reference beams by using a single LCD and show the vortex interference patterns. We expect that these HIG beams will be useful in optical trapping applications.

  1. On focusing of a ring ripple on a Gaussian electromagnetic beam in a plasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Misra, Shikha; Mishra, S. K.

    In this communication the authors have investigated the focusing of a ring ripple on a Gaussian electromagnetic beam propagating in a plasma, considering each of the three kinds of basic nonlinearities, namely, ponderomotive, collisional, and relativistic. In this analysis, the electric field profile of the propagating beam is assumed to be composed of the radial electric field distribution of the Gaussian beam as well as that of the ring ripple; a paraxial like approach has been adopted to analyze the characteristics of the propagation. Thus, one considers a unique dielectric function for the beam propagation and a radial field sensitivemore » diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple. Further, the variation of the phase associated with the beam on account of the r independent terms in the eikonal has also been accounted for.« less

  2. Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

    PubMed

    Tang, Bin; Jiang, Chun; Zhu, Haibin

    2012-08-01

    Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.

  3. Fiber-coupling efficiency of Gaussian-Schell model beams through an ocean to fiber optical communication link

    NASA Astrophysics Data System (ADS)

    Hu, Beibei; Shi, Haifeng; Zhang, Yixin

    2018-06-01

    We theoretically study the fiber-coupling efficiency of Gaussian-Schell model beams propagating through oceanic turbulence. The expression of the fiber-coupling efficiency is derived based on the spatial power spectrum of oceanic turbulence and the cross-spectral density function. Our work shows that the salinity fluctuation has a greater impact on the fiber-coupling efficiency than temperature fluctuation does. We can select longer λ in the "ocean window" and higher spatial coherence of light source to improve the fiber-coupling efficiency of the communication link. We also can achieve the maximum fiber-coupling efficiency by choosing design parameter according specific oceanic turbulence condition. Our results are able to help the design of optical communication link for oceanic turbulence to fiber sensor.

  4. Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

    PubMed

    Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

    2006-06-01

    We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

  5. Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

    PubMed

    Mitri, Farid G

    2015-10-01

    Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

  6. Propagation of rotational Risley-prism-array-based Gaussian beams in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Chen, Feng; Ma, Haotong; Dong, Li; Ren, Ge; Qi, Bo; Tan, Yufeng

    2018-03-01

    Limited by the size and weight of prism and optical assembling, Rotational Risley-prism-array system is a simple but effective way to realize high power and superior beam quality of deflecting laser output. In this paper, the propagation of the rotational Risley-prism-array-based Gaussian beam array in atmospheric turbulence is studied in detail. An analytical expression for the average intensity distribution at the receiving plane is derived based on nonparaxial ray tracing method and extended Huygens-Fresnel principle. Power in the diffraction-limited bucket is chosen to evaluate beam quality. The effect of deviation angle, propagation distance and intensity of turbulence on beam quality is studied in detail by quantitative simulation. It reveals that with the propagation distance increasing, the intensity distribution gradually evolves from multiple-petal-like shape into the pattern that contains one main-lobe in the center with multiple side-lobes in weak turbulence. The beam quality of rotational Risley-prism-array-based Gaussian beam array with lower deviation angle is better than its counterpart with higher deviation angle when propagating in weak and medium turbulent (i.e. Cn2 < 10-13m-2/3), the beam quality of higher deviation angle arrays degrades faster as the intensity of turbulence gets stronger. In the case of propagating in strong turbulence, the long propagation distance (i.e. z > 10km ) and deviation angle have no influence on beam quality.

  7. The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

    NASA Astrophysics Data System (ADS)

    Luo, Yamei; Lü, Baida

    2009-06-01

    The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.

  8. Intra-Beam and Touschek Scattering Computations for Beam with Non-Gaussian Longitudinal Distributions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Xiao, A.; Borland, M.

    Both intra-beamscattering (IBS) and the Touschek effect become prominent formulti-bend-achromat- (MBA-) based ultra-low-emittance storage rings. To mitigate the transverse emittance degradation and obtain a reasonably long beam lifetime, a higher harmonic rf cavity (HHC) is often proposed to lengthen the bunch. The use of such a cavity results in a non-gaussian longitudinal distribution. However, common methods for computing IBS and Touschek scattering assume Gaussian distributions. Modifications have been made to several simulation codes that are part of the elegant [1] toolkit to allow these computations for arbitrary longitudinal distributions. After describing thesemodifications, we review the results of detailed simulations formore » the proposed hybrid seven-bend-achromat (H7BA) upgrade lattice [2] for the Advanced Photon Source.« less

  9. Effects of a modulated vortex structure on the diffraction dynamics of ring Airy Gaussian beams.

    PubMed

    Huang, Xianwei; Shi, Xiaohui; Deng, Zhixiang; Bai, Yanfeng; Fu, Xiquan

    2017-09-01

    The evolution of the ring Airy Gaussian beams with a modulated vortex in free space is numerically investigated. Compared with the unmodulated vortex, the unique property is that the beam spots first break up, and then gather. The evolution of the beams is influenced by the parameters of the vortex modulation, and the splitting phenomenon gets enhanced with multiple rings becoming light spots if the modulation depth increases. The symmetric branch pattern of the beam spots gets changed when the number of phase folds increases, and the initial modulation phase only impacts the angle of the beam spots. Moreover, a large distribution factor correlates to a hollow Gaussian vortex shape and weakens the splitting and gathering trend. By changing the initial parameters of the vortex modulation and the distribution factor, the peak intensity is greatly affected. In addition, the energy flow and the angular momentum are elucidated with the beam evolution features being confirmed.

  10. Implementation of a Gaussian Beam Laser and Aspheric Optics for High Spatial Resolution MALDI Imaging MS

    NASA Astrophysics Data System (ADS)

    Zavalin, Andre; Yang, Junhai; Haase, Andreas; Holle, Armin; Caprioli, Richard

    2014-06-01

    We have investigated the use of a Gaussian beam laser for MALDI Imaging Mass Spectrometry to provide a precisely defined laser spot of 5 μm diameter on target using a commercial MALDI TOF instrument originally designed to produce a 20 μm diameter laser beam spot at its smallest setting. A Gaussian beam laser was installed in the instrument in combination with an aspheric focusing lens. This ion source produced sharp ion images at 5 μm spatial resolution with signals of high intensity as shown for images from thin tissue sections of mouse brain.

  11. Implementation of a Gaussian beam laser and aspheric optics for high spatial resolution MALDI imaging MS.

    PubMed

    Zavalin, Andre; Yang, Junhai; Haase, Andreas; Holle, Armin; Caprioli, Richard

    2014-06-01

    We have investigated the use of a Gaussian beam laser for MALDI Imaging Mass Spectrometry to provide a precisely defined laser spot of 5 μm diameter on target using a commercial MALDI TOF instrument originally designed to produce a 20 μm diameter laser beam spot at its smallest setting. A Gaussian beam laser was installed in the instrument in combination with an aspheric focusing lens. This ion source produced sharp ion images at 5 μm spatial resolution with signals of high intensity as shown for images from thin tissue sections of mouse brain.

  12. Angle-domain common-image gathers from anisotropic Gaussian beam migration and its application to anisotropy-induced imaging errors analysis

    NASA Astrophysics Data System (ADS)

    Han, Jianguang; Wang, Yun; Yu, Changqing; Chen, Peng

    2017-02-01

    An approach for extracting angle-domain common-image gathers (ADCIGs) from anisotropic Gaussian beam prestack depth migration (GB-PSDM) is presented in this paper. The propagation angle is calculated in the process of migration using the real-value traveltime information of Gaussian beam. Based on the above, we further investigate the effects of anisotropy on GB-PSDM, where the corresponding ADCIGs are extracted to assess the quality of migration images. The test results of the VTI syncline model and the TTI thrust sheet model show that anisotropic parameters ɛ, δ, and tilt angle 𝜃, have a great influence on the accuracy of the migrated image in anisotropic media, and ignoring any one of them will cause obvious imaging errors. The anisotropic GB-PSDM with the true anisotropic parameters can obtain more accurate seismic images of subsurface structures in anisotropic media.

  13. SU-F-T-158: Experimental Characterization of Field Size Dependence of Dose and Lateral Beam Profiles of Scanning Proton and Carbon Ion Beams for Empirical Model in Air

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Li, Y; Hsi, W; Zhao, J

    2016-06-15

    Purpose: The Gaussian model for the lateral profiles in air is crucial for an accurate treatment planning system. The field size dependence of dose and the lateral beam profiles of scanning proton and carbon ion beams are due mainly to particles undergoing multiple Coulomb scattering in the beam line components and secondary particles produced by nuclear interactions in the target, both of which depend upon the energy and species of the beam. In this work, lateral profile shape parameters were fitted to measurements of field size dependence dose at the center of field size in air. Methods: Previous studies havemore » employed empirical fits to measured profile data to significantly reduce the QA time required for measurements. From this approach to derive the weight and sigma of lateral profiles in air, empirical model formulations were simulated for three selected energies for both proton and carbon beams. Results: The 20%–80% lateral penumbras predicted by the double model for proton and single model for carbon with the error functions agreed with the measurements within 1 mm. The standard deviation between measured and fitted field size dependence of dose for empirical model in air has a maximum accuracy of 0.74% for proton with double Gaussian, and of 0.57% for carbon with single Gaussian. Conclusion: We have demonstrated that the double Gaussian model of lateral beam profiles is significantly better than the single Gaussian model for proton while a single Gaussian model is sufficient for carbon. The empirical equation may be used to double check the separately obtained model that is currently used by the planning system. The empirical model in air for dose of spot scanning proton and carbon ion beams cannot be directly used for irregular shaped patient fields, but can be to provide reference values for clinical use and quality assurance.« less

  14. Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam.

    PubMed

    Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M

    2005-11-01

    The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.

  15. Displacements and evolution of optical vortices in edge-diffracted Laguerre-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Bekshaev, Aleksandr; Chernykh, Aleksey; Khoroshun, Anna; Mikhaylovskaya, Lidiya

    2017-05-01

    Based on the Kirchhoff-Fresnel approximation, we consider the behavior of optical vortices (OV) upon propagation of diffracted Laguerre-Gaussian (LG) beams with topological charge ∣m∣ = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), these OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of the incident OV beam, so that the input wavefront curvature is transformed into the output azimuthal OV rotation. The results are expected to be useful in OV metrology and OV beam diagnostics.

  16. Optimal focusing conditions of lenses using Gaussian beams

    DOE PAGES

    Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; ...

    2016-04-02

    By using the analytical equations of the propagation of Gaussian beams in which truncation exhibits negligible consequences, we describe a method that uses the value of the focal length of a focusing lens to classify its focusing performance. In this study, we show that for different distances between a laser and a focusing lens there are different planes where best focusing conditions can be obtained and we demonstrate how the value of the focal length impacts the lens focusing properties. To perform the classification we introduce the term delimiting focal length. As the value of the focal length used inmore » wave propagation theory is nominal and difficult to measure accurately, we describe an experimental approach to calculate its value matching our analytical description. Finally, we describe possible applications of the results for characterizing Gaussian sources, for measuring focal lengths and/or alternatively for characterizing piston-like movements.« less

  17. Measurements of refractive index and size of a spherical drop from Gaussian beam scattering in the primary rainbow region

    NASA Astrophysics Data System (ADS)

    Yu, Haitao; Sun, Hui; Shen, Jianqi; Tropea, Cameron

    2018-03-01

    The primary rainbow observed when light is scattered by a spherical drop has been exploited in the past to measure drop size and relative refractive index. However, if higher spatial resolution is required in denser drop ensembles/sprays, and to avoid then multiple drops simultaneously appearing in the measurement volume, a highly focused beam is desirable, inevitably with a Gaussian intensity profile. The present study examines the primary rainbow pattern resulting when a Gaussian beam is scattered by a spherical drop and estimates the attainable accuracy when extracting size and refractive index. The scattering is computed using generalized Lorenz-Mie theory (GLMT) and Debye series decomposition of the Gaussian beam scattering. The results of these simulations show that the measurement accuracy is dependent on both the beam waist radius and the position of the drop in the beam waist.

  18. Optical trapping forces of a focused azimuthally polarized Bessel-Gaussian beam on a double-layered sphere

    NASA Astrophysics Data System (ADS)

    Wu, F. P.; Zhang, B.; Liu, Z. L.; Tang, Y.; Zhang, N.

    2017-12-01

    We calculate the trapping forces exerted by a highly focused Bessel-Gaussian beam on a double-layered sphere by means of vector diffraction integral, T-matrix method and Maxwell stress tensor integral. The Bessel-Gaussian beam is azimuthally polarized. Numerical results predicate that the double-layered sphere with air core can be stably trapped in three-dimensions. The trapping forces and efficiencies are dependent on the refraction index and size of the inner core. The trapping efficiency can be optimized by choosing the refraction indices of the inner core and outer layer. Our computational method can be easily modified for other laser beams and particles with arbitrary geometries and multilayers.

  19. Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models

    NASA Astrophysics Data System (ADS)

    Wen, Xian-Huan; Gómez-Hernández, J. Jaime

    1998-03-01

    The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than

  20. Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

    NASA Astrophysics Data System (ADS)

    Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

    2018-05-01

    In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

  1. Gaussian-input Gaussian mixture model for representing density maps and atomic models.

    PubMed

    Kawabata, Takeshi

    2018-07-01

    A new Gaussian mixture model (GMM) has been developed for better representations of both atomic models and electron microscopy 3D density maps. The standard GMM algorithm employs an EM algorithm to determine the parameters. It accepted a set of 3D points with weights, corresponding to voxel or atomic centers. Although the standard algorithm worked reasonably well; however, it had three problems. First, it ignored the size (voxel width or atomic radius) of the input, and thus it could lead to a GMM with a smaller spread than the input. Second, the algorithm had a singularity problem, as it sometimes stopped the iterative procedure due to a Gaussian function with almost zero variance. Third, a map with a large number of voxels required a long computation time for conversion to a GMM. To solve these problems, we have introduced a Gaussian-input GMM algorithm, which considers the input atoms or voxels as a set of Gaussian functions. The standard EM algorithm of GMM was extended to optimize the new GMM. The new GMM has identical radius of gyration to the input, and does not suddenly stop due to the singularity problem. For fast computation, we have introduced a down-sampled Gaussian functions (DSG) by merging neighboring voxels into an anisotropic Gaussian function. It provides a GMM with thousands of Gaussian functions in a short computation time. We also have introduced a DSG-input GMM: the Gaussian-input GMM with the DSG as the input. This new algorithm is much faster than the standard algorithm. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

  2. Research into Influence of Gaussian Beam on Terahertz Radar Cross Section of a Semicircular Boss

    NASA Astrophysics Data System (ADS)

    Li, Hui-Yu; Li, Qi; She, Jian-Yu; Zhao, Yong-Peng; Chen, De-Ying; Wang, Qi

    2013-08-01

    In radar cross section (RCS) calculation of a rough surface, the model can be simplified into the scattering of geometrically idealized bosses on a surface. Thus the problem of the RCS calculation of a rough surface is changed to the RCS calculation of the semicircular boss. The RCS measurement of scale model can help save time and money. The utilization of terahertz in RCS is attractive because of its special properties: the wavelength of the terahertz wave can help limit the size of the model in a suitable range in the measurement of the scale model and get more detailed data in the measurement of the real object. However, usually the incident beam of a terahertz source is a Gaussian beam; in the theoretical RCS estimation, usually a plane wave is assumed as the incident beam for sake of simplicity which may lead to an error between the measurement and calculation results. In this paper, the method of images is used to calculate the RCS of a semicircular boss at 2.52 THz and the results are compared to the one calculated when the incident beam is a plane wave.

  3. Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

    PubMed

    Sun, Dong; Zhao, Daomu

    2005-08-01

    By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

  4. Gaussian representation of high-intensity focused ultrasound beams.

    PubMed

    Soneson, Joshua E; Myers, Matthew R

    2007-11-01

    A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.

  5. Orthogonal Gaussian process models

    DOE PAGES

    Plumlee, Matthew; Joseph, V. Roshan

    2017-01-01

    Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.

  6. Orthogonal Gaussian process models

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Plumlee, Matthew; Joseph, V. Roshan

    Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads to poor estimation of the coefficients in the mean model, and thus the estimated mean model loses interpretability. This paper introduces a new Gaussian process model whose stochastic part is orthogonal to the mean part to address this issue. As a result, this paper also discusses applications to multi-fidelity simulations using data examples.

  7. Beam wander and M2-factor of partially coherent electromagnetic hollow Gaussian beam propagating through non-Kolmogorov turbulence

    NASA Astrophysics Data System (ADS)

    Xu, Yonggen; Tian, Huanhuan; Dan, Youquan; Feng, Hao; Wang, Shijian

    2017-04-01

    Propagation formulae for M2-factor and beam wander of partially coherent electromagnetic hollow Gaussian (PCEHG) beam in non-Kolmogorov turbulence are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. Our results indicate that the normalized M2-factors of PCEHG beam with larger beam order, waist width, inner scale of turbulence, the generalized exponent parameter, and smaller transverse coherent widths, outer scale of turbulence, the generalized structure parameter are less affected by the turbulence. The root mean square beam wander and relative beam wander are more obvious for PCEHG beam with smaller beam order, larger inner and outer scales of turbulence, exponent parameter, transverse coherent widths, and the generalized structure parameter. What is more, the beam wander properties of PCEHG beam in non-Kolmogorov turbulence are very different from M2-factor and spreading properties of beam in turbulence.

  8. Orbital angular momentum mode of Gaussian beam induced by atmospheric turbulence

    NASA Astrophysics Data System (ADS)

    Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Yan, Xu; Dong, Kangjun

    2018-02-01

    Superposition theory of the spiral harmonics is employed to numerical study the transmission property of the orbital angular momentum (OAM) mode of Gaussian beam induced by atmospheric turbulence. Results show that Gauss beam does not carry OAM at the source, but various OAM modes appear after affected by atmospheric turbulence. With the increase of atmospheric turbulence strength, the smaller order OAM modes appear firstly, followed by larger order OAM modes. The beam spreading of Gauss beams in the atmosphere enhance with the increasing topological charge of the OAM modes caused by atmospheric turbulence. The mode probability density of the OAM generated by atmospheric turbulence decreases, and peak position gradually deviate from the Gauss beam spot center with the increase of the topological charge. Our results may be useful for improving the performance of long distance laser digital spiral imaging system.

  9. Electron Acceleration by Beating of Two Intense Cross-Focused Hollow Gaussian Laser Beams in Plasma

    NASA Astrophysics Data System (ADS)

    Mahmoud, Saleh T.; Gauniyal, Rakhi; Ahmad, Nafis; Rawat, Priyanka; Purohit, Gunjan

    2018-01-01

    This paper presents propagation of two cross-focused intense hollow Gaussian laser beams (HGBs) in collisionless plasma and its effect on the generation of electron plasma wave (EPW) and electron acceleration process, when relativistic and ponderomotive nonlinearities are simultaneously operative. Nonlinear differential equations have been set up for beamwidth of laser beams, power of generated EPW, and energy gain by electrons using WKB and paraxial approximations. Numerical simulations have been carried out to investigate the effect of typical laser-plasma parameters on the focusing of laser beams in plasmas and further its effect on power of excited EPW and acceleration of electrons. It is observed that focusing of two laser beams in plasma increases for higher order of hollow Gaussian beams, which significantly enhanced the power of generated EPW and energy gain. The amplitude of EPW and energy gain by electrons is found to enhance with an increase in the intensity of laser beams and plasma density. This study will be useful to plasma beat wave accelerator and in other applications requiring multiple laser beams. Supported by United Arab Emirates University for Financial under Grant No. UPAR (2014)-31S164

  10. Fresnel zone plate with apodized aperture for hard X-ray Gaussian beam optics.

    PubMed

    Takeuchi, Akihisa; Uesugi, Kentaro; Suzuki, Yoshio; Itabashi, Seiichi; Oda, Masatoshi

    2017-05-01

    Fresnel zone plates with apodized apertures [apodization FZPs (A-FZPs)] have been developed to realise Gaussian beam optics in the hard X-ray region. The designed zone depth of A-FZPs gradually decreases from the center to peripheral regions. Such a zone structure forms a Gaussian-like smooth-shouldered aperture function which optically behaves as an apodization filter and produces a Gaussian-like focusing spot profile. Optical properties of two types of A-FZP, i.e. a circular type and a one-dimensional type, have been evaluated by using a microbeam knife-edge scan test, and have been carefully compared with those of normal FZP optics. Advantages of using A-FZPs are introduced.

  11. Flat-top beam for laser-stimulated pain

    NASA Astrophysics Data System (ADS)

    McCaughey, Ryan; Nadeau, Valerie; Dickinson, Mark

    2005-04-01

    One of the main problems during laser stimulation in human pain research is the risk of tissue damage caused by excessive heating of the skin. This risk has been reduced by using a laser beam with a flattop (or superGaussian) intensity profile, instead of the conventional Gaussian beam. A finite difference approximation to the heat conduction equation has been applied to model the temperature distribution in skin as a result of irradiation by flattop and Gaussian profile CO2 laser beams. The model predicts that a 15 mm diameter, 15 W, 100 ms CO2 laser pulse with an order 6 superGaussian profile produces a maximum temperature 6 oC less than a Gaussian beam with the same energy density. A superGaussian profile was created by passing a Gaussian beam through a pair of zinc selenide aspheric lenses which refract the more intense central region of the beam towards the less intense periphery. The profiles of the lenses were determined by geometrical optics. In human pain trials the superGaussian beam required more power than the Gaussian beam to reach sensory and pain thresholds.

  12. Gaussian beam profile shaping apparatus, method therefor and evaluation thereof

    DOEpatents

    Dickey, Fred M.; Holswade, Scott C.; Romero, Louis A.

    1999-01-01

    A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system.

  13. Gaussian beam profile shaping apparatus, method therefore and evaluation thereof

    DOEpatents

    Dickey, F.M.; Holswade, S.C.; Romero, L.A.

    1999-01-26

    A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system. 27 figs.

  14. Effect of turbulent atmosphere on the on-axis average intensity of Pearcey-Gaussian beam

    NASA Astrophysics Data System (ADS)

    F, Boufalah; L, Dalil-Essakali; H, Nebdi; A, Belafhal

    2016-06-01

    The propagation characteristics of the Pearcey-Gaussian (PG) beam in turbulent atmosphere are investigated in this paper. The Pearcey beam is a new kind of paraxial beam, based on the Pearcey function of catastrophe theory, which describes diffraction about a cusp caustic. By using the extended Huygens-Fresnel integral formula in the paraxial approximation and the Rytov theory, an analytical expression of axial intensity for the considered beam family is derived. Some numerical results for PG beam propagating in atmospheric turbulence are given by studying the influences of some factors, including incident beam parameters and turbulence strengths.

  15. Three-photon Gaussian-Gaussian-Laguerre-Gaussian excitation of a localized atom to a highly excited Rydberg state

    NASA Astrophysics Data System (ADS)

    Mashhadi, L.

    2017-12-01

    Optical vortices are currently one of the most intensively studied topics in light-matter interaction. In this work, a three-step axial Doppler- and recoil-free Gaussian-Gaussian-Laguerre-Gaussian (GGLG) excitation of a localized atom to the highly excited Rydberg state is presented. By assuming a large detuning for intermediate states, an effective quadrupole excitation related to the Laguerre-Gaussian (LG) excitation to the highly excited Rydberg state is obtained. This special excitation system radially confines the single highly excited Rydberg atom independently of the trapping system into a sharp potential landscape into the so-called ‘far-off-resonance optical dipole-quadrupole trap’ (FORDQT). The key parameters of the Rydberg excitation to the highly excited state, namely the effective Rabi frequency and the effective detuning including a position-dependent AC Stark shift, are calculated in terms of the basic parameters of the LG beam and of the polarization of the excitation lasers. It is shown that the obtained parameters can be tuned to have a precise excitation of a single atom to the desired Rydberg state as well. The features of transferring the optical orbital and spin angular momentum of the polarized LG beam to the atom via quadrupole Rydberg excitation offer a long-lived and controllable qudit quantum memory. In addition, in contrast to the Gaussian laser beam, the doughnut-shaped LG beam makes it possible to use a high intensity laser beam to increase the signal-to-noise ratio in quadrupole excitation with minimized perturbations coming from stray light broadening in the last Rydberg excitation process.

  16. Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

    PubMed

    Hirayama, Shusuke; Takayanagi, Taisuke; Fujii, Yusuke; Fujimoto, Rintaro; Fujitaka, Shinichiro; Umezawa, Masumi; Nagamine, Yoshihiko; Hosaka, Masahiro; Yasui, Keisuke; Omachi, Chihiro; Toshito, Toshiyuki

    2016-03-01

    The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. The authors investigated the difference

  17. Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams.

    PubMed

    Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis

    2013-02-01

    Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

  18. A Gaussian framework for modeling effects of frequency-dependent attenuation, frequency-dependent scattering, and gating.

    PubMed

    Wear, Keith A

    2002-11-01

    For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.

  19. Optical levitation of absorbing particles with a nominally Gaussian laser beam.

    PubMed

    Huisken, Jan; Stelzer, Ernst H K

    2002-07-15

    We use a Gaussian laser beam to study the levitation of absorbing Mie particles. Several metal oxide particles are stably levitated, and their movement over time is recorded. Our studies show that the position of each particle is highly dependent on the other particles' locations. The observations are explained by the phenomenon of thermal creep. The increased local pressure that is due to a temperature gradient along the particle's surface induces levitation. The particles rest close to minima in the intensity distribution near the optical axis. An experiment is suggested that can be used to locate these minima in a laser beam.

  20. Three-dimensional propagation and absorption of high frequency Gaussian beams in magnetoactive plasmas

    NASA Astrophysics Data System (ADS)

    Nowak, S.; Orefice, A.

    1994-05-01

    In today's high frequency systems employed for plasma diagnostics, power heating, and current drive the behavior of the wave beams is appreciably affected by the self-diffraction phenomena due to their narrow collimation. In the present article the three-dimensional propagation of Gaussian beams in inhomogeneous and anisotropic media is analyzed, starting from a properly formulated dispersion relation. Particular attention is paid, in the case of electromagnetic electron cyclotron (EC) waves, to the toroidal geometry characterizing tokamak plasmas, to the power density evolution on the advancing wave fronts, and to the absorption features occurring when a beam crosses an EC resonant layer.

  1. Tunable magic wavelengths for trapping with focused Laguerre-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Bhowmik, Anal; Dutta, Narendra Nath; Majumder, Sonjoy

    2018-02-01

    We present in this paper a theory of dynamic polarizability for an atomic state due to an external field of nonparaxial Laguerre-Gaussian (LG) beam using the sum-over-states technique. A highly correlated relativistic coupled-cluster theory is used to evaluate the most important and correlation-sensitive parts of the sum. The theory is applied on Sr+ to determine the magic wavelengths for 5 s1 /2→4 d3 /2,4 d5 /2 transitions. Results show the variation of magic wavelengths with the choice of orbital and spin angular momenta of the incident LG beam. Also, the tunability of the magic wavelengths is studied by using the focusing angle of the LG beam and its efficiency in the near-infrared region is observed. Evaluations of the wide spectrum of magic wavelengths from infrared to ultraviolet have substantial importance to experimentalists for carrying out high-precision measurements in fundamental physics. These magic wavelengths can be used to confine the atom or ion at the dark central node or at the high-intensity ring of the LG beam.

  2. Generation of tunable chain of three-dimensional optical bottle beams via focused multi-ring hollow Gaussian beam.

    PubMed

    Philip, Geo M; Viswanathan, Nirmal K

    2010-11-01

    We report here the generation of a chain of three-dimensional (3-D) optical bottle beams by focusing a π-phase shifted multi-ring hollow Gaussian beam (HGB) using a lens with spherical aberration. The rings of the HGB of suitable radial (k(r)) and axial (k(z)) wave vectors are generated using a double-negative axicon chemically etched in the optical fiber tips. Moving the lens position with respect to the fiber tip results in variation of the semi-angle of the cones of wave vectors of the HGBs and their diameter, using which we demonstrate tunability in the size and the periodicity of the 3-D optical bottle beams over a wide range, from micrometers to millimeters. The propagation characteristics of the beams resulting from focusing of single- and multi-ring HGBs and resulting in a quasi-non-diffracting beam and a chain of 3-D optical bottle beams, respectively, are simulated using only the input beam parameters and are found to agree well with experimental results.

  3. Focusing of a dark hollow Gaussian electromagnetic beam in a magnetoplasma

    NASA Astrophysics Data System (ADS)

    Sodha, Mahendra Singh; Mishra, S. K.; Misra, Shikha

    2009-12-01

    This paper presents an analysis and subsequent discussion of the self focusing of a dark hollow Gaussian electromagnetic beam (HGB) in a magnetoplasma, considering ponderomotive and collisional nonlinearities. A paraxial-like approach, in which the relevant parameters are expanded in terms of radial distance from the maximum of the irradiance rather than that from the axis, has been adopted to analyze the propagation of the HGB. The nature of self focusing is highlighted through the critical curves as a plot of dimensionless radius versus power of the beam. The effect of the magnetic field and the nature of the nonlinearity on self focusing of various order HGBs has also been explored.

  4. Average intensity and spreading of an astigmatic sinh-Gaussian beam with small beam width propagating in atmospheric turbulence

    NASA Astrophysics Data System (ADS)

    Zhu, Jie; Zhu, Kaicheng; Tang, Huiqin; Xia, Hui

    2017-10-01

    Propagation properties of astigmatic sinh-Gaussian beams (ShGBs) with small beam width in turbulent atmosphere are investigated. Based on the extended Huygens-Fresnel integral, analytical formulae for the average intensity and the effective beam size of an astigmatic ShGB are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of an astigmatic ShGB propagating in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of atmospheric turbulence on the propagation properties of astigmatic ShGBs are also discussed in detail. In particular, for sufficiently small beam width and sinh-part parameter as well as suitable astigmatism, we show that the average intensity pattern converts into a perfect dark-hollow profile from initial two-petal pattern when ShGBs with astigmatic aberration propagate through atmospheric turbulence.

  5. Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

    NASA Astrophysics Data System (ADS)

    Kiselev, A. P.

    2017-12-01

    An exact solution of the Helmholtz equation u xx + u yy + u zz + k 2 u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

  6. Evolution of coherence singularities of Schell-model beams.

    PubMed

    Rodrigo, José A; Alieva, Tatiana

    2015-08-01

    We show that the propagation of the widely used Schell-model partially coherent light can be easily understood using the ambiguity function. This approach is especially beneficial for the analysis of the mutual intensity of Schell-model beams (SMBs), which are associated with stable coherent beams such as Laguerre-, Hermite-, and Ince-Gaussian. We study the evolution of the coherence singularities during the SMB propagation. It is demonstrated that the distance of singularity formation depends on the coherence degree of the input beam. Moreover, it is proved that the shape, position, and number of singularity curves in far field are defined by the associated coherent beam.

  7. Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links.

    PubMed

    Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P J; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J; Ashrafi, Solyman; Molisch, Andreas F; Tur, Moshe; Willner, Alan E

    2016-03-01

    We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.

  8. Morphologies of femtosecond laser ablation of ITO thin films using gaussian or quasi-flat top beams for OLED repair

    NASA Astrophysics Data System (ADS)

    Kim, Hoon-Young; Choi, Won-Suk; Ji, Suk-Young; Shin, Young-Gwan; Jeon, Jin-Woo; Ahn, Sanghoon; Cho, Sung-Hak

    2018-02-01

    This study compares the ablation morphologies obtained with a femtosecond laser of both Gaussian and quasi-flat top beam profiles when applied to indium tin oxide (ITO) thin films for the purpose of OLED repair. A femtosecond laser system with a wavelength of 1030 nm and pulse duration of 190 fs is used to pattern an ITO thin film. The laser fluence is optimized for patterning at 1.38 J/cm2. The patterned ITO thin film is then evaluated through both optical microscope and atomic force microscope. Ablations with a square quasi-flat top beam are demonstrated using slits with varying x- y axes. With the Gaussian beam, the pattern width of the ablated area is shown to range from 9.17 to 9.99 μm when the number of irradiation pulse increases from one to six. In contrast, when slit control is used to obtain a quasi-flat top beam, the ablated pattern width remains constant at 10 μm, despite the increase in the number of pulse. The improved surface roughness is correlated with the quasi-flat top beam through measured Ra values. Furthermore, when using the Gaussian beam, the minimum resolution of the controllable ablation depth on the ITO thin film is found to be 60 nm. In contrast, when the quasi-flat top beam is used, the minimum ablation depth decreases to 40 nm.

  9. Effect of width of incident Gaussian beam on the longitudinal shifts and distortion in the reflected beam

    NASA Astrophysics Data System (ADS)

    Ziauddin; Qamar, Sajid

    2014-05-01

    Control of the longitudinal shifts, i.e., spatial and angular Goos-Hänchen (GH) shifts, is revisited to study the effect of width of incident Gaussian beam on the shifts and distortion in the reflected beam. The beam is incident on a cavity consisted of atomic medium where each four-level atom follows N-type atom-field configuration. The atom-field interaction leads to Raman gain process which has been used earlier to observe a significant enhancement of the negative group index, i.e., in the range -103 to -104 for 23Na condensate [G.S. Agarwal, S. Dasgupta, Phys. Rev. A 70 (2004) 023802]. The negative and positive longitudinal shifts could be observed in the reflected light corresponding to the anomalous and normal dispersions of the intracavity medium, respectively. It is observed that the shifts are relatively large for small range of beam width and these became small for large width of the incident beam. It is also noticed that the magnitudes of spatial and angular GH shifts behave differently when the beam width increases. Further, distortion in the reflected beam decreases with an increase in beam width.

  10. Axial acoustic radiation force on a sphere in Gaussian field

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wu, Rongrong; Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Gong, Xiufen

    2015-10-28

    Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated.more » Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.« less

  11. Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

    NASA Astrophysics Data System (ADS)

    Wang, Wei; Shen, Jianqi

    2018-06-01

    The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

  12. Backscattering enhancement factor dependence of a Laguerre-Gaussian laser beam propagating on the location path in the atmosphere on optical turbulence intensity

    NASA Astrophysics Data System (ADS)

    Rytchkov, D. S.

    2017-11-01

    The paper presents the results of a study of the backscattering enhancement factor (BSE) dependence of vortex LaguerreGaussian beams propagating on monostatic location paths in the atmosphere on optical turbulence intensity. The numeric simulation split-step method of laser beam propagation was used to obtain BSE factor values of a laser beam propagated on monostatic location path in the turbulent atmosphere and reflected from a diffuse target. It is shown that BSE factor of the averaged intensity of a backscattered vortex laser beam of any topological charge is less than BSE factor values of backscattered Gaussian beam in arbitrary turbulent conditions.

  13. Direction-dependent waist-shift-difference of Gaussian beam in a multiple-pass zigzag slab amplifier and geometrical optics compensation method.

    PubMed

    Li, Zhaoyang; Kurita, Takashi; Miyanaga, Noriaki

    2017-10-20

    Zigzag and non-zigzag beam waist shifts in a multiple-pass zigzag slab amplifier are investigated based on the propagation of a Gaussian beam. Different incident angles in the zigzag and non-zigzag planes would introduce a direction-dependent waist-shift-difference, which distorts the beam quality in both the near- and far-fields. The theoretical model and analytical expressions of this phenomenon are presented, and intensity distributions in the two orthogonal planes are simulated and compared. A geometrical optics compensation method by a beam with 90° rotation is proposed, which not only could correct the direction-dependent waist-shift-difference but also possibly average the traditional thermally induced wavefront-distortion-difference between the horizontal and vertical beam directions.

  14. Transformations of Gaussian Light Beams Caused by Reflection in FEL (free Electron Lasers) Resonators

    DTIC Science & Technology

    1988-10-27

    il FILE COPy Naval Research Laboratory Washingon, DC 20375-500 NRL Memorandum Report 6347 ,qJ. o Transformations of Gaussian Light Beams N Caused by...Transformations of 7aussian Light Beams Caused by Reflection in FEL Resonators 12 PERSONAL AUTHOR(S) Riyopoulos,* S., Tang, C.M. and Sprangle, P...34 𔃾-6603 -"I, -,’ SECURITY CLASSIFICATION OF THIS PAGE 19. ABSTRACTS (Continued) cross-coupling among vector components of the radiation field, caused

  15. Optical apparatus for conversion of whispering-gallery modes into a free space gaussian like beam

    DOEpatents

    Stallard, Barry W.; Makowski, Michael A.; Byers, Jack A.

    1992-01-01

    An optical converter for efficient conversion of millimeter wavelength whispering-gallery gyrotron output into a linearly polarized, free-space Gaussian-like beam. The converter uses a mode-converting taper and three mirror optics. The first mirror has an azimuthal tilt to eliminate the k.sub..phi. component of the propagation vector of the gyrotron output beam. The second mirror has a twist reflector to linearly polarize the beam. The third mirror has a constant phase surface so the converter output is in phase.

  16. Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence

    NASA Astrophysics Data System (ADS)

    Gökçe, Muhsin Caner; Baykal, Yahya

    2018-03-01

    In an underwater wireless optical communication (UWOC) link, power fluctuations over finite-sized collecting lens are investigated for a horizontally propagating Gaussian beam wave. The power scintillation index, also known as the irradiance flux variance, for the received irradiance is evaluated in weak oceanic turbulence by using the Rytov method. This lets us further quantify the associated performance indicators, namely, the aperture averaging factor and the average bit-error rate (). The effects on the UWOC link performance of the oceanic turbulence parameters, i.e., the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, Kolmogorov microscale, the ratio of temperature to salinity contributions to the refractive index spectrum as well as system parameters, i.e., the receiver aperture diameter, Gaussian source size, laser wavelength and the link distance are investigated.

  17. Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links

    PubMed Central

    Ahmed, Nisar; Zhao, Zhe; Li, Long; Huang, Hao; Lavery, Martin P. J.; Liao, Peicheng; Yan, Yan; Wang, Zhe; Xie, Guodong; Ren, Yongxiong; Almaiman, Ahmed; Willner, Asher J.; Ashrafi, Solyman; Molisch, Andreas F.; Tur, Moshe; Willner, Alan E.

    2016-01-01

    We experimentally investigate the potential of using ‘self-healing’ Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively. PMID:26926068

  18. Polarization singularity indices in Gaussian laser beams

    NASA Astrophysics Data System (ADS)

    Freund, Isaac

    2002-01-01

    Two types of point singularities in the polarization of a paraxial Gaussian laser beam are discussed in detail. V-points, which are vector point singularities where the direction of the electric vector of a linearly polarized field becomes undefined, and C-points, which are elliptic point singularities where the ellipse orientations of elliptically polarized fields become undefined. Conventionally, V-points are characterized by the conserved integer valued Poincaré-Hopf index η, with generic value η=±1, while C-points are characterized by the conserved half-integer singularity index IC, with generic value IC=±1/2. Simple algorithms are given for generating V-points with arbitrary positive or negative integer indices, including zero, at arbitrary locations, and C-points with arbitrary positive or negative half-integer or integer indices, including zero, at arbitrary locations. Algorithms are also given for generating continuous lines of these singularities in the plane, V-lines and C-lines. V-points and C-points may be transformed one into another. A topological index based on directly measurable Stokes parameters is used to discuss this transformation. The evolution under propagation of V-points and C-points initially embedded in the beam waist is studied, as is the evolution of V-dipoles and C-dipoles.

  19. Uniform versus Gaussian Beams: A Comparison of the Effects of Diffraction, Obscuration, and Aberations.

    DTIC Science & Technology

    1985-12-16

    balancing is discussed for the two types of beams. Zernike polynomials representing balanced primary aberration for uniform and Gaussian annular beams...plotted on a logarithmic scale (Figs. 3c and 3d ). The positions of maxima and minima and the correspond- ing irradiance and encircled-power values are...aberration 2 4 (representing a term in the expansion of the aberration in terms of a set of " Zernike " polynomials which are orthonormal over the amplitude

  20. NGMIX: Gaussian mixture models for 2D images

    NASA Astrophysics Data System (ADS)

    Sheldon, Erin

    2015-08-01

    NGMIX implements Gaussian mixture models for 2D images. Both the PSF profile and the galaxy are modeled using mixtures of Gaussians. Convolutions are thus performed analytically, resulting in fast model generation as compared to methods that perform the convolution in Fourier space. For the galaxy model, NGMIX supports exponential disks and de Vaucouleurs and Sérsic profiles; these are implemented approximately as a sum of Gaussians using the fits from Hogg & Lang (2013). Additionally, any number of Gaussians can be fit, either completely free or constrained to be cocentric and co-elliptical.

  1. SU-D-BRC-01: An Automatic Beam Model Commissioning Method for Monte Carlo Simulations in Pencil-Beam Scanning Proton Therapy

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Qin, N; Shen, C; Tian, Z

    Purpose: Monte Carlo (MC) simulation is typically regarded as the most accurate dose calculation method for proton therapy. Yet for real clinical cases, the overall accuracy also depends on that of the MC beam model. Commissioning a beam model to faithfully represent a real beam requires finely tuning a set of model parameters, which could be tedious given the large number of pencil beams to commmission. This abstract reports an automatic beam-model commissioning method for pencil-beam scanning proton therapy via an optimization approach. Methods: We modeled a real pencil beam with energy and spatial spread following Gaussian distributions. Mean energy,more » and energy and spatial spread are model parameters. To commission against a real beam, we first performed MC simulations to calculate dose distributions of a set of ideal (monoenergetic, zero-size) pencil beams. Dose distribution for a real pencil beam is hence linear superposition of doses for those ideal pencil beams with weights in the Gaussian form. We formulated the commissioning task as an optimization problem, such that the calculated central axis depth dose and lateral profiles at several depths match corresponding measurements. An iterative algorithm combining conjugate gradient method and parameter fitting was employed to solve the optimization problem. We validated our method in simulation studies. Results: We calculated dose distributions for three real pencil beams with nominal energies 83, 147 and 199 MeV using realistic beam parameters. These data were regarded as measurements and used for commission. After commissioning, average difference in energy and beam spread between determined values and ground truth were 4.6% and 0.2%. With the commissioned model, we recomputed dose. Mean dose differences from measurements were 0.64%, 0.20% and 0.25%. Conclusion: The developed automatic MC beam-model commissioning method for pencil-beam scanning proton therapy can determine beam model parameters with

  2. Electron acceleration by a tightly focused Hermite-Gaussian beam: higher-order corrections

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhao Zhiguo; Institute of Laser Physics and Chemistry, Sichuan University, Chengdu 610064; Yang Dangxiao

    2008-03-15

    Taking the TEM{sub 1,0}-mode Hermite-Gaussian (H-G) beam as a numerical calculation example, and based on the method of the perturbation series expansion, the higher-order field corrections of H-G beams are derived and used to study the electron acceleration by a tightly focused H-G beam in vacuum. For the case of the off-axis injection the field corrections to the terms of order f{sup 3} (f=1/kw{sub 0}, k and w{sub 0} being the wavenumber and waist width, respectively) are considered, and for the case of the on-axis injection the contributions of the terms of higher orders are negligible. By a suitable optimizationmore » of injection parameters the energy gain in the giga-electron-volt regime can be achieved.« less

  3. Subwavelength dark hollow focus of spirally polarized axisymmetric Bessel-modulated Gaussian beam

    NASA Astrophysics Data System (ADS)

    Gao, X. M.; Zhan, Q. F.; Wang, Q.; Yun, M. J.; Guo, H. M.; Zhuang, S. L.

    2011-09-01

    Dark hollow focus plays an important role in many optical systems. In this paper, dark hollow focal shaping of spirally polarized axisymmetric Bessel-modulated Gaussian beam is investigated by vector diffraction theory in detail. Results show that the dark hollow focus can be altered considerably by beam parameter and spiral parameter that indicates polarization spiral degree. One dark hollow focus and two dark hollow foci pattern may occur for certain spiral parameter, and the transverse size of dark hollow focus can be less than the diffraction limit size of bright focus. In addition, there may also appear two triangle dark hollow foci that are connected by one dark line focus.

  4. Energy, momentum and propagation of non-paraxial high-order Gaussian beams in the presence of an aperture

    NASA Astrophysics Data System (ADS)

    Stilgoe, Alexander B.; Nieminen, Timo A.; Rubinsztein-Dunlop, Halina

    2015-12-01

    Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre-, Hermite- and Ince-Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light-matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter.

  5. Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.

    PubMed

    Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R

    2013-11-01

    A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.

  6. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate.

    PubMed

    Kotlyar, Victor V; Almazov, Anton A; Khonina, Svetlana N; Soifer, Victor A; Elfstrom, Henna; Turunen, Jari

    2005-05-01

    We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

  7. Acoustic Radiation Force of a Quasi-Gaussian Beam on an Elastic Sphere in a Fluid.

    PubMed

    Nikolaeva, A V; Sapozhnikov, O A; Bailey, M R

    2016-09-01

    Acoustic radiation force has many applications. One of the related technologies is the ability to noninvasively expel stones from the kidney. To optimize the procedure it is important to develop theoretical approaches that can provide rapid calculations of the radiation force depending in stone size and elastic properties, together with ultrasound beam diameter, intensity, and frequency. We hypothesize that the radiation force nonmonotonically depends on the ratio between the acoustic beam width and stone diameter because of coupling between the acoustic wave in the fluid and shear waves in the stone. Testing this hypothesis by considering a spherical stone and a quasi-Gaussian beam was performed in the current work. The calculation of the radiation force was conducted for elastic spheres of two types. Dependence of the magnitude of the radiation force on the beam diameter at various fixed values of stone diameters was modeled. In addition to using real material properties, speed of shear wave in the stone was varied to reveal the importance of shear waves in the stone. It was found that the radiation force reaches its maximum at the beamwidth comparable to the stone diameter; the gain in the force magnitude can reach 40% in comparison with the case of a narrow beam.

  8. Gaussian Finite Element Method for Description of Underwater Sound Diffraction

    NASA Astrophysics Data System (ADS)

    Huang, Dehua

    A new method for solving diffraction problems is presented in this dissertation. It is based on the use of Gaussian diffraction theory. The Rayleigh integral is used to prove the core of Gaussian theory: the diffraction field of a Gaussian is described by a Gaussian function. The parabolic approximation used by previous authors is not necessary to this proof. Comparison of the Gaussian beam expansion and Fourier series expansion reveals that the Gaussian expansion is a more general and more powerful technique. The method combines the Gaussian beam superposition technique (Wen and Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)) and the Finite element solution to the parabolic equation (Huang, J. Acoust. Soc. Am. 84, 1405-1413 (1988)). Computer modeling shows that the new method is capable of solving for the sound field even in an inhomogeneous medium, whether the source is a Gaussian source or a distributed source. It can be used for horizontally layered interfaces or irregular interfaces. Calculated results are compared with experimental results by use of a recently designed and improved Gaussian transducer in a laboratory water tank. In addition, the power of the Gaussian Finite element method is demonstrated by comparing numerical results with experimental results from use of a piston transducer in a water tank.

  9. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

    PubMed

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu

    2006-07-10

    The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

  10. 1D array of dark spot traps formed by counter-propagating nested Gaussian laser beams for trapping and moving atomic qubits

    NASA Astrophysics Data System (ADS)

    Gillen-Christandl, Katharina; Frazer, Travis D.

    2017-04-01

    The standing wave of two identical counter-propagating Gaussian laser beams constitutes a 1D array of bright spots that can serve as traps for single neutral atoms for quantum information operations. Detuning the frequency of one of the beams causes the array to start moving, effectively forming a conveyor belt for the qubits. Using a pair of nested Gaussian laser beams with different beam waists, however, forms a standing wave with a 1D array of dark spot traps confined in all dimensions. We have computationally explored the trap properties and limitations of this configuration and, trading off trap depth and frequencies with the number of traps and trap photon scattering rates, we determined the laser powers and beam waists needed for useful 1D arrays of dark spot traps for trapping and transporting atomic qubits in neutral atom quantum computing platforms.

  11. Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

    PubMed

    Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

    2016-02-01

    A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

  12. Sensitivity of a three-mirror cavity to thermal and nonlinear lensing: Gaussian-beam analysis.

    PubMed

    Anctil, G; McCarthy, N; Piché, M

    2000-12-20

    We consider a compact three-mirror cavity consisting of a flat output coupler, a curved folding mirror, and an active medium with one facet cut at the Brewster angle and the other facet coated for unit reflectivity. We examine the sensitivity to thermal lensing and to self-focusing in the active medium of the Gaussian beam that is circulating in that cavity. We use a simple thin-lens model; the astigmatism of the beam that is circulating in the cavity and the nonlinear coupling between the field distributions along the two orthogonal axes are taken into account. We find configurations in which beam ellipticity is compensated for at either end of the cavity in the presence of thermal lensing. We have derived an analytical criterion that predicts the sensitivity of the beam size to nonlinear lensing. The ability of the cavity to favor self-mode locking is found to be sensitive to the strength of thermal lensing. In the absence of thermal lensing, cavities operated as telescopic systems (C = 0) or self-imaging systems (B = 0) are most appropriate for achieving self-mode locking, with nonlinear mode selection accomplished through saturation of the spatially varying laser gain. We identify conditions for which self-mode locking can be produced by variable-reflectivity output couplers with either maximum or minimum reflectivity at the center of the coupler. We use our model to estimate the nonlinear gain produced in laser cavities equipped with such output couplers. We identify a cavity configuration for which nonlinear lensing can simultaneously produce mode locking and correction of beam ellipticity at the output coupler.

  13. Sensitivity of a Three-Mirror Cavity to Thermal and Nonlinear Lensing: Gaussian-Beam Analysis

    NASA Astrophysics Data System (ADS)

    Anctil, Geneviève; McCarthy, Nathalie; Piché, Michel

    2000-12-01

    We consider a compact three-mirror cavity consisting of a flat output coupler, a curved folding mirror, and an active medium with one facet cut at the Brewster angle and the other facet coated for unit reflectivity. We examine the sensitivity to thermal lensing and to self-focusing in the active medium of the Gaussian beam that is circulating in that cavity. We use a simple thin-lens model; the astigmatism of the beam that is circulating in the cavity and the nonlinear coupling between the field distributions along the two orthogonal axes are taken into account. We find configurations in which beam ellipticity is compensated for at either end of the cavity in the presence of thermal lensing. We have derived an analytical criterion that predicts the sensitivity of the beam size to nonlinear lensing. The ability of the cavity to favor self-mode locking is found to be sensitive to the strength of thermal lensing. In the absence of thermal lensing, cavities operated as telescopic systems ( C 0 ) or self-imaging systems ( B 0 ) are most appropriate for achieving self-mode locking, with nonlinear mode selection accomplished through saturation of the spatially varying laser gain. We identify conditions for which self-mode locking can be produced by variable-reflectivity output couplers with either maximum or minimum reflectivity at the center of the coupler. We use our model to estimate the nonlinear gain produced in laser cavities equipped with such output couplers. We identify a cavity configuration for which nonlinear lensing can simultaneously produce mode locking and correction of beam ellipticity at the output coupler.

  14. Terahertz radiation generation through the nonlinear interaction of Hermite and Laguerre Gaussian laser beams with collisional plasma: Field profile optimization

    NASA Astrophysics Data System (ADS)

    Safari, Samaneh; Niknam, Ali Reza; Jahangiri, Fazel; Jazi, Bahram

    2018-04-01

    The nonlinear interaction of Hermite-Gaussian and Laguerre-Gaussian (LG) laser beams with a collisional inhomogeneous plasma is studied, and the amplitude of the emitted terahertz (THz) electric field is evaluated. The effects of laser beams and plasma parameters, including the beams width, LG modes, the plasma collision frequency, and the amplitude of density ripple on the evolution of THz electric field amplitude, are examined. It is found that the shape of the generated THz radiation pattern can be tuned by the laser parameters. In addition, the optimum values of the effective parameters for achieving the maximum THz electric field amplitude are proposed. It is shown that a significant enhancement up to 4.5% can be obtained in our scheme, which is much greater than the maximum efficiency obtained for laser beams with the same profiles.

  15. Connections between Graphical Gaussian Models and Factor Analysis

    ERIC Educational Resources Information Center

    Salgueiro, M. Fatima; Smith, Peter W. F.; McDonald, John W.

    2010-01-01

    Connections between graphical Gaussian models and classical single-factor models are obtained by parameterizing the single-factor model as a graphical Gaussian model. Models are represented by independence graphs, and associations between each manifest variable and the latent factor are measured by factor partial correlations. Power calculations…

  16. Optical apparatus for conversion of whispering-gallery modes into a free space gaussian like beam

    DOEpatents

    Stallard, B.W.; Makowski, M.A.; Byers, J.A.

    1992-05-19

    An optical converter for efficient conversion of millimeter wavelength whispering-gallery gyrotron output into a linearly polarized, free-space Gaussian-like beam is described. The converter uses a mode-converting taper and three mirror optics. The first mirror has an azimuthal tilt to eliminate the k[sub [phi

  17. Gaussian Mixture Model of Heart Rate Variability

    PubMed Central

    Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

    2012-01-01

    Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386

  18. A Simple Model for Nonlinear Confocal Ultrasonic Beams

    NASA Astrophysics Data System (ADS)

    Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

    2007-01-01

    A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

  19. Coherent superposition of propagation-invariant laser beams

    NASA Astrophysics Data System (ADS)

    Soskind, R.; Soskind, M.; Soskind, Y. G.

    2012-10-01

    The coherent superposition of propagation-invariant laser beams represents an important beam-shaping technique, and results in new beam shapes which retain the unique property of propagation invariance. Propagation-invariant laser beam shapes depend on the order of the propagating beam, and include Hermite-Gaussian and Laguerre-Gaussian beams, as well as the recently introduced Ince-Gaussian beams which additionally depend on the beam ellipticity parameter. While the superposition of Hermite-Gaussian and Laguerre-Gaussian beams has been discussed in the past, the coherent superposition of Ince-Gaussian laser beams has not received significant attention in literature. In this paper, we present the formation of propagation-invariant laser beams based on the coherent superposition of Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian beams of different orders. We also show the resulting field distributions of the superimposed Ince-Gaussian laser beams as a function of the ellipticity parameter. By changing the beam ellipticity parameter, we compare the various shapes of the superimposed propagation-invariant laser beams transitioning from Laguerre-Gaussian beams at one ellipticity extreme to Hermite-Gaussian beams at the other extreme.

  20. Gaussian broad-beam excimer laser: clinical and experimental results.

    PubMed

    Schraepen, P; Eskina, E; Gobin, L; Trau, R; Timmermans, J; Tassignon, M J

    2005-01-01

    To evaluate the mid-term (1-3 years) results of the Gaussian broad-beam excimer laser Delivery System (DS) after single treatment for the correction of myopia. To study the corneal surface with scanning electron microscopy (SEM) after excimer laser ablation using a flying spot delivery system (Bausch & Lomb) and a Gaussian Delivery System (GDS) (InPro). The 1035 consecutive eyes studied were split in four groups with respect to the treated myopia, expressed in spherical equivalent: low myopia up to -3.00 D (183 eyes), moderate myopia from -3.25 D to -6.00 D (540 eyes), high myopia from -6.25 D to -10.00 D (210 eyes) and very high myopia from -10.25 D to -20.00 D (102 eyes). Four post-mortem eyes of two donors were treated using the flying spot DS on one eye and the GDS on the other eye. We achieved postoperative spheriqual equivalent within +/- 1 D of emmetropia in respectively 99.1%, 98.9%, 83% and 21% of the eyes of group 1, 2, 3 and 4. UCVA was 10/10 or better in respectively 65%, 51% and 19% of group 1, 2 and 3. UCVA was 5/10 or better in respectively 86% and 75% of group 3 and 4. The defocus equivalent refraction was 1.0 or less in respectively 98%, 93%, 62%, and 7% of the four groups. On SEM, the corneal surface presented a smooth and polished profile for the GDS. The Gaussian Delivery System gives comparable results to the flying spot laser system for surface laser ablation in myopic eyes up to -10 D. Advantages of this system are: smooth ablation surface, short treatment time, low haze rate, high reliability and easy maintenance of the device due to the optical DS. It is an interesting alternative for the more complex mechanical DS.

  1. Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction

    NASA Astrophysics Data System (ADS)

    Masoume, Mansouri; Mohsen, Askarbioki; Saeed Ghavami, Sabouri; Alireza, Khorsandi

    2015-02-01

    To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO4 and type I β-BaB2O4 optical crystals, and the Gaussian output beam of a Q-switched Nd:YAG laser, a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness. By rotating the plate up to 35° along the beam direction, we reduced the walk-off angle up to ˜ 13%. The same phenomenon is predicted by the model, confirming the performance of the model. It is found that, due to the walk-off effect, the intensity profile of the third-harmonic generation beam is slightly degraded. To compensate for the observed phenomena and further reduce the walk-off, we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form. As a result, the walk-off is decreased to ˜48.81 mrad, providing ˜30% relative reduction. By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction, the walk-off angle is further reduced to 38.9 mrad. Moreover, it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.

  2. Analytic expression and propagation properties of hollow Gaussian beams for the off-waist incident case in strongly nonlocal media

    NASA Astrophysics Data System (ADS)

    Dai, Zhiping; Ling, Xiaohui; Tang, Shiqing

    2018-06-01

    In this paper, the propagation properties of hollow Gaussian beams (HGBs) are discussed in detail when they are off-waist incident in strongly nonlocal media. A set of mathematic expressions are given to describe the evolutions of the beam intensity, the beam width, and the real beam radius. Numerical simulations are carried out to illustrate these propagation properties depended on the off-waist incidence. It is found that a HGB always periodically transforms its transverse patterns during propagation. Accordingly, the beam width and the real beam radius are also periodic during propagation.

  3. Response to "Comment on 'Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma'" [Phys. Plasmas 21, 064701 (2014)

    NASA Astrophysics Data System (ADS)

    Patil, S. D.; Takale, M. V.

    2014-06-01

    Habibi and Ghamari have presented a Comment on our paper [Phys. Plasmas 20, 072703 (2013)] by examining quantum dielectric response in thermal quantum plasma. They have modeled the relativistic self-focusing of Gaussian laser beam in cold and warm quantum plasmas and reported that self-focusing length does not change in both situations. In this response, we have reached the following important conclusions about the comment itself.

  4. Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory

    PubMed Central

    Ambrosio, Leonardo A.; Hernández-Figueroa, Hugo E.

    2010-01-01

    Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised. PMID:21258549

  5. Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory.

    PubMed

    Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E

    2010-11-04

    Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised.

  6. The Gaussian Laser Angular Distribution in HYDRA's 3D Laser Ray Trace Package

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sepke, Scott M.

    In this note, the angular distribution of rays launched by the 3D LZR ray trace package is derived for Gaussian beams (npower==2) with bm model=3±. Beams with bm model=+3 have a nearly at distribution, and beams with bm model=-3 have a nearly linear distribution when the spot size is large compared to the wavelength.

  7. Influence of light absorption on relativistic self-focusing of Gaussian laser beam in cold quantum plasma

    NASA Astrophysics Data System (ADS)

    Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.

    2018-05-01

    When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.

  8. Scintillation analysis of pseudo-Bessel-Gaussian Schell-mode beams propagating through atmospheric turbulence with wave optics simulation

    NASA Astrophysics Data System (ADS)

    Zheng, Guo; Wang, Jue; Wang, Lin; Zhou, Muchun; Chen, Yanru; Song, Minmin

    2018-03-01

    The scintillation index of pseudo-Bessel-Gaussian Schell-mode (PBGSM) beams propagating through atmospheric turbulence is analyzed with the help of wave optics simulation due to the analytic difficulties. It is found that in the strong fluctuation regime, the PBGSM beams are more resistant to the turbulence with the appropriate parameters β and δ . However, the case is contrary in the weak fluctuation regime. Our simulation results indicate that the PBGSM beams may be applied to free-space optical (FSO) communication systems only when the turbulence is strong or the propagation distance is long.

  9. Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite-Gaussian beams

    NASA Astrophysics Data System (ADS)

    Chen, Y. F.; Chang, C. C.; Lee, C. Y.; Tung, J. C.; Liang, H. C.; Huang, K. F.

    2018-01-01

    Theoretical wave functions are analytically derived to characterize the propagation evolution of the Hermite-Gaussian (HG) beams transformed by a single-lens astigmatic mode converter with arbitrary angle. The derived wave functions are related to the combination of the rotation transform and the antisymmetric fractional Fourier transform. The derived formula is systematically validated by using an off-axis diode-pumped solid-state laser to generate various high-order HG beams for mode conversions. In addition to validation, the creation and evolution of vortex structures in the transformed HG beams are numerically manifested. The present theoretical analyses can be used not only to characterize the evolution of the transformed beams but to design the optical vortex beams with various forms.

  10. Beam wander of dark hollow, flat-topped and annular beams

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, H. T.; Çil, C. Z.

    2008-11-01

    Benefiting from the earlier derivations for the Gaussian beam, we formulate beam wander for dark hollow (DH) and flat-topped (FT) beams, also covering the annular Gaussian (AG) beam as a special case. Via graphical illustrations, beam wander variations of these beams are analyzed and compared among themselves and to the fundamental Gaussian beam against changes in propagation length, amplitude factor, source size, wavelength of operation, inner and outer scales of turbulence. These comparisons show that in relation to the fundamental Gaussian beam, DH and FT beams will exhibit less beam wander, particularly at small primary beam source sizes, lower amplitude factors of the secondary beam and higher beam orders. Furthermore, DH and FT beams will continue to preserve this advantageous position all throughout the considered range of wavelengths, inner and outer scales of turbulence. FT beams, in particular, are observed to have the smallest beam wander values among all, up to certain source sizes.

  11. Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

    NASA Astrophysics Data System (ADS)

    Wang, Xiaohui; Song, Yingxiong

    2018-02-01

    By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.

  12. Beyond Gaussians: a study of single spot modeling for scanning proton dose calculation

    PubMed Central

    Li, Yupeng; Zhu, Ronald X.; Sahoo, Narayan; Anand, Aman; Zhang, Xiaodong

    2013-01-01

    Active spot scanning proton therapy is becoming increasingly adopted by proton therapy centers worldwide. Unlike passive-scattering proton therapy, active spot scanning proton therapy, especially intensity-modulated proton therapy, requires proper modeling of each scanning spot to ensure accurate computation of the total dose distribution contributed from a large number of spots. During commissioning of the spot scanning gantry at the Proton Therapy Center in Houston, it was observed that the long-range scattering protons in a medium may have been inadequately modeled for high-energy beams by a commercial treatment planning system, which could lead to incorrect prediction of field-size effects on dose output. In the present study, we developed a pencil-beam algorithm for scanning-proton dose calculation by focusing on properly modeling individual scanning spots. All modeling parameters required by the pencil-beam algorithm can be generated based solely on a few sets of measured data. We demonstrated that low-dose halos in single-spot profiles in the medium could be adequately modeled with the addition of a modified Cauchy-Lorentz distribution function to a double-Gaussian function. The field-size effects were accurately computed at all depths and field sizes for all energies, and good dose accuracy was also achieved for patient dose verification. The implementation of the proposed pencil beam algorithm also enabled us to study the importance of different modeling components and parameters at various beam energies. The results of this study may be helpful in improving dose calculation accuracy and simplifying beam commissioning and treatment planning processes for spot scanning proton therapy. PMID:22297324

  13. Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

    PubMed

    Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

    2015-02-01

    We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

  14. Two particle tracking and detection in a single Gaussian beam optical trap.

    PubMed

    Praveen, P; Yogesha; Iyengar, Shruthi S; Bhattacharya, Sarbari; Ananthamurthy, Sharath

    2016-01-20

    We have studied in detail the situation wherein two microbeads are trapped axially in a single-beam Gaussian intensity profile optical trap. We find that the corner frequency extracted from a power spectral density analysis of intensity fluctuations recorded on a quadrant photodetector (QPD) is dependent on the detection scheme. Using forward- and backscattering detection schemes with single and two laser wavelengths along with computer simulations, we conclude that fluctuations detected in backscattering bear true position information of the bead encountered first in the beam propagation direction. Forward scattering, on the other hand, carries position information of both beads with substantial contribution from the bead encountered first along the beam propagation direction. Mie scattering analysis further reveals that the interference term from the scattering of the two beads contributes significantly to the signal, precluding the ability to resolve the positions of the individual beads in forward scattering. In QPD-based detection schemes, detection through backscattering, thereby, is imperative to track the true displacements of axially trapped microbeads for possible studies on light-mediated interbead interactions.

  15. An alternative model for a partially coherent elliptical dark hollow beam

    NASA Astrophysics Data System (ADS)

    Li, Xu; Wang, Fei; Cai, Yangjian

    2011-04-01

    An alternative theoretical model named partially coherent hollow elliptical Gaussian beam (HEGB) is proposed to describe a partially coherent beam with an elliptical dark hollow profile. Explicit expression for the propagation factors of a partially coherent HEGB is derived. Based on the generalized Collins formula, analytical formulae for the cross-spectral density and mean-squared beam width of a partially coherent HEGB, propagating through a paraxial ABCD optical system, are derived. Propagation properties of a partially coherent HEGB in free space are studied as a numerical example.

  16. Acceleration and evolution of a hollow electron beam in wakefields driven by a Laguerre-Gaussian laser pulse

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhang, Guo-Bo; College of Science, National University of Defense Technology, Changsha 410073; Chen, Min, E-mail: minchen@sjtu.edu.cn, E-mail: yanyunma@126.com

    2016-03-15

    We show that a ring-shaped hollow electron beam can be injected and accelerated by using a Laguerre-Gaussian laser pulse and ionization-induced injection in a laser wakefield accelerator. The acceleration and evolution of such a hollow, relativistic electron beam are investigated through three-dimensional particle-in-cell simulations. We find that both the ring size and the beam thickness oscillate during the acceleration. The beam azimuthal shape is angularly dependent and evolves during the acceleration. The beam ellipticity changes resulting from the electron angular momenta obtained from the drive laser pulse and the focusing forces from the wakefield. The dependence of beam ring radiusmore » on the laser-plasma parameters (e.g., laser intensity, focal size, and plasma density) is studied. Such a hollow electron beam may have potential applications for accelerating and collimating positively charged particles.« less

  17. Contribution of High-Order Rainbows to the Scattering of a Gaussian Laser Beam by a Spherical Particle

    NASA Technical Reports Server (NTRS)

    Lock, James A.

    1993-01-01

    I review the theory of the scattering of a Gaussian laser beam by a dielectric spherical particle and give the details for constructing a computer program to implement the theory. Computational results indicate that if the width of the laser beam is much less than the diameter of the particle and if the axis of the beam is incident near the edge of the particle, the fifth-, sixth-, and ninth-order rainbows should be evident in the far-field scattered intensity. I performed an experiment that yielded tentative evidence for the presence of the sixth- order rainbow.

  18. Evolution of a Gaussian laser beam in warm collisional magnetoplasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jafari, M. J.; Jafari Milani, M. R., E-mail: mrj.milani@gmail.com; Niknam, A. R.

    2016-07-15

    In this paper, the spatial evolution of an intense circularly polarized Gaussian laser beam propagated through a warm plasma is investigated, taking into account the ponderomotive force, Ohmic heating, external magnetic field, and collisional effects. Using the momentum transfer and energy equations, both modified electron temperature and electron density in plasma are obtained. By introducing the complex dielectric permittivity of warm magnetized plasma and using the complex eikonal function, coupled differential equations for beam width parameter are established and solved numerically. The effects of polarization state of laser and magnetic field on the laser spot size evolution are studied. Itmore » is observed that in case of the right-handed polarization, an increase in the value of external magnetic field causes an increase in the strength of the self-focusing, especially in the higher values, and consequently, the self-focusing occurs in shorter distance of propagation. Moreover, the results demonstrate the existence of laser intensity and electron temperature ranges where self-focusing can occur, while the beam diverges outside of these regions; meanwhile, in these intervals, there exists a turning point for each of intensity and temperature in which the self-focusing process has its strongest strength. Finally, it is found that the self-focusing effect can be enhanced by increasing the plasma frequency (plasma density).« less

  19. Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models

    PubMed Central

    Marias, Kostas; Lambregts, Doenja M. J.; Nikiforaki, Katerina; van Heeswijk, Miriam M.; Bakers, Frans C. H.; Beets-Tan, Regina G. H.

    2017-01-01

    Purpose The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Material and methods Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. Results All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. Conclusion No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono

  20. Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

    PubMed

    Manikis, Georgios C; Marias, Kostas; Lambregts, Doenja M J; Nikiforaki, Katerina; van Heeswijk, Miriam M; Bakers, Frans C H; Beets-Tan, Regina G H; Papanikolaou, Nikolaos

    2017-01-01

    The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer. Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2) at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG) and non-Gaussian (MNG and BNG) were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE). To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC) and F-ratio. All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area. No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

  1. Comparisons of non-Gaussian statistical models in DNA methylation analysis.

    PubMed

    Ma, Zhanyu; Teschendorff, Andrew E; Yu, Hong; Taghia, Jalil; Guo, Jun

    2014-06-16

    As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance.

  2. Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis

    PubMed Central

    Ma, Zhanyu; Teschendorff, Andrew E.; Yu, Hong; Taghia, Jalil; Guo, Jun

    2014-01-01

    As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. PMID:24937687

  3. Mode coupling in vortex beams

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, Halil T.

    2018-05-01

    We examine the mode coupling in vortex beams. Mode coupling also known as the crosstalk takes place due to turbulent characteristics of the atmospheric communication medium. This way, the transmitted intrinsic mode of the vortex beam leaks power to other extrinsic modes, thus preventing the correct detection of the transmitted symbol which is usually encoded into the mode index or the orbital angular momentum state of the vortex beam. Here we investigate the normalized power mode coupling ratios of several types of vortex beams, namely, Gaussian vortex beam, Bessel Gaussian beam, hypergeometric Gaussian beam and Laguerre Gaussian beam. It is found that smaller mode numbers lead to less mode coupling. The same is partially observed for increasing source sizes. Comparing the vortex beams amongst themselves, it is seen that hypergeometric Gaussian beam is the one retaining the most power in intrinsic mode during propagation, but only at lowest mode index of unity. At higher mode indices this advantage passes over to the Gaussian vortex beam.

  4. Coherent mode decomposition using mixed Wigner functions of Hermite-Gaussian beams.

    PubMed

    Tanaka, Takashi

    2017-04-15

    A new method of coherent mode decomposition (CMD) is proposed that is based on a Wigner-function representation of Hermite-Gaussian beams. In contrast to the well-known method using the cross spectral density (CSD), it directly determines the mode functions and their weights without solving the eigenvalue problem. This facilitates the CMD of partially coherent light whose Wigner functions (and thus CSDs) are not separable, in which case the conventional CMD requires solving an eigenvalue problem with a large matrix and thus is numerically formidable. An example is shown regarding the CMD of synchrotron radiation, one of the most important applications of the proposed method.

  5. Cylindrical particle manipulation and negative spinning using a nonparaxial Hermite-Gaussian light-sheet beam

    NASA Astrophysics Data System (ADS)

    Mitri, F. G.

    2016-10-01

    Based on the angular spectrum decomposition method (ASDM), a nonparaxial solution for the Hermite-Gaussian (HG m ) light-sheet beam of any order m is derived. The beam-shape coefficients (BSCs) are expressed in a compact form and computed using the standard Simpson’s rule for numerical integration. Subsequently, the analysis is extended to evaluate the longitudinal and transverse radiation forces as well as the spin torque on an absorptive dielectric cylindrical particle in 2D without any restriction to a specific range of frequencies. The dynamics of the cylindrical particle are also examined based on Newton’s second law of motion. The numerical results show that a Rayleigh or Mie cylindrical particle can be trapped, pulled or propelled in the optical field depending on its initial position in the cross-sectional plane of the HG m light-sheet. Moreover, negative or positive axial spin torques can arise depending on the choice of the non-dimensional size parameter ka (where k is the wavenumber and a is the radius of the cylinder) and the location of the absorptive cylinder in the beam. This means that the HG m light-sheet beam can induce clockwise or anti-clockwise rotations depending on its shift from the center of the cylinder. In addition, individual vortex behavior can arise in the cross-sectional plane of wave propagation. The present analysis presents an analytical model to predict the optical radiation forces and torque induced by a HG m light-sheet beam on an absorptive cylinder for applications in optical light-sheet tweezers, optical micro-machines, particle manipulation and opto-fluidics to name a few areas of research.

  6. GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.

    PubMed

    Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi

    2017-05-24

    As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is < 50%, CpG obs /CpG exp varies, and the length of CGI ranges from eight nucleotides to a few thousand of nucleotides. It implies that CGI detection is not just a straightly statistical task and some unrevealed rules probably are hidden. A novel Gaussian model, GaussianCpG, is developed for detection of CpG islands on human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.

  7. Second harmonic generation by self-focusing of intense hollow Gaussian laser beam in collisionless plasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka; Gauniyal, Rakhi

    2016-01-15

    The effect of self focused hollow Gaussian laser beam (HGLB) (carrying null intensity in center) on the excitation of electron plasma wave (EPW) and second harmonic generation (SHG) has been investigated in collisionless plasma, where relativistic-ponderomotive and only relativistic nonlinearities are operative. The relativistic change of electron mass and the modification of the background electron density due to ponderomotive nonlinearity lead to self-focusing of HGLB in plasma. Paraxial ray theory has been used to derive coupled equations for the self focusing of HGLB in plasma, generation of EPW, and second harmonic. These coupled equations are solved analytically and numerically tomore » study the laser intensity in the plasma, electric field associated with the excited EPW, and the power of SHG. Second harmonic emission is generated due to nonlinear coupling between incident HGLB and EPW satisfying the proper phase matching conditions. The results show that the effect of including the ponderomotive nonlinearity is significant on the generation of EPW and second harmonic. The electric field associated with EPW and the power of SHG are found to be highly sensitive to the order of the hollow Gaussian beam.« less

  8. Analysis of EM penetration into and scattering by electrically large open waveguide cavities using Gaussian beam shooting

    NASA Technical Reports Server (NTRS)

    Burkholder, Robert J.; Pathak, Prabhakar H.

    1991-01-01

    Gaussian beam (GB) representation methods are used to analyze the electromagnetic coupling into and the scattering by a large nonuniform cavity. The aperture field in the cavity is decomposed into beams using the Gabor expansion, and shooting techniques are then employed. The method is illustrated only for the two-dimensional (2-D) case. The GBs are tracked axially using the rules of beam optics which ignore any beam distortion upon reflection at the walls. The effects of beam distortion are not significant for relatively slowly varying waveguide cavities. The field scattered into the exterior by the termination within the cavity is found using a reciprocity integral formulation which requires a knowledge of the beam fields near the termination. Numerical results based on this GB approach are presented and compared with results based on an independent reference solution.

  9. Acceleration of on-axis and ring-shaped electron beams in wakefields driven by Laguerre-Gaussian pulses

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhang, Guo-Bo; Key Laboratory for Laser Plasmas; Chen, Min, E-mail: minchen@sjtu.edu.cn, E-mail: yanyunma@126.com

    2016-03-14

    The acceleration of electron beams with multiple transverse structures in wakefields driven by Laguerre-Gaussian pulses has been studied through three-dimensional (3D) particle-in-cell simulations. Under different laser-plasma conditions, the wakefield shows different transverse structures. In general cases, the wakefield shows a donut-like structure and it accelerates the ring-shaped hollow electron beam. When a lower plasma density or a smaller laser spot size is used, besides the donut-like wakefield, a central bell-like wakefield can also be excited. The wake sets in the center of the donut-like wake. In this case, both a central on-axis electron beam and a ring-shaped electron beam aremore » simultaneously accelerated. Further, reducing the plasma density or laser spot size leads to an on-axis electron beam acceleration only. The research is beneficial for some potential applications requiring special pulse beam structures, such as positron acceleration and collimation.« less

  10. The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise

    NASA Astrophysics Data System (ADS)

    Guo, Qin; Sun, Zhongkui; Xu, Wei

    2016-05-01

    The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.

  11. Modeling the ponderomotive interaction of high-power laser beams with collisional plasma: the FDTD-based approach.

    PubMed

    Lin, Zhili; Chen, Xudong; Ding, Panfeng; Qiu, Weibin; Pu, Jixiong

    2017-04-03

    The ponderomotive interaction of high-power laser beams with collisional plasma is modeled in the nonrelativistic regime and is simulated using the powerful finite-difference time-domain (FDTD) method for the first time in literature. The nonlinear and dissipative dielectric constant function of the collisional plasma is deduced that takes the ponderomotive effect into account and is implemented in the discrete framework of FDTD algorithms. Maclaurin series expansion approach is applied for implementing the obtained physical model and the time average of the square of light field is extracted by numerically evaluating an integral identity based on the composite trapezoidal rule for numerical integration. Two numerical examples corresponding to two different types of laser beams, Gaussian beam and vortex Laguerre-Gaussian beam, propagating in collisional plasma, are presented for specified laser and plasma parameters to verify the validity of the proposed FDTD-based approach. Simulation results show the anticipated self-focusing and attenuation phenomena of laser beams and the deformation of the spatial density distributions of electron plasma along the beam propagation path. Due to the flexibility of FDTD method in light beam excitation and accurate complex material modeling, the proposed approach has a wide application prospect in the study of the complex laser-plasma interactions in a small scale.

  12. Reflection of a TE-polarised Gaussian beam from a layered structure under conditions of resonance excitation of waveguide modes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sokolov, V I; Marusin, N V; Molchanova, S I

    2014-11-30

    The problem of reflection of a TE-polarised Gaussian light beam from a layered structure under conditions of resonance excitation of waveguide modes using a total internal reflection prism is considered. Using the spectral approach we have derived the analytic expressions for the mode propagation lengths, widths and depths of m-lines (sharp and narrow dips in the angular dependence of the specular reflection coefficient), depending on the structure parameters. It is shown that in the case of weak coupling, when the propagation lengths l{sub m} of the waveguide modes are mainly determined by the extinction coefficient in the film, the depthmore » of m-lines grows with the mode number m. In the case of strong coupling, when l{sub m} is determined mainly by the radiation of modes into the prism, the depth of m-lines decreases with increasing m. The change in the TE-polarised Gaussian beam shape after its reflection from the layered structure is studied, which is determined by the energy transfer from the incident beam into waveguide modes that propagate along the structure by the distance l{sub m}, are radiated in the direction of specular reflection and interfere with a part of the beam reflected from the working face of the prism. It is shown that this interference can lead to the field intensity oscillations near m-lines. The analysis of different methods for determining the parameters of thin-film structures is presented, including the measurement of mode angles θ{sub m} and the reflected beam shape. The methods are based on simultaneous excitation of a few waveguide modes in the film with a strongly focused monochromatic Gaussian beam, the waist width of which is much smaller than the propagation length of the modes. As an example of using these methods, the refractive index and the thickness of silicon monoxide film on silica substrate at the wavelength 633 nm are determined. (fibre and integrated-optical structures)« less

  13. Shaping propagation invariant laser beams

    NASA Astrophysics Data System (ADS)

    Soskind, Michael; Soskind, Rose; Soskind, Yakov

    2015-11-01

    Propagation-invariant structured laser beams possess several unique properties and play an important role in various photonics applications. The majority of propagation invariant beams are produced in the form of laser modes emanating from stable laser cavities. Therefore, their spatial structure is limited by the intracavity mode formation. We show that several types of anamorphic optical systems (AOSs) can be effectively employed to shape laser beams into a variety of propagation invariant structured fields with different shapes and phase distributions. We present a propagation matrix approach for designing AOSs and defining mode-matching conditions required for preserving propagation invariance of the output shaped fields. The propagation matrix approach was selected, as it provides a more straightforward approach in designing AOSs for shaping propagation-invariant laser beams than the alternative technique based on the Gouy phase evolution, especially in the case of multielement AOSs. Several practical configurations of optical systems that are suitable for shaping input laser beams into a diverse variety of structured propagation invariant laser beams are also presented. The laser beam shaping approach was applied by modeling propagation characteristics of several input laser beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian structured field distributions. The influence of the Ince-Gaussian beam semifocal separation parameter and the azimuthal orientation between the input laser beams and the AOSs onto the resulting shape of the propagation invariant laser beams is presented as well.

  14. Dynamic generation of Ince-Gaussian modes with a digital micromirror device

    NASA Astrophysics Data System (ADS)

    Ren, Yu-Xuan; Fang, Zhao-Xiang; Gong, Lei; Huang, Kun; Chen, Yue; Lu, Rong-De

    2015-04-01

    Ince-Gaussian (IG) beam with elliptical profile, as a connection between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams, has showed unique advantages in some applications such as quantum entanglement and optical micromanipulation. However, its dynamic generation with high switching frequency is still challenging. Here, we experimentally reported the quick generation of Ince-Gaussian beam by using a digital micro-mirror device (DMD), which has the highest switching frequency of 5.2 kHz in principle. The configurable properties of DMD allow us to observe the quasi-smooth variation from LG (with ellipticity ɛ = 0 ) to IG and HG ( ɛ = ∞ ) beam. This approach might pave a path to high-speed quantum communication in terms of IG beam. Additionally, the characterized axial plane intensity distribution exhibits a 3D mould potentially being employed for optical micromanipulation.

  15. Dynamic generation of Ince-Gaussian modes with a digital micromirror device

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ren, Yu-Xuan, E-mail: yxren@ustc.edu.cn; Fang, Zhao-Xiang; Chen, Yue

    Ince-Gaussian (IG) beam with elliptical profile, as a connection between Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) beams, has showed unique advantages in some applications such as quantum entanglement and optical micromanipulation. However, its dynamic generation with high switching frequency is still challenging. Here, we experimentally reported the quick generation of Ince-Gaussian beam by using a digital micro-mirror device (DMD), which has the highest switching frequency of 5.2 kHz in principle. The configurable properties of DMD allow us to observe the quasi-smooth variation from LG (with ellipticity ε=0) to IG and HG (ε=∞) beam. This approach might pave a path to high-speedmore » quantum communication in terms of IG beam. Additionally, the characterized axial plane intensity distribution exhibits a 3D mould potentially being employed for optical micromanipulation.« less

  16. Propagation factors of multi-sinc Schell-model beams in non-Kolmogorov turbulence.

    PubMed

    Song, Zhenzhen; Liu, Zhengjun; Zhou, Keya; Sun, Qiongge; Liu, Shutian

    2016-01-25

    We derive several analytical expressions for the root-mean-square (rms) angular width and the M(2)-factor of the multi-sinc Schell-model (MSSM) beams propagating in non-Kolmogorov turbulence with the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. Numerical results show that a MSSM beam with dark-hollow far fields in free space has advantage over the one with flat-topped or multi-rings far fields for reducing the turbulence-induced degradation, which will become more obvious with larger dark-hollow size. Beam quality of MSSM beams can be further improved with longer wavelength and larger beam width, or under the condition of weaker turbulence. We also demonstrate that the non-Kolmogorov turbulence has significantly less effect on the MSSM beams than the Gaussian Schell-model beam.

  17. Effect of beam types on the scintillations: a review

    NASA Astrophysics Data System (ADS)

    Baykal, Yahya; Eyyuboglu, Halil T.; Cai, Yangjian

    2009-02-01

    When different incidences are launched in atmospheric turbulence, it is known that the intensity fluctuations exhibit different characteristics. In this paper we review our work done in the evaluations of the scintillation index of general beam types when such optical beams propagate in horizontal atmospheric links in the weak fluctuations regime. Variation of scintillation indices versus the source and medium parameters are examined for flat-topped-Gaussian, cosh- Gaussian, cos-Gaussian, annular, elliptical Gaussian, circular (i.e., stigmatic) and elliptical (i.e., astigmatic) dark hollow, lowest order Bessel-Gaussian and laser array beams. For flat-topped-Gaussian beam, scintillation is larger than the single Gaussian beam scintillation, when the source sizes are much less than the Fresnel zone but becomes smaller for source sizes much larger than the Fresnel zone. Cosh-Gaussian beam has lower on-axis scintillations at smaller source sizes and longer propagation distances as compared to Gaussian beams where focusing imposes more reduction on the cosh- Gaussian beam scintillations than that of the Gaussian beam. Intensity fluctuations of a cos-Gaussian beam show favorable behaviour against a Gaussian beam at lower propagation lengths. At longer propagation lengths, annular beam becomes advantageous. In focused cases, the scintillation index of annular beam is lower than the scintillation index of Gaussian and cos-Gaussian beams starting at earlier propagation distances. Cos-Gaussian beams are advantages at relatively large source sizes while the reverse is valid for annular beams. Scintillations of a stigmatic or astigmatic dark hollow beam can be smaller when compared to stigmatic or astigmatic Gaussian, annular and flat-topped beams under conditions that are closely related to the beam parameters. Intensity fluctuation of an elliptical Gaussian beam can also be smaller than a circular Gaussian beam depending on the propagation length and the ratio of the beam

  18. Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

    NASA Technical Reports Server (NTRS)

    Burkholder, R. J.; Pathak, P. H.

    1988-01-01

    The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.

  19. The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems

    NASA Astrophysics Data System (ADS)

    Trappe, Neil; Murphy, J. Anthony; Withington, Stafford

    2003-07-01

    Gaussian beam mode analysis (GBMA) offers a more intuitive physical insight into how light beams evolve as they propagate than the conventional Fresnel diffraction integral approach. In this paper we illustrate that GBMA is a computationally efficient, alternative technique for tracing the evolution of a diffracting coherent beam. In previous papers we demonstrated the straightforward application of GBMA to the computation of the classical diffraction patterns associated with a range of standard apertures. In this paper we show how the GBMA technique can be expanded to investigate the effects of aberrations in the presence of diffraction by introducing the appropriate phase error term into the propagating quasi-optical beam. We compare our technique to the standard diffraction integral calculation for coma, astigmatism and spherical aberration, taking—for comparison—examples from the classic text 'Principles of Optics' by Born and Wolf. We show the advantages of GBMA for allowing the defocusing of an aberrated image to be evaluated quickly, which is particularly important and useful for probing the consequences of astigmatism and spherical aberration.

  20. Beam-width spreading of vortex beams in free space

    NASA Astrophysics Data System (ADS)

    Wang, Weiwei; Li, Jinhong; Duan, Meiling

    2018-01-01

    Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function, the analytical expression for the beam-width spreading of Gaussian Schell-model (GSM) vortex beams in free space are derived, and used to study the influence of beam parameters on the beam-width spreading of GSM vortex beams. With the increment of the propagation distance, the beam-width spreading of GSM vortex beams will increase; the bigger the topological charge, spatial correlation length, wavelength and waist width are, the smaller the beam-width spreading is.

  1. Revisiting non-Gaussianity from non-attractor inflation models

    NASA Astrophysics Data System (ADS)

    Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

    2018-05-01

    Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.

  2. Response to “Comment on ‘Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma’” [Phys. Plasmas 21, 064701 (2014)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Patil, S. D., E-mail: sdpatil-phy@rediffmail.com; Takale, M. V.

    2014-06-15

    Habibi and Ghamari have presented a Comment on our paper [Phys. Plasmas 20, 072703 (2013)] by examining quantum dielectric response in thermal quantum plasma. They have modeled the relativistic self-focusing of Gaussian laser beam in cold and warm quantum plasmas and reported that self-focusing length does not change in both situations. In this response, we have reached the following important conclusions about the comment itself.

  3. Modeling of the laser beam shape for high-power applications

    NASA Astrophysics Data System (ADS)

    Jabczyński, Jan K.; Kaskow, Mateusz; Gorajek, Lukasz; Kopczyński, Krzysztof; Zendzian, Waldemar

    2018-04-01

    Aperture losses and thermo-optic effects (TOE) inside optics as well as the effective beam width in far field should be taken into account in the analysis of the most appropriate laser beam profile for high-power applications. We have theoretically analyzed such a problem for a group of super-Gaussian beams taking first only diffraction limitations. Furthermore, we have investigated TOE on far-field parameters of such beams to determine the influence of absorption in optical elements on beam quality degradation. The best compromise gives the super-Gaussian profile of index p = 5, for which beam quality does not decrease noticeably and the thermo-optic higher order aberrations are compensated. The simplified formulas were derived for beam quality metrics (parameter M2 and Strehl ratio), which enable estimation of the influence of heat deposited in optics on degradation of beam quality. The method of dynamic compensation of such effect was proposed.

  4. Speech Enhancement Using Gaussian Scale Mixture Models

    PubMed Central

    Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

    2011-01-01

    This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

  5. Generation of Ince-Gaussian beams in highly efficient, nanosecond Cr, Nd:YAG microchip lasers

    NASA Astrophysics Data System (ADS)

    Dong, J.; Ma, J.; Ren, Y. Y.; Xu, G. Z.; Kaminskii, A. A.

    2013-08-01

    Direct generation of higher-order Ince-Gaussian (IG) beams from laser-diode end-pumped Cr, Nd:YAG self-Q-switched microchip lasers was achieved with high efficiency and high repetition rate. An average output power of over 2 W was obtained at an absorbed pump power of 8.2 W a corresponding optical-to-optical efficiency of 25% was achieved. Various IG modes with nanosecond pulse width and peak power of over 2 kW were obtained in laser-diode pumped Cr, Nd:YAG microchip lasers under different pump power levels by applying a tilted, large area pump beam. The effect of the inversion population distribution induced by the tilted pump beam and nonlinear absorption of Cr4+-ions for different pump power levels on the oscillation of higher-order IG modes in Cr, Nd:YAG microchip lasers is addressed. The higher-order IG mode oscillation has a great influence on the laser performance of Cr, Nd:YAG microchip lasers.

  6. Comment on “Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma” [Phys. Plasmas 20, 072703 (2013)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Habibi, M., E-mail: habibi.physics@gmail.com; Ghamari, F.

    2014-06-15

    Patil and Takale in their recent article [Phys. Plasmas 20, 072703 (2013)], by evaluating the quantum dielectric response in thermal quantum plasma, have modeled the relativistic self-focusing of Gaussian laser beam in a plasma. We have found that there are some important shortcomings and fundamental mistakes in Patil and Takale [Phys. Plasmas 20, 072703 (2013)] that we give a brief description about them and refer readers to important misconception about the use of the Fermi temperature in quantum plasmas, appearing in Patil and Takale [Phys. Plasmas 20, 072703 (2013)].

  7. Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

    2015-11-15

    This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« less

  8. Recent advances in scalable non-Gaussian geostatistics: The generalized sub-Gaussian model

    NASA Astrophysics Data System (ADS)

    Guadagnini, Alberto; Riva, Monica; Neuman, Shlomo P.

    2018-07-01

    Geostatistical analysis has been introduced over half a century ago to allow quantifying seemingly random spatial variations in earth quantities such as rock mineral content or permeability. The traditional approach has been to view such quantities as multivariate Gaussian random functions characterized by one or a few well-defined spatial correlation scales. There is, however, mounting evidence that many spatially varying quantities exhibit non-Gaussian behavior over a multiplicity of scales. The purpose of this minireview is not to paint a broad picture of the subject and its treatment in the literature. Instead, we focus on very recent advances in the recognition and analysis of this ubiquitous phenomenon, which transcends hydrology and the Earth sciences, brought about largely by our own work. In particular, we use porosity data from a deep borehole to illustrate typical aspects of such scalable non-Gaussian behavior, describe a very recent theoretical model that (for the first time) captures all these behavioral aspects in a comprehensive manner, show how this allows generating random realizations of the quantity conditional on sampled values, point toward ways of incorporating scalable non-Gaussian behavior in hydrologic analysis, highlight the significance of doing so, and list open questions requiring further research.

  9. Generation of various partially coherent beams and their propagation properties in turbulent atmosphere: a review

    NASA Astrophysics Data System (ADS)

    Cai, Yangjian

    2011-03-01

    Partially coherent beams, such as Gaussian Schell-model beam, partially coherent dark hollow beam, partially coherent flat-topped beam and electromagnetic Gaussian Schell-model beam, have important applications in free space optical communications, optical imaging, optical trapping, inertial confinement fusion and nonlinear optics. In this paper, experimental generations of various partially coherent beams are introduced. Furthermore, with the help of a tensor method, analytical formulae for such beams propagating in turbulent atmosphere are derived, and the propagation properties of such beams in turbulent atmosphere are reviewed.

  10. IBS for non-gaussian distributions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.

    In many situations distribution can significantly deviate from Gaussian which requires accurate treatment of IBS. Our original interest in this problem was motivated by the need to have an accurate description of beam evolution due to IBS while distribution is strongly affected by the external electron cooling force. A variety of models with various degrees of approximation were developed and implemented in BETACOOL in the past to address this topic. A more complete treatment based on the friction coefficient and full 3-D diffusion tensor was introduced in BETACOOL at the end of 2007 under the name 'local IBS model'. Suchmore » a model allowed us calculation of IBS for an arbitrary beam distribution. The numerical benchmarking of this local IBS algorithm and its comparison with other models was reported before. In this paper, after briefly describing the model and its limitations, they present its comparison with available experimental data.« less

  11. Gaussian mixture models as flux prediction method for central receivers

    NASA Astrophysics Data System (ADS)

    Grobler, Annemarie; Gauché, Paul; Smit, Willie

    2016-05-01

    Flux prediction methods are crucial to the design and operation of central receiver systems. Current methods such as the circular and elliptical (bivariate) Gaussian prediction methods are often used in field layout design and aiming strategies. For experimental or small central receiver systems, the flux profile of a single heliostat often deviates significantly from the circular and elliptical Gaussian models. Therefore a novel method of flux prediction was developed by incorporating the fitting of Gaussian mixture models onto flux profiles produced by flux measurement or ray tracing. A method was also developed to predict the Gaussian mixture model parameters of a single heliostat for a given time using image processing. Recording the predicted parameters in a database ensures that more accurate predictions are made in a shorter time frame.

  12. Non-Gaussian Multi-resolution Modeling of Magnetosphere-Ionosphere Coupling Processes

    NASA Astrophysics Data System (ADS)

    Fan, M.; Paul, D.; Lee, T. C. M.; Matsuo, T.

    2016-12-01

    The most dynamic coupling between the magnetosphere and ionosphere occurs in the Earth's polar atmosphere. Our objective is to model scale-dependent stochastic characteristics of high-latitude ionospheric electric fields that originate from solar wind magnetosphere-ionosphere interactions. The Earth's high-latitude ionospheric electric field exhibits considerable variability, with increasing non-Gaussian characteristics at decreasing spatio-temporal scales. Accurately representing the underlying stochastic physical process through random field modeling is crucial not only for scientific understanding of the energy, momentum and mass exchanges between the Earth's magnetosphere and ionosphere, but also for modern technological systems including telecommunication, navigation, positioning and satellite tracking. While a lot of efforts have been made to characterize the large-scale variability of the electric field in the context of Gaussian processes, no attempt has been made so far to model the small-scale non-Gaussian stochastic process observed in the high-latitude ionosphere. We construct a novel random field model using spherical needlets as building blocks. The double localization of spherical needlets in both spatial and frequency domains enables the model to capture the non-Gaussian and multi-resolutional characteristics of the small-scale variability. The estimation procedure is computationally feasible due to the utilization of an adaptive Gibbs sampler. We apply the proposed methodology to the computational simulation output from the Lyon-Fedder-Mobarry (LFM) global magnetohydrodynamics (MHD) magnetosphere model. Our non-Gaussian multi-resolution model results in characterizing significantly more energy associated with the small-scale ionospheric electric field variability in comparison to Gaussian models. By accurately representing unaccounted-for additional energy and momentum sources to the Earth's upper atmosphere, our novel random field modeling

  13. Moving target detection method based on improved Gaussian mixture model

    NASA Astrophysics Data System (ADS)

    Ma, J. Y.; Jie, F. R.; Hu, Y. J.

    2017-07-01

    Gaussian Mixture Model is often employed to build background model in background difference methods for moving target detection. This paper puts forward an adaptive moving target detection algorithm based on improved Gaussian Mixture Model. According to the graylevel convergence for each pixel, adaptively choose the number of Gaussian distribution to learn and update background model. Morphological reconstruction method is adopted to eliminate the shadow.. Experiment proved that the proposed method not only has good robustness and detection effect, but also has good adaptability. Even for the special cases when the grayscale changes greatly and so on, the proposed method can also make outstanding performance.

  14. Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space.

    PubMed

    Peng, Yulian; Chen, Bo; Peng, Xi; Zhou, Meiling; Zhang, Liping; Li, Dongdong; Deng, Dongmei

    2016-08-22

    The evolution of the three-dimensional (3D) self-accelerating Airy-Ince-Gaussian (AiIG) and Airy-Helical-Ince-Gaussian (AiHIG) light bullets is investigated by solving the (3+1)D linear spatiotemporal evolution equation of an optical field analytically. As far as we know, the numerical experimental demonstrations of the Ince-Gaussian (IG) and Helical-Ince-Gaussian (HIG) beams in various modes are first developed to study the evolution characteristics of the different 3D spatiotemporal light bullets. A conclusion can be drawn that the different photoelastics, pulse stacked, boundary, elliptical ring and physically separated in-line vortices can be achieved by adjusting the ellipticity, the evolution distance and the mode-number of light bullets.

  15. Linear velocity fields in non-Gaussian models for large-scale structure

    NASA Technical Reports Server (NTRS)

    Scherrer, Robert J.

    1992-01-01

    Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

  16. Diffraction study of duty-cycle error in ferroelectric quasi-phase-matching gratings with Gaussian beam illumination

    NASA Astrophysics Data System (ADS)

    Dwivedi, Prashant Povel; Kumar, Challa Sesha Sai Pavan; Choi, Hee Joo; Cha, Myoungsik

    2016-02-01

    Random duty-cycle error (RDE) is inherent in the fabrication of ferroelectric quasi-phase-matching (QPM) gratings. Although a small RDE may not affect the nonlinearity of QPM devices, it enhances non-phase-matched parasitic harmonic generations, limiting the device performance in some applications. Recently, we demonstrated a simple method for measuring the RDE in QPM gratings by analyzing the far-field diffraction pattern obtained by uniform illumination (Dwivedi et al. in Opt Express 21:30221-30226, 2013). In the present study, we used a Gaussian beam illumination for the diffraction experiment to measure noise spectra that are less affected by the pedestals of the strong diffraction orders. Our results were compared with our calculations based on a random grating model, demonstrating improved resolution in the RDE estimation.

  17. Automatic image equalization and contrast enhancement using Gaussian mixture modeling.

    PubMed

    Celik, Turgay; Tjahjadi, Tardi

    2012-01-01

    In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types.

  18. TH-C-BRD-02: Analytical Modeling and Dose Calculation Method for Asymmetric Proton Pencil Beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gelover, E; Wang, D; Hill, P

    2014-06-15

    Purpose: A dynamic collimation system (DCS), which consists of two pairs of orthogonal trimmer blades driven by linear motors has been proposed to decrease the lateral penumbra in pencil beam scanning proton therapy. The DCS reduces lateral penumbra by intercepting the proton pencil beam near the lateral boundary of the target in the beam's eye view. The resultant trimmed pencil beams are asymmetric and laterally shifted, and therefore existing pencil beam dose calculation algorithms are not capable of trimmed beam dose calculations. This work develops a method to model and compute dose from trimmed pencil beams when using the DCS.more » Methods: MCNPX simulations were used to determine the dose distributions expected from various trimmer configurations using the DCS. Using these data, the lateral distribution for individual beamlets was modeled with a 2D asymmetric Gaussian function. The integral depth dose (IDD) of each configuration was also modeled by combining the IDD of an untrimmed pencil beam with a linear correction factor. The convolution of these two terms, along with the Highland approximation to account for lateral growth of the beam along the depth direction, allows a trimmed pencil beam dose distribution to be analytically generated. The algorithm was validated by computing dose for a single energy layer 5×5 cm{sup 2} treatment field, defined by the trimmers, using both the proposed method and MCNPX beamlets. Results: The Gaussian modeled asymmetric lateral profiles along the principal axes match the MCNPX data very well (R{sup 2}≥0.95 at the depth of the Bragg peak). For the 5×5 cm{sup 2} treatment plan created with both the modeled and MCNPX pencil beams, the passing rate of the 3D gamma test was 98% using a standard threshold of 3%/3 mm. Conclusion: An analytical method capable of accurately computing asymmetric pencil beam dose when using the DCS has been developed.« less

  19. Moving vehicles segmentation based on Gaussian motion model

    NASA Astrophysics Data System (ADS)

    Zhang, Wei; Fang, Xiang Z.; Lin, Wei Y.

    2005-07-01

    Moving objects segmentation is a challenge in computer vision. This paper focuses on the segmentation of moving vehicles in dynamic scene. We analyses the psychology of human vision and present a framework for segmenting moving vehicles in the highway. The proposed framework consists of two parts. Firstly, we propose an adaptive background update method in which the background is updated according to the change of illumination conditions and thus can adapt to the change of illumination sensitively. Secondly, we construct a Gaussian motion model to segment moving vehicles, in which the motion vectors of the moving pixels are modeled as a Gaussian model and an on-line EM algorithm is used to update the model. The Gaussian distribution of the adaptive model is elevated to determine which moving vectors result from moving vehicles and which from other moving objects such as waving trees. Finally, the pixels with motion vector result from the moving vehicles are segmented. Experimental results of several typical scenes show that the proposed model can detect the moving vehicles correctly and is immune from influence of the moving objects caused by the waving trees and the vibration of camera.

  20. Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI.

    PubMed

    Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong

    2016-12-09

    Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2  = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

  1. Optimisation of dispersion parameters of Gaussian plume model for CO₂ dispersion.

    PubMed

    Liu, Xiong; Godbole, Ajit; Lu, Cheng; Michal, Guillaume; Venton, Philip

    2015-11-01

    The carbon capture and storage (CCS) and enhanced oil recovery (EOR) projects entail the possibility of accidental release of carbon dioxide (CO2) into the atmosphere. To quantify the spread of CO2 following such release, the 'Gaussian' dispersion model is often used to estimate the resulting CO2 concentration levels in the surroundings. The Gaussian model enables quick estimates of the concentration levels. However, the traditionally recommended values of the 'dispersion parameters' in the Gaussian model may not be directly applicable to CO2 dispersion. This paper presents an optimisation technique to obtain the dispersion parameters in order to achieve a quick estimation of CO2 concentration levels in the atmosphere following CO2 blowouts. The optimised dispersion parameters enable the Gaussian model to produce quick estimates of CO2 concentration levels, precluding the necessity to set up and run much more complicated models. Computational fluid dynamics (CFD) models were employed to produce reference CO2 dispersion profiles in various atmospheric stability classes (ASC), different 'source strengths' and degrees of ground roughness. The performance of the CFD models was validated against the 'Kit Fox' field measurements, involving dispersion over a flat horizontal terrain, both with low and high roughness regions. An optimisation model employing a genetic algorithm (GA) to determine the best dispersion parameters in the Gaussian plume model was set up. Optimum values of the dispersion parameters for different ASCs that can be used in the Gaussian plume model for predicting CO2 dispersion were obtained.

  2. Characterization of elliptic dark hollow beams

    NASA Astrophysics Data System (ADS)

    Gutiérrez-Vega, Julio C.

    2008-08-01

    A dark hollow beam (DHB) is designed in general as a ringed shaped light beam with a null intensity center on the beam axis. DHBs have interesting physical properties such as a helical wavefront, a center vortex singularity, doughnut-shaped transverse intensity distribution, they may carry and transfer orbital and spin angular momentum, and may also exhibit a nondiffracting behavior upon propagation. Most of the known theoretical models to describe DHBs consider axially symmetric transverse intensity distributions. However, in recent years there has been an increasing interest in developing models to describe DHBs with elliptic symmetry. DHBs with elliptic symmetry can be regarded as transition beams between circular and rectangular DHBs. For example, the high-order modes emitted from resonators with neither completely rectangular nor completely circular symmetry, but in between them, cannot be described by the known HermiteGaussian or LaguerreGaussian beams. In this work, we review the current state of research on elliptic DHBs, with particular emphasis in Mathieu and Ince-Gauss beams.

  3. Generation of terahertz radiation by intense hollow Gaussian laser beam in magnetised plasma under relativistic-ponderomotive regime

    NASA Astrophysics Data System (ADS)

    Rawat, Priyanka; Rawat, Vinod; Gaur, Bineet; Purohit, Gunjan

    2017-07-01

    This paper explores the self-focusing of hollow Gaussian laser beam (HGLB) in collisionless magnetized plasma and its effect on the generation of THz radiation in the presence of relativistic-ponderomotive nonlinearity. The relativistic change of electron mass and electron density perturbation due to the ponderomotive force leads to self-focusing of the laser beam in plasma. Nonlinear coupling between the intense HGLB and electron plasma wave leads to generation of THz radiation in plasma. Resonant excitation of THz radiation at different frequencies of laser and electron plasma wave satisfies proper phase matching conditions. Appropriate expressions for the beam width parameter of the laser beam and the electric vector of the THz wave have been evaluated under the paraxial-ray and Wentzel-Kramers Brillouin approximations. It is found that the yield of THz amplitude depends on the focusing behaviour of laser beam, magnetic field, and background electron density. Numerical simulations have been carried out to investigate the effect of laser and plasma parameters on self-focusing of the laser beam and further its effect on the efficiency of the generated THz radiation.

  4. A non-gaussian model of continuous atmospheric turbulence for use in aircraft design

    NASA Technical Reports Server (NTRS)

    Reeves, P. M.; Joppa, R. G.; Ganzer, V. M.

    1976-01-01

    A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.

  5. Self-focusing and defocusing of Gaussian laser beams in collisional underdense magnetized plasmas with considering the nonlinear ohmic heating and ponderomotive force effects

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak, E-mail: b-shokri@sbu.ac.ir

    2015-10-15

    The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show thatmore » the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.« less

  6. Application of multivariate Gaussian detection theory to known non-Gaussian probability density functions

    NASA Astrophysics Data System (ADS)

    Schwartz, Craig R.; Thelen, Brian J.; Kenton, Arthur C.

    1995-06-01

    A statistical parametric multispectral sensor performance model was developed by ERIM to support mine field detection studies, multispectral sensor design/performance trade-off studies, and target detection algorithm development. The model assumes target detection algorithms and their performance models which are based on data assumed to obey multivariate Gaussian probability distribution functions (PDFs). The applicability of these algorithms and performance models can be generalized to data having non-Gaussian PDFs through the use of transforms which convert non-Gaussian data to Gaussian (or near-Gaussian) data. An example of one such transform is the Box-Cox power law transform. In practice, such a transform can be applied to non-Gaussian data prior to the introduction of a detection algorithm that is formally based on the assumption of multivariate Gaussian data. This paper presents an extension of these techniques to the case where the joint multivariate probability density function of the non-Gaussian input data is known, and where the joint estimate of the multivariate Gaussian statistics, under the Box-Cox transform, is desired. The jointly estimated multivariate Gaussian statistics can then be used to predict the performance of a target detection algorithm which has an associated Gaussian performance model.

  7. Robust Gaussian Graphical Modeling via l1 Penalization

    PubMed Central

    Sun, Hokeun; Li, Hongzhe

    2012-01-01

    Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l1 penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re-estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso. PMID:23020775

  8. Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels

    NASA Astrophysics Data System (ADS)

    Sabapathy, Krishna Kumar; Winter, Andreas

    2017-06-01

    We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

  9. Characterization of Adrenal Adenoma by Gaussian Model-Based Algorithm.

    PubMed

    Hsu, Larson D; Wang, Carolyn L; Clark, Toshimasa J

    2016-01-01

    We confirmed that computed tomography (CT) attenuation values of pixels in an adrenal nodule approximate a Gaussian distribution. Building on this and the previously described histogram analysis method, we created an algorithm that uses mean and standard deviation to estimate the percentage of negative attenuation pixels in an adrenal nodule, thereby allowing differentiation of adenomas and nonadenomas. The institutional review board approved both components of this study in which we developed and then validated our criteria. In the first, we retrospectively assessed CT attenuation values of adrenal nodules for normality using a 2-sample Kolmogorov-Smirnov test. In the second, we evaluated a separate cohort of patients with adrenal nodules using both the conventional 10HU unit mean attenuation method and our Gaussian model-based algorithm. We compared the sensitivities of the 2 methods using McNemar's test. A total of 183 of 185 observations (98.9%) demonstrated a Gaussian distribution in adrenal nodule pixel attenuation values. The sensitivity and specificity of our Gaussian model-based algorithm for identifying adrenal adenoma were 86.1% and 83.3%, respectively. The sensitivity and specificity of the mean attenuation method were 53.2% and 94.4%, respectively. The sensitivities of the 2 methods were significantly different (P value < 0.001). In conclusion, the CT attenuation values within an adrenal nodule follow a Gaussian distribution. Our Gaussian model-based algorithm can characterize adrenal adenomas with higher sensitivity than the conventional mean attenuation method. The use of our algorithm, which does not require additional postprocessing, may increase workflow efficiency and reduce unnecessary workup of benign nodules. Copyright © 2016 Elsevier Inc. All rights reserved.

  10. Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing.

    PubMed

    Mitri, F G; Fellah, Z E A

    2014-01-01

    The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. Copyright © 2013 Elsevier B.V. All rights reserved.

  11. Simulations of Gaussian electron guns for RHIC electron lens

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pikin, A.

    Simulations of two versions of the electron gun for RHIC electron lens are presented. The electron guns have to generate an electron beam with Gaussian radial profile of the electron beam density. To achieve the Gaussian electron emission profile on the cathode we used a combination of the gun electrodes and shaping of the cathode surface. Dependence of electron gun performance parameters on the geometry of electrodes and the margins for electrodes positioning are presented.

  12. Direct Importance Estimation with Gaussian Mixture Models

    NASA Astrophysics Data System (ADS)

    Yamada, Makoto; Sugiyama, Masashi

    The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.

  13. Poly-Gaussian model of randomly rough surface in rarefied gas flow

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Aksenova, Olga A.; Khalidov, Iskander A.

    2014-12-09

    Surface roughness is simulated by the model of non-Gaussian random process. Our results for the scattering of rarefied gas atoms from a rough surface using modified approach to the DSMC calculation of rarefied gas flow near a rough surface are developed and generalized applying the poly-Gaussian model representing probability density as the mixture of Gaussian densities. The transformation of the scattering function due to the roughness is characterized by the roughness operator. Simulating rough surface of the walls by the poly-Gaussian random field expressed as integrated Wiener process, we derive a representation of the roughness operator that can be appliedmore » in numerical DSMC methods as well as in analytical investigations.« less

  14. Gaussian processes: a method for automatic QSAR modeling of ADME properties.

    PubMed

    Obrezanova, Olga; Csanyi, Gabor; Gola, Joelle M R; Segall, Matthew D

    2007-01-01

    In this article, we discuss the application of the Gaussian Process method for the prediction of absorption, distribution, metabolism, and excretion (ADME) properties. On the basis of a Bayesian probabilistic approach, the method is widely used in the field of machine learning but has rarely been applied in quantitative structure-activity relationship and ADME modeling. The method is suitable for modeling nonlinear relationships, does not require subjective determination of the model parameters, works for a large number of descriptors, and is inherently resistant to overtraining. The performance of Gaussian Processes compares well with and often exceeds that of artificial neural networks. Due to these features, the Gaussian Processes technique is eminently suitable for automatic model generation-one of the demands of modern drug discovery. Here, we describe the basic concept of the method in the context of regression problems and illustrate its application to the modeling of several ADME properties: blood-brain barrier, hERG inhibition, and aqueous solubility at pH 7.4. We also compare Gaussian Processes with other modeling techniques.

  15. Trapping of a micro-bubble by non-paraxial Gaussian beam: computation using the FDTD method.

    PubMed

    Sung, Seung-Yong; Lee, Yong-Gu

    2008-03-03

    Optical forces on a micro-bubble were computed using the Finite Difference Time Domain method. Non-paraxial Gaussian beam equation was used to represent the incident laser with high numerical aperture, common in optical tweezers. The electromagnetic field distribution around a micro-bubble was computed using FDTD method and the electromagnetic stress tensor on the surface of a micro-bubble was used to compute the optical forces. By the analysis of the computational results, interesting relations between the radius of the circular trapping ring and the corresponding stability of the trap were found.

  16. Perturbative Gaussianizing transforms for cosmological fields

    NASA Astrophysics Data System (ADS)

    Hall, Alex; Mead, Alexander

    2018-01-01

    Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

  17. A technique for simultaneous detection of individual vortex states of Laguerre-Gaussian beams transmitted through an aqueous suspension of microparticles

    NASA Astrophysics Data System (ADS)

    Khonina, S. N.; Karpeev, S. V.; Paranin, V. D.

    2018-06-01

    A technique for simultaneous detection of individual vortex states of the beams propagating in a randomly inhomogeneous medium is proposed. The developed optical system relies on the correlation method that is invariant to the beam wandering. The intensity distribution formed at the optical system output does not require digital processing. The proposed technique based on a multi-order phase diffractive optical element (DOE) is studied numerically and experimentally. The developed detection technique is used for the analysis of Laguerre-Gaussian vortex beams propagating under conditions of intense absorption, reflection, and scattering in transparent and opaque microparticles in aqueous suspensions. The performed experimental studies confirm the relevance of the vortex phase dependence of a laser beam under conditions of significant absorption, reflection, and scattering of the light.

  18. Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization.

    PubMed

    Mata-Mendez, O; Avendaño, J; Chavez-Rivas, F

    2006-08-01

    Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered. The far-field diffraction patterns, the transmission coefficient tau, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Ntau/lambda, valid in the scalar region, is extended to the TM polarization case in the vectorial region, lambda being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength lambda. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.

  19. Effects of aperture averaging and beam width on a partially coherent Gaussian beam over free-space optical links with turbulence and pointing errors.

    PubMed

    Lee, It Ee; Ghassemlooy, Zabih; Ng, Wai Pang; Khalighi, Mohammad-Ali; Liaw, Shien-Kuei

    2016-01-01

    Joint effects of aperture averaging and beam width on the performance of free-space optical communication links, under the impairments of atmospheric loss, turbulence, and pointing errors (PEs), are investigated from an information theory perspective. The propagation of a spatially partially coherent Gaussian-beam wave through a random turbulent medium is characterized, taking into account the diverging and focusing properties of the optical beam as well as the scintillation and beam wander effects. Results show that a noticeable improvement in the average channel capacity can be achieved with an enlarged receiver aperture in the moderate-to-strong turbulence regime, even without knowledge of the channel state information. In particular, it is observed that the optimum beam width can be reduced to improve the channel capacity, albeit the presence of scintillation and PEs, given that either one or both of these adverse effects are least dominant. We show that, under strong turbulence conditions, the beam width increases linearly with the Rytov variance for a relatively smaller PE loss but changes exponentially with steeper increments for higher PE losses. Our findings conclude that the optimal beam width is dependent on the combined effects of turbulence and PEs, and this parameter should be adjusted according to the varying atmospheric channel conditions. Therefore, we demonstrate that the maximum channel capacity is best achieved through the introduction of a larger receiver aperture and a beam-width optimization technique.

  20. Spin angular momentum transfer from TEM00 focused Gaussian beams to negative refractive index spherical particles

    PubMed Central

    Ambrosio, Leonardo A.; Hernández-Figueroa, Hugo E.

    2011-01-01

    We investigate optical torques over absorbent negative refractive index spherical scatterers under the influence of linear and circularly polarized TEM00 focused Gaussian beams, in the framework of the generalized Lorenz-Mie theory with the integral localized approximation. The fundamental differences between optical torques due to spin angular momentum transfer in positive and negative refractive index optical trapping are outlined, revealing the effect of the Mie scattering coefficients in one of the most fundamental properties in optical trapping systems. PMID:21833372

  1. A trichrome beam model for biological dose calculation in scanned carbon-ion radiotherapy treatment planning.

    PubMed

    Inaniwa, T; Kanematsu, N

    2015-01-07

    In scanned carbon-ion (C-ion) radiotherapy, some primary C-ions undergo nuclear reactions before reaching the target and the resulting particles deliver doses to regions at a significant distance from the central axis of the beam. The effects of these particles on physical dose distribution are accounted for in treatment planning by representing the transverse profile of the scanned C-ion beam as the superposition of three Gaussian distributions. In the calculation of biological dose distribution, however, the radiation quality of the scanned C-ion beam has been assumed to be uniform over its cross-section, taking the average value over the plane at a given depth (monochrome model). Since these particles, which have relatively low radiation quality, spread widely compared to the primary C-ions, the radiation quality of the beam should vary with radial distance from the central beam axis. To represent its transverse distribution, we propose a trichrome beam model in which primary C-ions, heavy fragments with atomic number Z ≥ 3, and light fragments with Z ≤ 2 are assigned to the first, second, and third Gaussian components, respectively. Assuming a realistic beam-delivery system, we performed computer simulations using Geant4 Monte Carlo code for analytical beam modeling of the monochrome and trichrome models. The analytical beam models were integrated into a treatment planning system for scanned C-ion radiotherapy. A target volume of 20  ×  20  ×  40 mm(3) was defined within a water phantom. A uniform biological dose of 2.65 Gy (RBE) was planned for the target with the two beam models based on the microdosimetric kinetic model (MKM). The plans were recalculated with Geant4, and the recalculated biological dose distributions were compared with the planned distributions. The mean target dose of the recalculated distribution with the monochrome model was 2.72 Gy (RBE), while the dose with the trichrome model was 2.64 Gy (RBE). The monochrome

  2. A trichrome beam model for biological dose calculation in scanned carbon-ion radiotherapy treatment planning

    NASA Astrophysics Data System (ADS)

    Inaniwa, T.; Kanematsu, N.

    2015-01-01

    In scanned carbon-ion (C-ion) radiotherapy, some primary C-ions undergo nuclear reactions before reaching the target and the resulting particles deliver doses to regions at a significant distance from the central axis of the beam. The effects of these particles on physical dose distribution are accounted for in treatment planning by representing the transverse profile of the scanned C-ion beam as the superposition of three Gaussian distributions. In the calculation of biological dose distribution, however, the radiation quality of the scanned C-ion beam has been assumed to be uniform over its cross-section, taking the average value over the plane at a given depth (monochrome model). Since these particles, which have relatively low radiation quality, spread widely compared to the primary C-ions, the radiation quality of the beam should vary with radial distance from the central beam axis. To represent its transverse distribution, we propose a trichrome beam model in which primary C-ions, heavy fragments with atomic number Z ≥ 3, and light fragments with Z ≤ 2 are assigned to the first, second, and third Gaussian components, respectively. Assuming a realistic beam-delivery system, we performed computer simulations using Geant4 Monte Carlo code for analytical beam modeling of the monochrome and trichrome models. The analytical beam models were integrated into a treatment planning system for scanned C-ion radiotherapy. A target volume of 20  ×  20  ×  40 mm3 was defined within a water phantom. A uniform biological dose of 2.65 Gy (RBE) was planned for the target with the two beam models based on the microdosimetric kinetic model (MKM). The plans were recalculated with Geant4, and the recalculated biological dose distributions were compared with the planned distributions. The mean target dose of the recalculated distribution with the monochrome model was 2.72 Gy (RBE), while the dose with the trichrome model was 2.64 Gy (RBE). The monochrome model

  3. Theoretical model of a polarization diffractive elements for the light beams conversion holographic formation in PDLCs

    NASA Astrophysics Data System (ADS)

    Sharangovich, Sergey N.; Semkin, Artem O.

    2017-12-01

    In this work a theoretical model of the holographic formation of the polarization diffractive optical elements for the transformation of Gaussian light beams into Bessel-like ones in polymer-dispersed liquid crystals (PDLC) is developed. The model is based on solving the equations of photo-induced Fredericks transition processes for polarization diffractive elements formation by orthogonally polarized light beams with inhomogeneous amplitude and phase profiles. The results of numerical simulation of the material's dielectric tensor changing due to the structure's formation process are presented for various recording beams' polarization states. Based on the results of numerical simulation, the ability to form the diffractive optical elements for light beams transformation by the polarization holography methods is shown.

  4. Effect of turbulence on the beam quality of apertured partially coherent beams.

    PubMed

    Ji, Xiaoling; Ji, Guangming

    2008-06-01

    The effects of turbulence on the beam quality of apertured partially coherent beams have been studied both analytically and numerically. Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, closed-form expressions for the average intensity, mean-squared beam width, power in the bucket, beta parameter, and Strehl ratio of apertured partially coherent beams propagating through atmospheric turbulence are derived. It is shown that the smaller the beam truncation parameter is, the less affected by turbulence the apertured partially coherent beams are. Furthermore, the apertured partially coherent beams are less sensitive to the effects of turbulence than unapertured ones. The main results are interpreted physically.

  5. Non-Gaussian PDF Modeling of Turbulent Boundary Layer Fluctuating Pressure Excitation

    NASA Technical Reports Server (NTRS)

    Steinwolf, Alexander; Rizzi, Stephen A.

    2003-01-01

    The purpose of the study is to investigate properties of the probability density function (PDF) of turbulent boundary layer fluctuating pressures measured on the exterior of a supersonic transport aircraft. It is shown that fluctuating pressure PDFs differ from the Gaussian distribution even for surface conditions having no significant discontinuities. The PDF tails are wider and longer than those of the Gaussian model. For pressure fluctuations upstream of forward-facing step discontinuities and downstream of aft-facing step discontinuities, deviations from the Gaussian model are more significant and the PDFs become asymmetrical. Various analytical PDF distributions are used and further developed to model this behavior.

  6. Analysis of Flow and Transport in non-Gaussian Heterogeneous Formations Using a Generalized Sub-Gaussian Model

    NASA Astrophysics Data System (ADS)

    Guadagnini, A.; Riva, M.; Neuman, S. P.

    2016-12-01

    Environmental quantities such as log hydraulic conductivity (or transmissivity), Y(x) = ln K(x), and their spatial (or temporal) increments, ΔY, are known to be generally non-Gaussian. Documented evidence of such behavior includes symmetry of increment distributions at all separation scales (or lags) between incremental values of Y with sharp peaks and heavy tails that decay asymptotically as lag increases. This statistical scaling occurs in porous as well as fractured media characterized by either one or a hierarchy of spatial correlation scales. In hierarchical media one observes a range of additional statistical ΔY scaling phenomena, all of which are captured comprehensibly by a novel generalized sub-Gaussian (GSG) model. In this model Y forms a mixture Y(x) = U(x) G(x) of single- or multi-scale Gaussian processes G having random variances, U being a non-negative subordinator independent of G. Elsewhere we developed ways to generate unconditional and conditional random realizations of isotropic or anisotropic GSG fields which can be embedded in numerical Monte Carlo flow and transport simulations. Here we present and discuss expressions for probability distribution functions of Y and ΔY as well as their lead statistical moments. We then focus on a simple flow setting of mean uniform steady state flow in an unbounded, two-dimensional domain, exploring ways in which non-Gaussian heterogeneity affects stochastic flow and transport descriptions. Our expressions represent (a) lead order autocovariance and cross-covariance functions of hydraulic head, velocity and advective particle displacement as well as (b) analogues of preasymptotic and asymptotic Fickian dispersion coefficients. We compare them with corresponding expressions developed in the literature for Gaussian Y.

  7. Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path

    NASA Astrophysics Data System (ADS)

    Tian, Huanhuan; Xu, Yonggen; Yang, Ting; Ma, Zairu; Wang, Shijian; Dan, Youquan

    2017-02-01

    Based on the extended Huygens-Fresnel principal and the Wigner distribution function, the root mean square (rms) angular width and propagation factor (M2-factor) of partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam propagating through atmospheric turbulence along a slant path are studied in detail. Analytical formulae of the rms angular width and M2-factor of PCAEHG beam are derived. Our results show that the rms angular width increases with increasing of wavelength and zenith angle and with decreasing of transverse coherence length, beam waist sizes and inner scale. The M2-factor increases with increasing of zenith angle and with decreasing of wavelength, transverse coherence length, beam waist sizes and inner scale. The saturation propagation distances (SPDs) increase as zenith angle increases. The numerical calculations also indicate that the SPDs of rms angular width and M2-factor for uplink slant paths with zenith angle of π/12 are about 0.2 and 20 km, respectively.

  8. SU-C-BRC-04: Efficient Dose Calculation Algorithm for FFF IMRT with a Simplified Bivariate Gaussian Source Model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Li, F; Park, J; Barraclough, B

    2016-06-15

    Purpose: To develop an efficient and accurate independent dose calculation algorithm with a simplified analytical source model for the quality assurance and safe delivery of Flattening Filter Free (FFF)-IMRT on an Elekta Versa HD. Methods: The source model consisted of a point source and a 2D bivariate Gaussian source, respectively modeling the primary photons and the combined effect of head scatter, monitor chamber backscatter and collimator exchange effect. The in-air fluence was firstly calculated by back-projecting the edges of beam defining devices onto the source plane and integrating the visible source distribution. The effect of the rounded MLC leaf end,more » tongue-and-groove and interleaf transmission was taken into account in the back-projection. The in-air fluence was then modified with a fourth degree polynomial modeling the cone-shaped dose distribution of FFF beams. Planar dose distribution was obtained by convolving the in-air fluence with a dose deposition kernel (DDK) consisting of the sum of three 2D Gaussian functions. The parameters of the source model and the DDK were commissioned using measured in-air output factors (Sc) and cross beam profiles, respectively. A novel method was used to eliminate the volume averaging effect of ion chambers in determining the DDK. Planar dose distributions of five head-and-neck FFF-IMRT plans were calculated and compared against measurements performed with a 2D diode array (MapCHECK™) to validate the accuracy of the algorithm. Results: The proposed source model predicted Sc for both 6MV and 10MV with an accuracy better than 0.1%. With a stringent gamma criterion (2%/2mm/local difference), the passing rate of the FFF-IMRT dose calculation was 97.2±2.6%. Conclusion: The removal of the flattening filter represents a simplification of the head structure which allows the use of a simpler source model for very accurate dose calculation. The proposed algorithm offers an effective way to ensure the safe delivery

  9. Propagation of a general-type beam through a truncated fractional Fourier transform optical system.

    PubMed

    Zhao, Chengliang; Cai, Yangjian

    2010-03-01

    Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

  10. Correlation singularities in partially coherent electromagnetic beams.

    PubMed

    Raghunathan, Shreyas B; Schouten, Hugo F; Visser, Taco D

    2012-10-15

    We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for both interference experiments and correlation of intensity fluctuation measurements performed with such beams.

  11. Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Stein, Michael

    Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead tomore » predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over

  12. Model for non-Gaussian intraday stock returns

    NASA Astrophysics Data System (ADS)

    Gerig, Austin; Vicente, Javier; Fuentes, Miguel A.

    2009-12-01

    Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database for several stocks traded on the London Stock Exchange. We provide evidence that the return distribution for these stocks is non-Gaussian and similar in shape and that the distribution appears stable over intraday time scales. We explain these results by assuming the volatility of returns is constant intraday but varies over longer periods such that its inverse square follows a gamma distribution. This produces returns that are Student distributed for intraday time scales. The predicted results show excellent agreement with the data for all stocks in our study and over all regions of the return distribution.

  13. Experimental Method of Generating Electromagnetic Gaussian Schell-model Beams

    DTIC Science & Technology

    2015-03-26

    attracted special attention for the potential use in free-space optical communications, imaging through turbulence , and remote sensing applications [11...successful experiment demonstrated a reduction in scintillation of a completely unpolarized EGSM beam propagated through simulated 1 atmospheric turbulence [1...propagate through the atmosphere using either an atmospheric phase wheel or using additional SLMs to display atmospheric phase screens. Further, the source

  14. Bessel-Gauss beams as rigorous solutions of the Helmholtz equation.

    PubMed

    April, Alexandre

    2011-10-01

    The study of the nonparaxial propagation of optical beams has received considerable attention. In particular, the so-called complex-source/sink model can be used to describe strongly focused beams near the beam waist, but this method has not yet been applied to the Bessel-Gauss (BG) beam. In this paper, the complex-source/sink solution for the nonparaxial BG beam is expressed as a superposition of nonparaxial elegant Laguerre-Gaussian beams. This provides a direct way to write the explicit expression for a tightly focused BG beam that is an exact solution of the Helmholtz equation. It reduces correctly to the paraxial BG beam, the nonparaxial Gaussian beam, and the Bessel beam in the appropriate limits. The analytical expression can be used to calculate the field of a BG beam near its waist, and it may be useful in investigating the features of BG beams under tight focusing conditions.

  15. MO-FG-CAMPUS-TeP3-03: Calculation of Proton Pencil Beam Properties with Full Beamline Model in TOPAS

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wulff, J; Abel, E

    2016-06-15

    Purpose: Introducing Monte Carlo based dose calculation algorithms into proton therapy planning systems (TPS) leads to improved accuracy. However accurate modelling of the proton pencil beam impinging the patient is necessary. Current approaches rely on measurement-driven reconstruction of phase-space and spectrum properties, typically constrained to analytical model functions. In this study a detailed Monte Carlo model of the complete cyclotron-based delivery system was created with the aim of providing more representative beam properties at treatment position. Methods: A model of the Varian Probeam proton system from the cyclotron exit to isocenter was constructed in the TOPAS Monte Carlo framework. Themore » beam evolution through apertures and magnetic elements was validated using Transport/Turtle calculations and additionally against measurements from the Probeam™ system at Scripps Proton Therapy Center (SPTC) in San Diego, CA. A voxelized water phantom at isocenter allowed for comparison of the dose-depth curve from the Probeam model with that of a corresponding Gaussian beam over the entire energy range (70–240 MeV). Measurements of relative beam fluence cross-profiles and depth-dose curves at and around isocenter were also compared to the MC results. Results: The simulated TOPAS beam envelope was found to agree with both the Transport/Turtle and measurements to within 5% for most of the beamline. The MC predicted energy spectrum at isocenter was found to deviate increasingly from Gaussian at energies below 160 MeV. The corresponding effects on the depth dose curve agreed well with measurements. Conclusion: Given the flexibility of TOPAS and available details of the delivery system, an accurate characterization of a proton pencil beam at isocenter is possible. Incorporation of the MC derived properties of the proton pencil beam can eliminate analytical approximations and ultimately increase treatment plan accuracy and quality. Both authors are

  16. SU-F-T-138: Commissioning and Evaluating Dose Computation Models for a Dedicated Proton Line Scanning Beam Nozzle in Eclipse Treatment Planning System

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tsai, P; Chang Gung University, Taoyuan, Taiwan; Huang, H

    Purpose: In this study, we present an effective method to derive low dose envelope of the proton in-air spot fluence at beam positions other than the isocenter to reduce amount of measurements required for planning commission. Also, we demonstrate commissioning and validation results of this method to the Eclipse treatment planning system (version 13.0.29) for a Sumitomo dedicated proton line scanning beam nozzle. Methods: The in-air spot profiles at five beam-axis positions (±200, ±100 and 0 mm) were obtained in trigger mode using a MP3 Water tank (PTW-Freiburg) and a pinpoint ionization chamber (model 31014, PTW-Freiburg). Low dose envelope (belowmore » 1% of the center dose) of the spot profile at isocenter was obtained by repeated point measurements to minimize dosimetry uncertainty. The double Gaussian (DG) model was used to fit and obtain optimal σ1, σ2 and their corresponding weightings through our in-house MATLAB (Mathworks) program. σ1, σ2 were assumed to expand linearly along the beam axis from a virtual source position calculated by back projecting fitted sigmas from the single Gaussian (SG) model. Absolute doses in water were validated using an Advanced Markus chamber at the depth of 2cm with Pristine Peak (BP) R90d ranging from 5–32 cm for 10×10 cm2 scanned fields. The field size factors were verified with square fields from 2 to 20 cm at 2cm and before BP depth. Results: The absolute dose outputs were found to be within ±3%. For field size factor, the agreement between calculated and measurement were within ±2% at 2cm and ±3% before BP, except for the field size below 2×2 cm2. Conclusion: The double Gaussian model was found to be sufficient for characterizing the Sumitomo dedicated proton line scanning nozzle. With our effective double Gaussian fitting method, we are able to save significant proton beam time with acceptable output accuracy.« less

  17. Self-focusing and defocusing of Gaussian laser beams in collisional inhomogeneous plasmas with linear density and temperature ramps

    NASA Astrophysics Data System (ADS)

    Hashemzadeh, M.

    2018-01-01

    Self-focusing and defocusing of Gaussian laser beams in collisional inhomogeneous plasmas are investigated in the presence of various laser intensities and linear density and temperature ramps. Considering the ponderomotive force and using the momentum transfer and energy equations, the nonlinear electron density is derived. Taking into account the paraxial approximation and nonlinear electron density, a nonlinear differential equation, governing the focusing and defocusing of the laser beam, is obtained. Results show that in the absence of ramps the laser beam is focused between a minimum and a maximum value of laser intensity. For a certain value of laser intensity and initial electron density, the self-focusing process occurs in a temperature range which reaches its maximum at turning point temperature. However, the laser beam is converged in a narrow range for various amounts of initial electron density. It is indicated that the σ2 parameter and its sign can affect the self-focusing process for different values of laser intensity, initial temperature, and initial density. Finally, it is found that although the electron density ramp-down diverges the laser beam, electron density ramp-up improves the self-focusing process.

  18. On beam models and their paraxial approximation

    NASA Astrophysics Data System (ADS)

    Waters, W. J.; King, B.

    2018-01-01

    We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.

  19. Gaussian-reflectivity mirror resonator for a high-power transverse-flow CO2 laser.

    PubMed

    Ling, Dongxiong; Chen, Junruo; Li, Junchang

    2006-05-01

    A Gaussian-reflectivity mirror resonator is proposed to achieve high-quality laser beams. To analyze the laser fields in a Gaussian-reflectivity mirror resonator, the diffraction integral equations of a Gaussian-reflectivity mirror resonator are converted to the finite-sum matrix equations. Consequently, according to the Fox-Li laser self-reproducing principle, we describe the mode fields and their losses in the proposed resonator as eigenvectors and eigenvalues of a transfer matrix. The conclusion can be drawn from the numerical results that, if a Gaussian-reflectivity mirror is adopted for a plano-concave resonator, a fundamental mode can easily be obtained from a transverse-flow CO2 laser and high-quality laser beams can be expected.

  20. Data from fitting Gaussian process models to various data sets using eight Gaussian process software packages.

    PubMed

    Erickson, Collin B; Ankenman, Bruce E; Sanchez, Susan M

    2018-06-01

    This data article provides the summary data from tests comparing various Gaussian process software packages. Each spreadsheet represents a single function or type of function using a particular input sample size. In each spreadsheet, a row gives the results for a particular replication using a single package. Within each spreadsheet there are the results from eight Gaussian process model-fitting packages on five replicates of the surface. There is also one spreadsheet comparing the results from two packages performing stochastic kriging. These data enable comparisons between the packages to determine which package will give users the best results.

  1. Laser Beam Shaping

    NASA Astrophysics Data System (ADS)

    Aït-Ameur, Kamel; Passilly, Nicolas; de Saint Denis, R.; Fromager, Michaël

    2008-09-01

    We consider the promising properties of very simple Diffractive Optical Elements (DOE) for reshaping the intensity profile of a laser beam. The first type of DOE that we have considered is a phase aperture which consists in a transparent plate with a circular relief introducing a π phase shift in the central region of the incident beam. The phase aperture is able to convert a Gaussian beam into a super-Gaussian, a ring-shaped or a doughnut profile. The second DOE that has been considered is an adjustable axicon able to transform a Gaussian laser beam into a dark hollow beam or a Bessel-Gauss beam. The desired conical geometry is obtained from a deformable mirror formed by a 2 inches, 0.25mm thick silicon wafer supported by a standard 2 inches optical mount. To achieve the adequate deformation a small metallic ball pushes the back of the mirror wafer. The realized shape is monitored with a Shack-Hartmann wave-front sensor and it is shown that conical shape cannot be achieved. Nevertheless, recorded wave fronts exhibit important third order spherical aberration able to achieve beam profile transformation as conical lenses.

  2. 3D Gaussian Beam Modeling

    DTIC Science & Technology

    2011-09-01

    optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

  3. Effects of beam irregularity on uniform scanning

    NASA Astrophysics Data System (ADS)

    Kim, Chang Hyeuk; Jang, Sea duk; Yang, Tae-Keun

    2016-09-01

    An active scanning beam delivery method has many advantages in particle beam applications. For the beam is to be successfully delivered to the target volume by using the active scanning technique, the dose uniformity must be considered and should be at least 2.5% in the case of therapy application. During beam irradiation, many beam parameters affect the 2-dimensional uniformity at the target layer. A basic assumption in the beam irradiation planning stage is that the shape of the beam is symmetric and follows a Gaussian distribution. In this study, a pure Gaussian-shaped beam distribution was distorted by adding parasitic Gaussian distribution. An appropriate uniform scanning condition was deduced by using a quantitative analysis based on the gamma value of the distorted beam and 2-dimensional uniformities.

  4. Truncated Gaussians as tolerance sets

    NASA Technical Reports Server (NTRS)

    Cozman, Fabio; Krotkov, Eric

    1994-01-01

    This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

  5. Coherent beam combination of fiber lasers with a strongly confined waveguide: numerical model.

    PubMed

    Tao, Rumao; Si, Lei; Ma, Yanxing; Zhou, Pu; Liu, Zejin

    2012-08-20

    Self-imaging properties of fiber lasers in a strongly confined waveguide (SCW) and their application in coherent beam combination (CBC) are studied theoretically. Analytical formulas are derived for the positions, amplitudes, and phases of the N images at the end of an SCW, which is important for quantitative analysis of waveguide CBC. The formulas are verified with experimental results and numerical simulation of a finite difference beam propagation method (BPM). The error of our analytical formulas is less than 6%, which can be reduced to less than 1.5% with Goos-Hahnchen penetration depth considered. Based on the theoretical model and BPM, we studied the combination of two laser beams based on an SCW. The effects of the waveguide refractive index and Gaussian beam waist are studied. We also simulated the CBC of nine and 16 fiber lasers, and a single beam without side lobes was achieved.

  6. Modeling Sea-Level Change using Errors-in-Variables Integrated Gaussian Processes

    NASA Astrophysics Data System (ADS)

    Cahill, Niamh; Parnell, Andrew; Kemp, Andrew; Horton, Benjamin

    2014-05-01

    We perform Bayesian inference on historical and late Holocene (last 2000 years) rates of sea-level change. The data that form the input to our model are tide-gauge measurements and proxy reconstructions from cores of coastal sediment. To accurately estimate rates of sea-level change and reliably compare tide-gauge compilations with proxy reconstructions it is necessary to account for the uncertainties that characterize each dataset. Many previous studies used simple linear regression models (most commonly polynomial regression) resulting in overly precise rate estimates. The model we propose uses an integrated Gaussian process approach, where a Gaussian process prior is placed on the rate of sea-level change and the data itself is modeled as the integral of this rate process. The non-parametric Gaussian process model is known to be well suited to modeling time series data. The advantage of using an integrated Gaussian process is that it allows for the direct estimation of the derivative of a one dimensional curve. The derivative at a particular time point will be representative of the rate of sea level change at that time point. The tide gauge and proxy data are complicated by multiple sources of uncertainty, some of which arise as part of the data collection exercise. Most notably, the proxy reconstructions include temporal uncertainty from dating of the sediment core using techniques such as radiocarbon. As a result of this, the integrated Gaussian process model is set in an errors-in-variables (EIV) framework so as to take account of this temporal uncertainty. The data must be corrected for land-level change known as glacio-isostatic adjustment (GIA) as it is important to isolate the climate-related sea-level signal. The correction for GIA introduces covariance between individual age and sea level observations into the model. The proposed integrated Gaussian process model allows for the estimation of instantaneous rates of sea-level change and accounts for all

  7. Optimum Laser Beam Characteristics for Achieving Smoother Ablations in Laser Vision Correction.

    PubMed

    Verma, Shwetabh; Hesser, Juergen; Arba-Mosquera, Samuel

    2017-04-01

    Controversial opinions exist regarding optimum laser beam characteristics for achieving smoother ablations in laser-based vision correction. The purpose of the study was to outline a rigorous simulation model for simulating shot-by-shot ablation process. The impact of laser beam characteristics like super Gaussian order, truncation radius, spot geometry, spot overlap, and lattice geometry were tested on ablation smoothness. Given the super Gaussian order, the theoretical beam profile was determined following Lambert-Beer model. The intensity beam profile originating from an excimer laser was measured with a beam profiler camera. For both, the measured and theoretical beam profiles, two spot geometries (round and square spots) were considered, and two types of lattices (reticular and triangular) were simulated with varying spot overlaps and ablated material (cornea or polymethylmethacrylate [PMMA]). The roughness in ablation was determined by the root-mean-square per square root of layer depth. Truncating the beam profile increases the roughness in ablation, Gaussian profiles theoretically result in smoother ablations, round spot geometries produce lower roughness in ablation compared to square geometry, triangular lattices theoretically produce lower roughness in ablation compared to the reticular lattice, theoretically modeled beam profiles show lower roughness in ablation compared to the measured beam profile, and the simulated roughness in ablation on PMMA tends to be lower than on human cornea. For given input parameters, proper optimum parameters for minimizing the roughness have been found. Theoretically, the proposed model can be used for achieving smoothness with laser systems used for ablation processes at relatively low cost. This model may improve the quality of results and could be directly applied for improving postoperative surface quality.

  8. Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

    NASA Technical Reports Server (NTRS)

    Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

    2015-01-01

    When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating

  9. Interaction of Airy-Gaussian beams in saturable media

    NASA Astrophysics Data System (ADS)

    Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei

    2016-08-01

    Based on the nonlinear Schrödinger equation, the interactions of the two Airy-Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy-Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy-Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.

  10. Gaussian Beam Intensity Flattener

    NASA Technical Reports Server (NTRS)

    Griffin, DeVon W.

    1998-01-01

    The goal of this investigation was to use commercial elements and extend the correction to a 1/e(sup 2) diameter of 3 mm over long propagation distances. Shafer discussed the use of spherical elements to generate a uniform beam to the 1/e diameter.

  11. Light dosimetry for focused and defocused beam irradiation in multi-layered tissue models

    NASA Astrophysics Data System (ADS)

    Petrova, Kremena S.; Stoykova, Elena V.

    2006-09-01

    Treatment of acupuncture points, trigger points, joint inflammations in low level laser therapy as well as various applications of lasers for treatment of soft tissues in dental medicine, require irradiation by a narrow converging laser beam. The aim of this study is to compare light delivery produced by focused or defocused narrow beam irradiation in a multi-layered skin tissue model at increasing depth of the target. The task is solved by 3-D Monte-Carlo simulation for matched and mismatched refractive indices at the tissue/ambient medium interface. The modeled light beams have a circular cross-section at the tissue entrance with uniform or Gaussian intensity distribution. Three are the tissue models used in simulation : i) a bloodless skin layer; ii) a bloodless skin layer with embedded scattering object; iii) a skin layer with small blood vessels of varying size, which are modeled as infinite cylinders parallel to the tissue surface located at different depths. Optical properties (absorption coefficient, scattering coefficient, anisotropy factor, g, and index of refraction) of different tissue constituents are chosen from the literature.

  12. Shaping the beam profile of a partially coherent beam by a phase aperture

    NASA Astrophysics Data System (ADS)

    Wu, Gaofeng; Cai, Yangjian; Chen, Jun

    2011-08-01

    By use of a tensor method, an analytical formula for a partially coherent Gaussian Schell-model (GSM) beam truncated by a circular phase aperture propagating through a paraxial ABCD optical system is derived. The propagation properties of a GSM beam truncated by a circular phase aperture in free space are studied numerically. It is found that the circular phase aperture can be used to shape the beam profile of a GSM beam and generate partially coherent dark hollow or flat-topped beam, which is useful in many applications, e.g., optical trapping, free-space optical communication, and material thermal processing. The propagation factor of a GSM beam truncated by a circular phase aperture is also analyzed.

  13. Adaptive conversion of a high-order mode beam into a near-diffraction-limited beam.

    PubMed

    Zhao, Haichuan; Wang, Xiaolin; Ma, Haotong; Zhou, Pu; Ma, Yanxing; Xu, Xiaojun; Zhao, Yijun

    2011-08-01

    We present a new method for efficiently transforming a high-order mode beam into a nearly Gaussian beam with much higher beam quality. The method is based on modulation of phases of different lobes by stochastic parallel gradient descent algorithm and coherent addition after phase flattening. We demonstrate the method by transforming an LP11 mode into a nearly Gaussian beam. The experimental results reveal that the power in the diffraction-limited bucket in the far field is increased by more than a factor of 1.5.

  14. Gaussian discriminating strength

    NASA Astrophysics Data System (ADS)

    Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.

    2015-10-01

    We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.

  15. Gaussian entanglement distribution via satellite

    NASA Astrophysics Data System (ADS)

    Hosseinidehaj, Nedasadat; Malaney, Robert

    2015-02-01

    In this work we analyze three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme, the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the tradeoff between space-based engineering complexity and the rate of ground-station entanglement generation.

  16. Self-pumped Gaussian beam-coupling and stimulated backscatter due to reflection gratings in a photorefractive material

    NASA Astrophysics Data System (ADS)

    Saleh, Mohammad Abu

    2007-05-01

    When overlapping monochromatic light beams interfere in a photorefractive material, the resulting intensity fringes create a spatially modulated charge distribution. The resulting refractive index grating may cause power transfer from one beam (the pump) to the other beam (the signal). In a special case of the reflection grating geometry, the Fresnel reflection of the pump beam from the rear surface of the crystal is used as the signal beam. It has been noted that for this self-pumped, contra-directional two-beam coupling (SPCD-TBC) geometry, the coupling efficiency seems to be strongly dependent on the focal position and spot size, which is attributed to diffraction and the resulting change in the spatial overlaps between the pump and signal. In this work a full diffraction based simulation of SPCD-TBC for a Gaussian beam is developed with a novel algorithm. In a related context involving reflection gratings, a particular phenomenon named six-wave mixing has received some interest in the photorefractive research. The generation of multiple waves during near-oblique incidence of a 532 nm weakly focused laser light on photorefractive iron doped lithium niobate in a typical reflection geometry configuration is studied. It is shown that these waves are produced through two-wave coupling (self-diffraction) and four-wave mixing (parametric diffraction). One of these waves, the stimulated photorefractive backscatter produced from parametric diffraction, contains the self-phase conjugate. The dynamics of six-wave mixing, and their dependence on crystal parameters, angle of incidence, and pump power are analyzed. A novel order analysis of the interaction equations provides further insight into experimental observations in the steady state. The quality of the backscatter is evaluated through image restoration, interference experiments, and visibility measurement. Reduction of two-wave coupling may significantly improve the quality of the self-phase conjugate.

  17. Topology in two dimensions. IV - CDM models with non-Gaussian initial conditions

    NASA Astrophysics Data System (ADS)

    Coles, Peter; Moscardini, Lauro; Plionis, Manolis; Lucchin, Francesco; Matarrese, Sabino; Messina, Antonio

    1993-02-01

    The results of N-body simulations with both Gaussian and non-Gaussian initial conditions are used here to generate projected galaxy catalogs with the same selection criteria as the Shane-Wirtanen counts of galaxies. The Euler-Poincare characteristic is used to compare the statistical nature of the projected galaxy clustering in these simulated data sets with that of the observed galaxy catalog. All the models produce a topology dominated by a meatball shift when normalized to the known small-scale clustering properties of galaxies. Models characterized by a positive skewness of the distribution of primordial density perturbations are inconsistent with the Lick data, suggesting problems in reconciling models based on cosmic textures with observations. Gaussian CDM models fit the distribution of cell counts only if they have a rather high normalization but possess too low a coherence length compared with the Lick counts. This suggests that a CDM model with extra large scale power would probably fit the available data.

  18. Metasurface-assisted orbital angular momentum carrying Bessel-Gaussian Laser: proposal and simulation.

    PubMed

    Zhou, Nan; Wang, Jian

    2018-05-23

    Bessel-Gaussian beams have distinct properties of suppressed diffraction divergence and self-reconstruction. In this paper, we propose and simulate metasurface-assisted orbital angular momentum (OAM) carrying Bessel-Gaussian laser. The laser can be regarded as a Fabry-Perot cavity formed by one partially transparent output plane mirror and the other metasurface-based reflector mirror. The gain medium of Nd:YVO 4 enables the lasing wavelength at 1064 nm with a 808 nm laser serving as the pump. The sub-wavelength structure of metasurface facilitates flexible spatial light manipulation. The compact metasurface-based reflector provides combined phase functions of an axicon and a spherical mirror. By appropriately selecting the size of output mirror and inserting mode-selection element in the laser cavity, different orders of OAM-carrying Bessel-Gaussian lasing modes are achievable. The lasing Bessel-Gaussian 0 , Bessel-Gaussian 01 + , Bessel-Gaussian 02 + and Bessel-Gaussian 03 + modes have high fidelities of ~0.889, ~0.889, ~0.881 and ~0.879, respectively. The metasurface fabrication tolerance and the dependence of threshold power and output lasing power on the length of gain medium, beam radius of pump and transmittance of output mirror are also discussed. The obtained results show successful implementation of metasurface-assisted OAM-carrying Bessel-Gaussian laser with favorable performance. The metasurface-assisted OAM-carrying Bessel-Gaussian laser may find wide OAM-enabled communication and non-communication applications.

  19. Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

    NASA Astrophysics Data System (ADS)

    Červený, Vlastislav; Pšenčík, Ivan

    2017-08-01

    Integral superposition of Gaussian beams is a useful generalization of the standard ray theory. It removes some of the deficiencies of the ray theory like its failure to describe properly behaviour of waves in caustic regions. It also leads to a more efficient computation of seismic wavefields since it does not require the time-consuming two-point ray tracing. We present the formula for a high-frequency elementary Green function expressed in terms of the integral superposition of Gaussian beams for inhomogeneous, isotropic or anisotropic, layered structures, based on the dynamic ray tracing (DRT) in Cartesian coordinates. For the evaluation of the superposition formula, it is sufficient to solve the DRT in Cartesian coordinates just for the point-source initial conditions. Moreover, instead of seeking 3 × 3 paraxial matrices in Cartesian coordinates, it is sufficient to seek just 3 × 2 parts of these matrices. The presented formulae can be used for the computation of the elementary Green function corresponding to an arbitrary direct, multiply reflected/transmitted, unconverted or converted, independently propagating elementary wave of any of the three modes, P, S1 and S2. Receivers distributed along or in a vicinity of a target surface may be situated at an arbitrary part of the medium, including ray-theory shadow regions. The elementary Green function formula can be used as a basis for the computation of wavefields generated by various types of point sources (explosive, moment tensor).

  20. Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models

    NASA Astrophysics Data System (ADS)

    Yang, Linxiao; Fang, Jun; Duan, Huiping; Li, Hongbin; Zeng, Bing

    2018-06-01

    The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, a variational Bayesian method is developed for matrix completion, where the generalized approximate massage passing (GAMP) technique is embedded into the variational Bayesian inference in order to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over existing state-of-the-art matrix completion methods.

  1. Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam

    NASA Astrophysics Data System (ADS)

    Bokor, Nándor; Davidson, Nir

    2006-01-01

    The properties of the focal spot for 4pi focusing with radially polarized first-order Laguerre-Gaussian beams are calculated. It is shown that a focal spot that has an extremely sharp dark region at the center and an almost-perfect spherical symmetry can be achieved. When such a hollow dark spherical spot is used in 4pi fluorescence depletion microscopy, an axial FWHM spot size of ˜39 nm and a transverse FWHM spot size of ˜64 nm can be achieved simultaneously in a practical system.

  2. Generation of a hollow dark spherical spot by 4pi focusing of a radially polarized Laguerre-Gaussian beam.

    PubMed

    Bokor, Nándor; Davidson, Nir

    2006-01-15

    The properties of the focal spot for 4pi focusing with radially polarized first-order Laguerre-Gaussian beams are calculated. It is shown that a focal spot that has an extremely sharp dark region at the center and an almost-perfect spherical symmetry can be achieved. When such a hollow dark spherical spot is used in 4pi fluorescence depletion microscopy, an axial FWHM spot size of approximately 39 nm and a transverse FWHM spot size of approximately 64 nm can be achieved simultaneously in a practical system.

  3. Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

    NASA Astrophysics Data System (ADS)

    Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

    2012-09-01

    Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

  4. Arbitrage with fractional Gaussian processes

    NASA Astrophysics Data System (ADS)

    Zhang, Xili; Xiao, Weilin

    2017-04-01

    While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.

  5. Circularly symmetric cusped random beams in free space and atmospheric turbulence.

    PubMed

    Wang, Fei; Korotkova, Olga

    2017-03-06

    A class of random stationary, scalar sources producing cusped average intensity profiles (i.e. profiles with concave curvature) in the far field is introduced by modeling the source degree of coherence as a Fractional Multi-Gaussian-correlated Schell-Model (FMGSM) function with rotational symmetry. The average intensity (spectral density) generated by such sources is investigated on propagation in free space and isotropic and homogeneous atmospheric turbulence. It is found that the FMGSM beam can retain the cusped shape on propagation at least in weak or moderate turbulence regimes; however, strong turbulence completely suppresses the cusped intensity profile. Under the same atmospheric conditions the spectral density of the FMGSM beam at the receiver is found to be much higher than that of the conventional Gaussian Schell-model (GSM) beam within the narrow central area, implying that for relatively small collecting apertures the power-in-bucket of the FMGSM beam is higher than that of the GSM beam. Our results are of importance to energy delivery, Free-Space Optical communications and imaging in the atmosphere.

  6. Beam shaping with vortex beam generated by liquid crystal spatial light modulator

    NASA Astrophysics Data System (ADS)

    Gao, Yue; Liu, Ke; Sun, Zeng-yu; Guo, Lei; Gan, Yu

    2015-02-01

    An optical vortex is a beam of light with phase varying in a corkscrew-like manner along its direction of propagation and so has a helical wavefront. When such a vectorial vortex beam and the Gaussian beam with orthogonal polarization are focused by low NA lens, the Gaussian component causes a focal intensity distribution with a solid center and the vortex component causes a donut distribution with hollow dark center. The shape of the focus can be continuously varied by continuously adjusting the relative weight of the two components. Flat top focusing can be obtained under appropriate conditions. It is demonstrated through experiments with a liquid crystal spatial light modulator in such a beam, that flattop focus can be obtained by vectorial vortex beams with topological charge of +1 to achieve beam shaping vortex.

  7. Signal Partitioning Algorithm for Highly Efficient Gaussian Mixture Modeling in Mass Spectrometry

    PubMed Central

    Polanski, Andrzej; Marczyk, Michal; Pietrowska, Monika; Widlak, Piotr; Polanska, Joanna

    2015-01-01

    Mixture - modeling of mass spectra is an approach with many potential applications including peak detection and quantification, smoothing, de-noising, feature extraction and spectral signal compression. However, existing algorithms do not allow for automated analyses of whole spectra. Therefore, despite highlighting potential advantages of mixture modeling of mass spectra of peptide/protein mixtures and some preliminary results presented in several papers, the mixture modeling approach was so far not developed to the stage enabling systematic comparisons with existing software packages for proteomic mass spectra analyses. In this paper we present an efficient algorithm for Gaussian mixture modeling of proteomic mass spectra of different types (e.g., MALDI-ToF profiling, MALDI-IMS). The main idea is automated partitioning of protein mass spectral signal into fragments. The obtained fragments are separately decomposed into Gaussian mixture models. The parameters of the mixture models of fragments are then aggregated to form the mixture model of the whole spectrum. We compare the elaborated algorithm to existing algorithms for peak detection and we demonstrate improvements of peak detection efficiency obtained by using Gaussian mixture modeling. We also show applications of the elaborated algorithm to real proteomic datasets of low and high resolution. PMID:26230717

  8. Gaussian Filtering with Tapered Oil-Filled Photonic Bandgap Fibers

    NASA Astrophysics Data System (ADS)

    Brunetti, A. C.; Scolari, L.; Weirich, J.; Eskildsen, L.; Bellanca, G.; Bassi, P.; Bjarklev, A.

    2008-10-01

    A tunable Gaussian filter based on a tapered oil-filled photonic crystal fiber is demonstrated. The filter is centered at λ = 1364 nm with a bandwidth (FWHM) of 237nm. Tunability is achieved by changing the temperature of the filter. A shift of 210nm of the central wavelength has been observed by increasing the temperature from 25 °C to 100 °C. The measurements are compared to a simulated spectrum obtained by means of a vectorial Beam Propagation Method model.

  9. Generation of ultra-long pure magnetization needle and multiple spots by phase modulated doughnut Gaussian beam

    NASA Astrophysics Data System (ADS)

    Udhayakumar, M.; Prabakaran, K.; Rajesh, K. B.; Jaroszewicz, Z.; Belafhal, Abdelmajid; Velauthapillai, Dhayalan

    2018-06-01

    Based on vector diffraction theory and inverse Faraday effect (IFE), the light induced magnetization distribution of a tightly focused azimuthally polarized doughnut Gaussian beam superimposed with a helical phase and modulated by an optimized multi belt complex phase filter (MBCPF) is analysed numerically. It is noted that by adjusting the radii of different rings of the complex phase filter, one can achieve many novel magnetization focal distribution such as sub wavelength scale (0.29λ) and super long (52.2λ) longitudinal magnetic probe suitable for all optical magnetic recording and the formation of multiple magnetization chain with four, six and eight sub-wavelength spherical magnetization spots suitable for multiple trapping of magnetic particles are achieved.

  10. The Gaussian atmospheric transport model and its sensitivity to the joint frequency distribution and parametric variability.

    PubMed

    Hamby, D M

    2002-01-01

    Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.

  11. ATF neutral beam injection: optimization of beam alignment and aperturing

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Morris, R.N.; Fowler, R.H.; Rome, J.A.

    1985-12-01

    The application of the existing Impurity Study Experiment (ISX-B) neutral beam injectors for the Advanced Toroidal Facility (ATF) is studied. It is determined that with the practical considerations of beam aperturing, ATF vacuum vessel complexity, and realistic beam modeling, the power absorbed by the plasma will be approximately 57% of the extracted neutral beam power, which corresponds to an injected power of about 1.5 MW. By reducing the beam divergence to a 1/sup 0/ Gaussian distribution, the absorbed power could be increased to 93%. The power delivered to the plasma is found to be a strong function of the beammore » divergence but only a weak function of the beam focal length. Shinethrough can be a serious problem if very low density startups are necessary. Preliminary calculations indicate that there will be no excessive fast-ion losses. 12 refs., 17 figs., 1 tab.« less

  12. Two kinds of Airy-related beams

    NASA Astrophysics Data System (ADS)

    Xu, Yiqing; Zhou, Guoquan; Zhang, Lijun; Ru, Guoyun

    2015-08-01

    Two kinds of Airy-related beams are introduced in this manuscript. The normalized intensity distribution in the x-direction of the two kinds of Airy-related beams is close to that of the Gaussian beam. The normalized intensity distribution in the y-direction of the two kinds of Airy-related beams is close to that of the second-order and the third-order elegant Hermite-Gaussian beams, respectively. Analytical expressions of the two kinds of Airy-related beams passing through an ABCD paraxial optical system are derived. The beam propagation factors for the two kinds of Airy-related beams are 1.933 and 2.125, respectively. Analytical expressions of the beam half widths and the kurtosis parameters of the two kinds of Airy-related beams passing through an ABCD paraxial optical system are also presented. As a numerical example, the propagation properties of the two kinds of Airy-related beams are demonstrated in free space. Moreover, the comparison between the two kinds of Airy-related beams and their corresponding elegant Hermite-Gaussian beams along the two transverse directions are performed in detail. Upon propagation, the former kind of Airy-related beam will evolve from the central bright beam into the dark hollow beam. Contrarily, the latter kind of Airy-related beam will evolve from the dark hollow beam into the central bright beam. These two kinds of Airy-related beams can be used to describe specially distributed beams.

  13. Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.

    PubMed

    Mao, Tianqi; Wang, Zhaocheng; Wang, Qi

    2017-01-23

    Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.

  14. 'The formula that killed Wall Street': the Gaussian copula and modelling practices in investment banking.

    PubMed

    MacKenzie, Donald; Spears, Taylor

    2014-06-01

    Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance.

  15. Coherent and incoherent combination of Gaussian beams employing lens array distributed on the spherical chamber.

    PubMed

    Huang, Zhihua; Wei, Xiaofeng; Li, Mingzhong; Wang, Jianjun; Lin, Honghuan; Xu, Dangpeng; Deng, Ying; Zhang, Rui

    2012-04-01

    Coherent and incoherent combination of Gaussian beams employing a lens array distributed on the spherical chamber is theoretically analyzed. The output field of each source in the array is coupled through an individual optical system whose local optical axis coincides with the radial direction of the chamber. The resulting intensity profile near the origin is derived. The intensity profile and power in the bucket on the target for rectangular and hexagonal arrangement are numerically calculated. The influences of the center-to-center separation and the ring number of the focusing lens array are given. The synthetic intensity profile of incoherent combination changes little for a lens array scale much smaller than the chamber size. In contrast, the synthetic intensity profile of coherent combination shows an interference pattern with a sharp central peak and sidelobes.

  16. X-ray beam-shaping via deformable mirrors: surface profile and point spread function computation for Gaussian beams using physical optics.

    PubMed

    Spiga, D

    2018-01-01

    X-ray mirrors with high focusing performances are commonly used in different sectors of science, such as X-ray astronomy, medical imaging and synchrotron/free-electron laser beamlines. While deformations of the mirror profile may cause degradation of the focus sharpness, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuators. The resulting profile can be characterized with suitable metrology tools and correlated with the expected optical quality via a wavefront propagation code or, sometimes, predicted using geometric optics. In the latter case and for the special class of profile deformations with monotonically increasing derivative, i.e. concave upwards, the point spread function (PSF) can even be predicted analytically. Moreover, under these assumptions, the relation can also be reversed: from the desired PSF the required profile deformation can be computed analytically, avoiding the use of trial-and-error search codes. However, the computation has been so far limited to geometric optics, which entailed some limitations: for example, mirror diffraction effects and the size of the coherent X-ray source were not considered. In this paper, the beam-shaping formalism in the framework of physical optics is reviewed, in the limit of small light wavelengths and in the case of Gaussian intensity wavefronts. Some examples of shaped profiles are also shown, aiming at turning a Gaussian intensity distribution into a top-hat one, and checks of the shaping performances computing the at-wavelength PSF by means of the WISE code are made.

  17. Beam wander of coherent and partially coherent Airy beam arrays in a turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Wen, Wei; Jin, Ying; Hu, Mingjun; Liu, Xianlong; Cai, Yangjian; Zou, Chenjuan; Luo, Mi; Zhou, Liwang; Chu, Xiuxiang

    2018-05-01

    The beam wander properties of coherent and partially coherent Airy beam arrays in a turbulent atmosphere are investigated. Based on the analytical results, we find that the beam wander of partially coherent Airy beam arrays is significantly reduced compared with the wander of a partially coherent Airy beam by numerical simulation. Moreover, the beam wander of a 2 × 2 partially coherent Airy beam arrays is significantly reduced compared with the wander of a 2 × 2 partially coherent Gaussian beam arrays. By using the definition of beam wander arrays factor which is used to characterize the capability of beam arrays for reducing the beam wander effect compared with a single beam, we find that the arrays factor of partially coherent Airy beam arrays is significantly less than that of partially coherent Gaussian beam arrays with the same arrays order. We also find that an artificial reduction of the initial coherence of laser arrays can be used to decrease the beam wander effect. These results indicate that the partially coherent Airy beam arrays have potential applications in long-distance free-space optical communications.

  18. Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

    PubMed

    Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

    2014-06-10

    The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

  19. A Gaussian Mixture Model Representation of Endmember Variability in Hyperspectral Unmixing

    NASA Astrophysics Data System (ADS)

    Zhou, Yuan; Rangarajan, Anand; Gader, Paul D.

    2018-05-01

    Hyperspectral unmixing while considering endmember variability is usually performed by the normal compositional model (NCM), where the endmembers for each pixel are assumed to be sampled from unimodal Gaussian distributions. However, in real applications, the distribution of a material is often not Gaussian. In this paper, we use Gaussian mixture models (GMM) to represent the endmember variability. We show, given the GMM starting premise, that the distribution of the mixed pixel (under the linear mixing model) is also a GMM (and this is shown from two perspectives). The first perspective originates from the random variable transformation and gives a conditional density function of the pixels given the abundances and GMM parameters. With proper smoothness and sparsity prior constraints on the abundances, the conditional density function leads to a standard maximum a posteriori (MAP) problem which can be solved using generalized expectation maximization. The second perspective originates from marginalizing over the endmembers in the GMM, which provides us with a foundation to solve for the endmembers at each pixel. Hence, our model can not only estimate the abundances and distribution parameters, but also the distinct endmember set for each pixel. We tested the proposed GMM on several synthetic and real datasets, and showed its potential by comparing it to current popular methods.

  20. Generation of high-order Hermite-Gaussian modes in end-pumped solid-state lasers for square vortex array laser beam generation.

    PubMed

    Chu, Shu-Chun; Chen, Yun-Ting; Tsai, Ko-Fan; Otsuka, Kenju

    2012-03-26

    This study reports the first systematic approach to the excitation of all high-order Hermite-Gaussian modes (HGMs) in end-pumped solid-state lasers. This study uses a metal-wire-inserted laser resonator accompanied with the "off axis pumping" approach. This study presents numerical analysis of the excitation of HGMs in end-pumped solid-state lasers and experimentally generated HGM patterns. This study also experimentally demonstrates the generation of an square vortex array laser beams by passing specific high-order HGMs (HGn,n + 1 or HGn + 1,n modes) through a Dove prism-embedded unbalanced Mach-Zehnder interferometer [Optics Express 16, 19934-19949]. The resulting square vortex array laser beams with embedded vortexes aligned in a square array can be applied to multi-spot dark optical traps in the future.

  1. Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mitri, F. G., E-mail: F.G.Mitri@ieee.org

    2015-11-14

    Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elementsmore » require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.« less

  2. XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling

    NASA Astrophysics Data System (ADS)

    Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.

    2017-08-01

    XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.

  3. Elegant Hermite-Airy beams

    NASA Astrophysics Data System (ADS)

    Zhou, Guoquan; Zhang, Lijun; Ru, Guoyun

    2015-09-01

    As Ai(x)Ai(-x) can be approximated by \\text{exp}≤ft(-{{x}2}/2\\right) , a kind of elegant Hermite-Airy (EHA) beam that is similar to the elegant Hermite-Gaussian (EHG) beam is introduced in this paper. Analytical expression of the EHA beams passing through an ABCD paraxial optical system is derived. By using the method of numerical fitting, the approximate expressions of 02> , 04> , <\\Thetaj2> , <\\Thetaj4> , and 02\\Thetaj2> for an EHA beam are presented, respectively. When the transverse mode number is larger than 2, 02> , 04> , <\\Thetaj2> , <\\Thetaj4> , and 02\\Thetaj2> of an EHA beam are all larger than those of the EHG beam. Based on the higher-order intensity moments, one can calculate the beam propagation factor, the beam half width, and the kurtosis parameter of the EHA beam passing through an ABCD paraxial optical system. As a numerical example, the propagation characteristics of the EHA beam are demonstrated in free space. Moreover, the propagation properties of the EHA beam are compared with those of the corresponding EHG beam. The evolutionary process of the EHA beam is far slower than that of the corresponding EHG beam. The research denotes that the EHA beams can be used to describe specially distributed optical beams that can not be characterized by the existing EHG beam model. The EHA beam model enriches and replenishes the existing beam model.

  4. Gaussian temporal modulation for the behavior of multi-sinc Schell-model pulses in dispersive media

    NASA Astrophysics Data System (ADS)

    Liu, Xiayin; Zhao, Daomu; Tian, Kehan; Pan, Weiqing; Zhang, Kouwen

    2018-06-01

    A new class of pulse source with correlation being modeled by the convolution operation of two legitimate temporal correlation function is proposed. Particularly, analytical formulas for the Gaussian temporally modulated multi-sinc Schell-model (MSSM) pulses generated by such pulse source propagating in dispersive media are derived. It is demonstrated that the average intensity of MSSM pulses on propagation are reshaped from flat profile or a train to a distribution with a Gaussian temporal envelope by adjusting the initial correlation width of the Gaussian pulse. The effects of the Gaussian temporal modulation on the temporal degree of coherence of the MSSM pulse are also analyzed. The results presented here show the potential of coherence modulation for pulse shaping and pulsed laser material processing.

  5. Curvaton scenario within the minimal supersymmetric standard model and predictions for non-Gaussianity.

    PubMed

    Mazumdar, Anupam; Nadathur, Seshadri

    2012-03-16

    We provide a model in which both the inflaton and the curvaton are obtained from within the minimal supersymmetric standard model, with known gauge and Yukawa interactions. Since now both the inflaton and curvaton fields are successfully embedded within the same sector, their decay products thermalize very quickly before the electroweak scale. This results in two important features of the model: first, there will be no residual isocurvature perturbations, and second, observable non-Gaussianities can be generated with the non-Gaussianity parameter f(NL)~O(5-1000) being determined solely by the combination of weak-scale physics and the standard model Yukawa interactions.

  6. Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

    NASA Astrophysics Data System (ADS)

    Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

    2016-09-01

    The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

  7. Radius of curvature variations for annular, dark hollow and flat topped beams in turbulence

    NASA Astrophysics Data System (ADS)

    Eyyuboğlu, H. T.; Baykal, Y. K.; Ji, X. L.

    2010-06-01

    For propagation in turbulent atmosphere, the radius of curvature variations for annular, dark hollow and flat topped beams are examined under a single formulation. Our results show that for collimated beams, when examined against propagation length, the dark hollow, flat topped and annular Gaussian beams behave nearly the same as the Gaussian beam, but have larger radius of curvature values. Increased partial coherence and turbulence levels tend to lower the radius of curvature. Bigger source sizes on the other hand give rise to larger radius of curvature. Dark hollow and flat topped beams have reduced radius of curvature at longer wavelengths, whereas the annular Gaussian beam seems to be unaffected by wavelength changes; the radius of curvature of the Gaussian beam meanwhile rises with increasing wavelength.

  8. GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

    PubMed Central

    Mukherjee, Chiranjit; Rodriguez, Abel

    2016-01-01

    Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

  9. GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

    PubMed

    Mukherjee, Chiranjit; Rodriguez, Abel

    2016-01-01

    Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

  10. Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

    NASA Astrophysics Data System (ADS)

    Teneng, Dean

    2013-09-01

    We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

  11. Transverse-mode beam splitter of a light beam and its application to quantum cryptography

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sasada, Hiroyuki; Okamoto, Megumi

    2003-07-01

    We have theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, HG{sub 10}, HG{sub 01}, LG{sub 01}, and LG{sub 0-1} (HG denotes Hermite-Gaussian mode; LG denotes Laguerre-Gaussian mode). In certain conditions, the interferometer divides the incident beam into the HG{sub 10} and HG{sub 01} components as a transverse-mode beam splitter. We propose a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and the transverse mode.

  12. Mode conversion efficiency to Laguerre-Gaussian OAM modes using spiral phase optics.

    PubMed

    Longman, Andrew; Fedosejevs, Robert

    2017-07-24

    An analytical model for the conversion efficiency from a TEM 00 mode to an arbitrary Laguerre-Gaussian (LG) mode with null radial index spiral phase optics is presented. We extend this model to include the effects of stepped spiral phase optics, spiral phase optics of non-integer topological charge, and the reduction in conversion efficiency due to broad laser bandwidth. We find that through optimization, an optimal beam waist ratio of the input and output modes exists and is dependent upon the output azimuthal mode number.

  13. Modeling Multi-Variate Gaussian Distributions and Analysis of Higgs Boson Couplings with the ATLAS Detector

    NASA Astrophysics Data System (ADS)

    Krohn, Olivia; Armbruster, Aaron; Gao, Yongsheng; Atlas Collaboration

    2017-01-01

    Software tools developed for the purpose of modeling CERN LHC pp collision data to aid in its interpretation are presented. Some measurements are not adequately described by a Gaussian distribution; thus an interpretation assuming Gaussian uncertainties will inevitably introduce bias, necessitating analytical tools to recreate and evaluate non-Gaussian features. One example is the measurements of Higgs boson production rates in different decay channels, and the interpretation of these measurements. The ratios of data to Standard Model expectations (μ) for five arbitrary signals were modeled by building five Poisson distributions with mixed signal contributions such that the measured values of μ are correlated. Algorithms were designed to recreate probability distribution functions of μ as multi-variate Gaussians, where the standard deviation (σ) and correlation coefficients (ρ) are parametrized. There was good success with modeling 1-D likelihood contours of μ, and the multi-dimensional distributions were well modeled within 1- σ but the model began to diverge after 2- σ due to unmerited assumptions in developing ρ. Future plans to improve the algorithms and develop a user-friendly analysis package will also be discussed. NSF International Research Experiences for Students

  14. Improvement of Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size.

    PubMed

    Ma, Haotong; Liu, Zejin; Jiang, Pengzhi; Xu, Xiaojun; Du, Shaojun

    2011-07-04

    We propose and demonstrate the improvement of conventional Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size. Based on the detailed study of the refractive beam shaping system, we found that the conventional Galilean beam shaper can only work well for the magnifying beam shaping. Taking the transformation of input beam with Gaussian irradiance distribution into target beam with high order Fermi-Dirac flattop profile as an example, the shaper can only work well at the condition that the size of input and target beam meets R(0) ≥ 1.3 w(0). For the improvement, the shaper is regarded as the combination of magnifying and demagnifying beam shaping system. The surface and phase distributions of the improved Galilean beam shaping system are derived based on Geometric and Fourier Optics. By using the improved Galilean beam shaper, the accurate transformation of input beam with Gaussian irradiance distribution into target beam with flattop irradiance distribution is realized. The irradiance distribution of the output beam is coincident with that of the target beam and the corresponding phase distribution is maintained. The propagation performance of the output beam is greatly improved. Studies of the influences of beam size and beam order on the improved Galilean beam shaping system show that restriction of beam size has been greatly reduced. This improvement can also be used to redistribute the input beam with complicated irradiance distribution into output beam with complicated irradiance distribution.

  15. Direct Simulation of Multiple Scattering by Discrete Random Media Illuminated by Gaussian Beams

    NASA Technical Reports Server (NTRS)

    Mackowski, Daniel W.; Mishchenko, Michael I.

    2011-01-01

    The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GB can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.

  16. Simulation of the usage of Gaussian mixture models for the purpose of modelling virtual mass spectrometry data.

    PubMed

    Plechawska, Małgorzata; Polańska, Joanna

    2009-01-01

    This article presents the method of the processing of mass spectrometry data. Mass spectra are modelled with Gaussian Mixture Models. Every peak of the spectrum is represented by a single Gaussian. Its parameters describe the location, height and width of the corresponding peak of the spectrum. An authorial version of the Expectation Maximisation Algorithm was used to perform all calculations. Errors were estimated with a virtual mass spectrometer. The discussed tool was originally designed to generate a set of spectra within defined parameters.

  17. Propagation dynamics of Helical Hermite-Gaussian beams

    NASA Astrophysics Data System (ADS)

    López-Mariscal, Carlos; Gutiérrez-Vega, Julio C.

    2007-09-01

    We investigate theoretically and experimentally the propagation characteristics of the Helical Hermite-Gauss beams corresponding to the helical Ince-Gauss beams in the limit of infinite ellipticity. Particular attention is paid to the transverse irradiance structure, the orbital angular momentum density, and the vortex distribution.

  18. Generation of cylindrically polarized vector vortex beams with digital micromirror device

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gong, Lei; Liu, Weiwei; Wang, Meng

    We propose a novel technique to directly transform a linearly polarized Gaussian beam into vector-vortex beams with various spatial patterns. Full high-quality control of amplitude and phase is implemented via a Digital Micro-mirror Device (DMD) binary holography for generating Laguerre-Gaussian, Bessel-Gaussian, and helical Mathieu–Gaussian modes, while a radial polarization converter (S-waveplate) is employed to effectively convert the optical vortices into cylindrically polarized vortex beams. Additionally, the generated vector-vortex beams maintain their polarization symmetry after arbitrary polarization manipulation. Due to the high frame rates of DMD, rapid switching among a series of vector modes carrying different orbital angular momenta paves themore » way for optical microscopy, trapping, and communication.« less

  19. On the representation of the diffracted field of Hermite-Gaussian modes in an alien basis and the young diffraction principle

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Smirnov, V.N.; Strokovskii, G.A.

    An analytical form of expansion coefficients of a diffracted field for an arbitrary Hermite-Gaussian beam in an alien Hermite-Gaussian basis is obtained. A possible physical interpretation of the well-known Young phenomenological diffraction principle and experiments on diffraction of Hermite-Gaussian beams of the lowest types (n = 0 - 5) from half-plane are discussed. The case of nearly homogenous expansion corresponding to misalignment and mismatch of optical systems is also analyzed. 7 refs., 2 figs.

  20. Linear Quadratic Gaussian Controller Design Using a Graphical User Interface: Application to the Beam-Waveguide Antennas

    NASA Astrophysics Data System (ADS)

    Maneri, E.; Gawronski, W.

    1999-10-01

    The linear quadratic Gaussian (LQG) design algorithms described in [2] and [5] have been used in the controller design of JPL's beam-waveguide [5] and 70-m [6] antennas. This algorithm significantly improves tracking precision in a windy environment. This article describes the graphical user interface (GUI) software for the design LQG controllers. It consists of two parts: the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display.

  1. Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.

    PubMed

    Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O; Gelfand, Alan E

    2016-01-01

    Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.

  2. Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

    PubMed Central

    Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E.

    2018-01-01

    Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. PMID:29720777

  3. Smoothing the Marmousi Model

    NASA Astrophysics Data System (ADS)

    Žáček, K.

    Summary- The only way to make an excessively complex velocity model suitable for application of ray-based methods, such as the Gaussian beam or Gaussian packet methods, is to smooth it. We have smoothed the Marmousi model by choosing a coarser grid and by minimizing the second spatial derivatives of the slowness. This was done by minimizing the relevant Sobolev norm of slowness. We show that minimizing the relevant Sobolev norm of slowness is a suitable technique for preparing the optimum models for asymptotic ray theory methods. However, the price we pay for a model suitable for ray tracing is an increase of the difference between the smoothed and original model. Similarly, the estimated error in the travel time also increases due to the difference between the models. In smoothing the Marmousi model, we have found the estimated error of travel times at the verge of acceptability. Due to the low frequencies in the wavefield of the original Marmousi data set, we have found the Gaussian beams and Gaussian packets at the verge of applicability even in models sufficiently smoothed for ray tracing.

  4. SU-F-BRD-08: A Novel Technique to Derive a Clinically-Acceptable Beam Model for Proton Pencil-Beam Scanning in a Commercial Treatment Planning System

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Scholey, J. E.; Lin, L.; Ainsley, C. G.

    2015-06-15

    Purpose: To evaluate the accuracy and limitations of a commercially-available treatment planning system’s (TPS’s) dose calculation algorithm for proton pencil-beam scanning (PBS) and present a novel technique to efficiently derive a clinically-acceptable beam model. Methods: In-air fluence profiles of PBS spots were modeled in the TPS alternately as single-(SG) and double-Gaussian (DG) functions, based on fits to commissioning data. Uniform-fluence, single-energy-layer square fields of various sizes and energies were calculated with both beam models and delivered to water. Dose was measured at several depths. Motivated by observed discrepancies in measured-versus-calculated dose comparisons, a third model was constructed based on double-Gaussianmore » parameters contrived through a novel technique developed to minimize these differences (DGC). Eleven cuboid-dose-distribution-shaped fields with varying range/modulation and field size were subsequently generated in the TPS, using each of the three beam models described, and delivered to water. Dose was measured at the middle of each spread-out Bragg peak. Results: For energies <160 MeV, the DG model fit square-field measurements to <2% at all depths, while the SG model could disagree by >6%. For energies >160 MeV, both SG and DG models fit square-field measurements to <1% at <4 cm depth, but could exceed 6% deeper. By comparison, disagreement with the DGC model was always <3%. For the cuboid plans, calculation-versus-measured percent dose differences exceeded 7% for the SG model, being larger for smaller fields. The DG model showed <3% disagreement for all field sizes in shorter-range beams, although >5% differences for smaller fields persisted in longer-range beams. In contrast, the DGC model predicted measurements to <2% for all beams. Conclusion: Neither the TPS’s SG nor DG models, employed as intended, are ideally suited for routine clinical use. However, via a novel technique to be presented, its DG

  5. Experimental generation of partially coherent beams with different complex degrees of coherence.

    PubMed

    Wang, Fei; Liu, Xianlong; Yuan, Yangsheng; Cai, Yangjian

    2013-06-01

    We established an experimental setup for generating partially coherent beams with different complex degrees of coherence, and we report experimental generation of an elliptical Gaussian Schell-model (GSM) beam and a Laguerre-GSM beam for the first time. It has been demonstrated experimentally that an elliptical GSM beam and a Laguerre-GSM beam produce an elliptical beam spot and a dark hollow beam spot in the focal plane (or in the far field), respectively, which agrees with theoretical predictions. Our results are useful for beam shaping and particle trapping.

  6. Potentials of radial partially coherent beams in free-space optical communication: a numerical investigation.

    PubMed

    Wang, Minghao; Yuan, Xiuhua; Ma, Donglin

    2017-04-01

    Nonuniformly correlated partially coherent beams (PCBs) have extraordinary propagation properties, making it possible to further improve the performance of free-space optical communications. In this paper, a series of PCBs with varying degrees of coherence in the radial direction, academically called radial partially coherent beams (RPCBs), are considered. RPCBs with arbitrary coherence distributions can be created by adjusting the amplitude profile of a spatial modulation function imposed on a uniformly correlated phase screen. Since RPCBs cannot be well characterized by the coherence length, a modulation depth factor is introduced as an indicator of the overall distribution of coherence. By wave optics simulation, free-space and atmospheric propagation properties of RPCBs with (inverse) Gaussian and super-Gaussian coherence distributions are examined in comparison with conventional Gaussian Schell-model beams. Furthermore, the impacts of varying central coherent areas are studied. Simulation results reveal that under comparable overall coherence, beams with a highly coherent core and a less coherent margin exhibit a smaller beam spread and greater on-axis intensity, which is mainly due to the self-focusing phenomenon right after the beam exits the transmitter. Particularly, those RPCBs with super-Gaussian coherence distributions will repeatedly focus during propagation, resulting in even greater intensities. Additionally, RPCBs also have a considerable ability to reduce scintillation. And it is demonstrated that those properties have made RPCBs very effective in improving the mean signal-to-noise ratio of small optical receivers, especially in relatively short, weakly fluctuating links.

  7. White Gaussian Noise - Models for Engineers

    NASA Astrophysics Data System (ADS)

    Jondral, Friedrich K.

    2018-04-01

    This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.

  8. Designing Multi-target Compound Libraries with Gaussian Process Models.

    PubMed

    Bieler, Michael; Reutlinger, Michael; Rodrigues, Tiago; Schneider, Petra; Kriegl, Jan M; Schneider, Gisbert

    2016-05-01

    We present the application of machine learning models to selecting G protein-coupled receptor (GPCR)-focused compound libraries. The library design process was realized by ant colony optimization. A proprietary Boehringer-Ingelheim reference set consisting of 3519 compounds tested in dose-response assays at 11 GPCR targets served as training data for machine learning and activity prediction. We compared the usability of the proprietary data with a public data set from ChEMBL. Gaussian process models were trained to prioritize compounds from a virtual combinatorial library. We obtained meaningful models for three of the targets (5-HT2c , MCH, A1), which were experimentally confirmed for 12 of 15 selected and synthesized or purchased compounds. Overall, the models trained on the public data predicted the observed assay results more accurately. The results of this study motivate the use of Gaussian process regression on public data for virtual screening and target-focused compound library design. © 2016 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

  9. Generation of low-divergence laser beams

    DOEpatents

    Kronberg, James W.

    1993-01-01

    Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source.

  10. Generation of low-divergence laser beams

    DOEpatents

    Kronberg, J.W.

    1993-09-14

    Apparatus for transforming a conventional beam of coherent light, having a Gaussian energy distribution and relatively high divergence, into a beam in which the energy distribution approximates a single, non-zero-order Bessel function and which therefore has much lower divergence. The apparatus comprises a zone plate having transmitting and reflecting zones defined by the pattern of light interference produced by the combination of a beam of coherent light with a Gaussian energy distribution and one having such a Bessel distribution. The interference pattern between the two beams is a concentric array of multiple annuli, and is preferably recorded as a hologram. The hologram is then used to form the transmitting and reflecting zones by photo-etching portions of a reflecting layer deposited on a plate made of a transmitting material. A Bessel beam, containing approximately 50% of the energy of the incident beam, is produced by passing a Gaussian beam through such a Bessel zone plate. The reflected beam, also containing approximately 50% of the incident beam energy and having a Bessel energy distribution, can be redirected in the same direction and parallel to the transmitted beam. Alternatively, a filter similar to the Bessel zone plate can be placed within the resonator cavity of a conventional laser system having a front mirror and a rear mirror, preferably axially aligned with the mirrors and just inside the front mirror to generate Bessel energy distribution light beams at the laser source. 11 figures.

  11. Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach.

    PubMed

    Naik, Dinesh N; Saad, Nabil A; Rao, D Narayana; Viswanathan, Nirmal K

    2017-05-24

    The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω λ with correlated linear phase (ϕ 0  ≥ 0.025 λ) and lateral shear (y 0  ≥ 0.05 ω λ ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

  12. A Gaussian Model-Based Probabilistic Approach for Pulse Transit Time Estimation.

    PubMed

    Jang, Dae-Geun; Park, Seung-Hun; Hahn, Minsoo

    2016-01-01

    In this paper, we propose a new probabilistic approach to pulse transit time (PTT) estimation using a Gaussian distribution model. It is motivated basically by the hypothesis that PTTs normalized by RR intervals follow the Gaussian distribution. To verify the hypothesis, we demonstrate the effects of arterial compliance on the normalized PTTs using the Moens-Korteweg equation. Furthermore, we observe a Gaussian distribution of the normalized PTTs on real data. In order to estimate the PTT using the hypothesis, we first assumed that R-waves in the electrocardiogram (ECG) can be correctly identified. The R-waves limit searching ranges to detect pulse peaks in the photoplethysmogram (PPG) and to synchronize the results with cardiac beats--i.e., the peaks of the PPG are extracted within the corresponding RR interval of the ECG as pulse peak candidates. Their probabilities of being the actual pulse peak are then calculated using a Gaussian probability function. The parameters of the Gaussian function are automatically updated when a new pulse peak is identified. This update makes the probability function adaptive to variations of cardiac cycles. Finally, the pulse peak is identified as the candidate with the highest probability. The proposed approach is tested on a database where ECG and PPG waveforms are collected simultaneously during the submaximal bicycle ergometer exercise test. The results are promising, suggesting that the method provides a simple but more accurate PTT estimation in real applications.

  13. Research on Bayes matting algorithm based on Gaussian mixture model

    NASA Astrophysics Data System (ADS)

    Quan, Wei; Jiang, Shan; Han, Cheng; Zhang, Chao; Jiang, Zhengang

    2015-12-01

    The digital matting problem is a classical problem of imaging. It aims at separating non-rectangular foreground objects from a background image, and compositing with a new background image. Accurate matting determines the quality of the compositing image. A Bayesian matting Algorithm Based on Gaussian Mixture Model is proposed to solve this matting problem. Firstly, the traditional Bayesian framework is improved by introducing Gaussian mixture model. Then, a weighting factor is added in order to suppress the noises of the compositing images. Finally, the effect is further improved by regulating the user's input. This algorithm is applied to matting jobs of classical images. The results are compared to the traditional Bayesian method. It is shown that our algorithm has better performance in detail such as hair. Our algorithm eliminates the noise well. And it is very effectively in dealing with the kind of work, such as interested objects with intricate boundaries.

  14. Quantum steering of Gaussian states via non-Gaussian measurements

    NASA Astrophysics Data System (ADS)

    Ji, Se-Wan; Lee, Jaehak; Park, Jiyong; Nha, Hyunchul

    2016-07-01

    Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.

  15. Formation of propagation invariant laser beams with anamorphic optical systems

    NASA Astrophysics Data System (ADS)

    Soskind, Y. G.

    2015-03-01

    Propagation invariant structured laser beams play an important role in several photonics applications. A majority of propagation invariant beams are usually produced in the form of laser modes emanating from stable laser cavities. This work shows that anamorphic optical systems can be effectively employed to transform input propagation invariant laser beams and produce a variety of alternative propagation invariant structured laser beam distributions with different shapes and phase structures. This work also presents several types of anamorphic lens systems suitable for transforming the input laser modes into a variety of structured propagation invariant beams. The transformations are applied to different laser mode types, including Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian field distributions. The influence of the relative azimuthal orientation between the input laser modes and the anamorphic optical systems on the resulting transformed propagation invariant beams is presented as well.

  16. Propagation of a laser beam in a plasma

    NASA Technical Reports Server (NTRS)

    Chapman, J. M.; Kevorkian, J.; Steinhauer, L. C.; Vagners, J.

    1975-01-01

    This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent.

  17. Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling

    PubMed Central

    Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just

    2003-01-01

    A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531

  18. Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.

    PubMed

    Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H

    2016-11-01

    Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.

  19. Partially coherent isodiffracting pulsed beams

    NASA Astrophysics Data System (ADS)

    Koivurova, Matias; Ding, Chaoliang; Turunen, Jari; Pan, Liuzhan

    2018-02-01

    We investigate a class of isodiffracting pulsed beams, which are superpositions of transverse modes supported by spherical-mirror laser resonators. By employing modal weights that, for stationary light, produce a Gaussian Schell-model beam, we extend this standard model to pulsed beams. We first construct the two-frequency cross-spectral density function that characterizes the spatial coherence in the space-frequency domain. By assuming a power-exponential spectral profile, we then employ the generalized Wiener-Khintchine theorem for nonstationary light to derive the two-time mutual coherence function that describes the space-time coherence of the ensuing beams. The isodiffracting nature of the laser resonator modes permits all (paraxial-domain) calculations at any propagation distance to be performed analytically. Significant spatiotemporal coupling is revealed in subcycle, single-cycle, and few-cycle domains, where the partial spatial coherence also leads to reduced temporal coherence even though full spectral coherence is assumed.

  20. Beam shaping with vectorial vortex beams under low numerical aperture illumination condition

    NASA Astrophysics Data System (ADS)

    Dai, Jianning; Zhan, Qiwen

    2008-08-01

    In this paper we propose and demonstrate a novel beam shaping method using vectorial vortex beam. A vectorial vortex beam is laser beam with polarization singularity in the beam cross section. This type of beams can be decomposed into two orthogonally polarized components. Each of the polarized components could have different vortex characteristics, and consequently, different intensity distribution when focused by lens. Beam shaping in the far field can be achieved by adjusting the relative weighing of these two components. As one example, we study the vectorial vortex that consists of a linearly polarized Gaussian component and a vortex component polarized orthogonally. When such a vectorial vortex beam is focus by low NA lens, the Gaussian component gives rise to a focal intensity distribution with a solid centre while the vortex component gives rise to a donut distribution with hollow dark center. The shape of the focus can be continuously varied by continuously adjusting the relative weight of the two components. Under appropriate conditions, flat top focusing can be obtained. We experimentally demonstrate the creation of such beams with a liquid crystal spatial light modulator. Flattop focus obtained by vectorial vortex beams with topological charge of +1 has been obtained.

  1. Fractional Gaussian model in global optimization

    NASA Astrophysics Data System (ADS)

    Dimri, V. P.; Srivastava, R. P.

    2009-12-01

    Earth system is inherently non-linear and it can be characterized well if we incorporate no-linearity in the formulation and solution of the problem. General tool often used for characterization of the earth system is inversion. Traditionally inverse problems are solved using least-square based inversion by linearizing the formulation. The initial model in such inversion schemes is often assumed to follow posterior Gaussian probability distribution. It is now well established that most of the physical properties of the earth follow power law (fractal distribution). Thus, the selection of initial model based on power law probability distribution will provide more realistic solution. We present a new method which can draw samples of posterior probability density function very efficiently using fractal based statistics. The application of the method has been demonstrated to invert band limited seismic data with well control. We used fractal based probability density function which uses mean, variance and Hurst coefficient of the model space to draw initial model. Further this initial model is used in global optimization inversion scheme. Inversion results using initial models generated by our method gives high resolution estimates of the model parameters than the hitherto used gradient based liner inversion method.

  2. Transfer of non-Gaussian quantum states of mechanical oscillator to light

    NASA Astrophysics Data System (ADS)

    Filip, Radim; Rakhubovsky, Andrey A.

    2015-11-01

    Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.

  3. Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

    NASA Astrophysics Data System (ADS)

    Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

    2018-05-01

    We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

  4. Discrimination of numerical proportions: A comparison of binomial and Gaussian models.

    PubMed

    Raidvee, Aire; Lember, Jüri; Allik, Jüri

    2017-01-01

    Observers discriminated the numerical proportion of two sets of elements (N = 9, 13, 33, and 65) that differed either by color or orientation. According to the standard Thurstonian approach, the accuracy of proportion discrimination is determined by irreducible noise in the nervous system that stochastically transforms the number of presented visual elements onto a continuum of psychological states representing numerosity. As an alternative to this customary approach, we propose a Thurstonian-binomial model, which assumes discrete perceptual states, each of which is associated with a certain visual element. It is shown that the probability β with which each visual element can be noticed and registered by the perceptual system can explain data of numerical proportion discrimination at least as well as the continuous Thurstonian-Gaussian model, and better, if the greater parsimony of the Thurstonian-binomial model is taken into account using AIC model selection. We conclude that Gaussian and binomial models represent two different fundamental principles-internal noise vs. using only a fraction of available information-which are both plausible descriptions of visual perception.

  5. The effect of noise and lipid signals on determination of Gaussian and non-Gaussian diffusion parameters in skeletal muscle.

    PubMed

    Cameron, Donnie; Bouhrara, Mustapha; Reiter, David A; Fishbein, Kenneth W; Choi, Seongjin; Bergeron, Christopher M; Ferrucci, Luigi; Spencer, Richard G

    2017-07-01

    This work characterizes the effect of lipid and noise signals on muscle diffusion parameter estimation in several conventional and non-Gaussian models, the ultimate objectives being to characterize popular fat suppression approaches for human muscle diffusion studies, to provide simulations to inform experimental work and to report normative non-Gaussian parameter values. The models investigated in this work were the Gaussian monoexponential and intravoxel incoherent motion (IVIM) models, and the non-Gaussian kurtosis and stretched exponential models. These were evaluated via simulations, and in vitro and in vivo experiments. Simulations were performed using literature input values, modeling fat contamination as an additive baseline to data, whereas phantom studies used a phantom containing aliphatic and olefinic fats and muscle-like gel. Human imaging was performed in the hamstring muscles of 10 volunteers. Diffusion-weighted imaging was applied with spectral attenuated inversion recovery (SPAIR), slice-select gradient reversal and water-specific excitation fat suppression, alone and in combination. Measurement bias (accuracy) and dispersion (precision) were evaluated, together with intra- and inter-scan repeatability. Simulations indicated that noise in magnitude images resulted in <6% bias in diffusion coefficients and non-Gaussian parameters (α, K), whereas baseline fitting minimized fat bias for all models, except IVIM. In vivo, popular SPAIR fat suppression proved inadequate for accurate parameter estimation, producing non-physiological parameter estimates without baseline fitting and large biases when it was used. Combining all three fat suppression techniques and fitting data with a baseline offset gave the best results of all the methods studied for both Gaussian diffusion and, overall, for non-Gaussian diffusion. It produced consistent parameter estimates for all models, except IVIM, and highlighted non-Gaussian behavior perpendicular to muscle fibers (

  6. Wavelength-tunable Hermite-Gaussian modes and an orbital-angular-momentum-tunable vortex beam in a dual-off-axis pumped Yb:CALGO laser.

    PubMed

    Shen, Yijie; Meng, Yuan; Fu, Xing; Gong, Mali

    2018-01-15

    A dual-off-axis pumping scheme is presented to generate wavelength-tunable high-order Hermite-Gaussian (HG) modes in Yb:CaGdAlO 4 lasers. The mode and wavelength can be actively controlled by the off-axis displacements and pump power. The purities of the output HG modes are quantified by intensity distributions and the measured M 2 values. The highest order reaches m=15 for stable HG m,0 mode, and wavelength-tunable width is about 10 nm. Moreover, through externally converting the HG m,0 modes, the vortex beams carrying orbital angular momentum (OAM) with a large OAM-tunable range from ±1ℏ to ±15ℏ are produced. This work is effective for largely scaling the spectral and OAM tunable ranges of optical vortex beams.

  7. Beam distribution reconstruction simulation for electron beam probe

    NASA Astrophysics Data System (ADS)

    Feng, Yong-Chun; Mao, Rui-Shi; Li, Peng; Kang, Xin-Cai; Yin, Yan; Liu, Tong; You, Yao-Yao; Chen, Yu-Cong; Zhao, Tie-Cheng; Xu, Zhi-Guo; Wang, Yan-Yu; Yuan, You-Jin

    2017-07-01

    An electron beam probe (EBP) is a detector which makes use of a low-intensity and low-energy electron beam to measure the transverse profile, bunch shape, beam neutralization and beam wake field of an intense beam with small dimensions. While it can be applied to many aspects, we limit our analysis to beam distribution reconstruction. This kind of detector is almost non-interceptive for all of the beam and does not disturb the machine environment. In this paper, we present the theoretical aspects behind this technique for beam distribution measurement and some simulation results of the detector involved. First, a method to obtain a parallel electron beam is introduced and a simulation code is developed. An EBP as a profile monitor for dense beams is then simulated using the fast scan method for various target beam profiles, including KV distribution, waterbag distribution, parabolic distribution, Gaussian distribution and halo distribution. Profile reconstruction from the deflected electron beam trajectory is implemented and compared with the actual profile, and the expected agreement is achieved. Furthermore, as well as fast scan, a slow scan, i.e. step-by-step scan, is considered, which lowers the requirement for hardware, i.e. Radio Frequency deflector. We calculate the three-dimensional electric field of a Gaussian distribution and simulate the electron motion in this field. In addition, a fast scan along the target beam direction and slow scan across the beam are also presented, and can provide a measurement of longitudinal distribution as well as transverse profile simultaneously. As an example, simulation results for the China Accelerator Driven Sub-critical System (CADS) and High Intensity Heavy Ion Accelerator Facility (HIAF) are given. Finally, a potential system design for an EBP is described.

  8. Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

    PubMed

    Kärkkäinen, Hanni P; Sillanpää, Mikko J

    2013-09-04

    Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

  9. Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

    PubMed Central

    Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

    2013-01-01

    Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

  10. Propagation of rotating elliptical Gaussian beams from right-handed material to left-handed material

    NASA Astrophysics Data System (ADS)

    Peng, Xi; Chen, Chi-Dao; Chen, Bo; Deng, Dong-Mei

    2015-12-01

    By applying the ABCD matrix method, we report the propagating properties of the rotating elliptical Gaussian beams (REGBs) from the right-handed material (RHM) to the left-handed material (LHM). Based on the propagation equation, we obtain the intensity distributions of the REGBs during the propagation. It is found that the rotating direction of the REGBs is opposite in the RHM and the LHM, and the rotation angles tend to be π/2 as the propagation distance is long enough. Then we analyze the relationship between the refractive index and the rotating velocity. Furthermore, the energy flow and the angular momentum (AM) of the REGBs which can rotate are also obtained. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Provincial Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province in China, and the Fund from the CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.

  11. Gaussian Process Regression Model in Spatial Logistic Regression

    NASA Astrophysics Data System (ADS)

    Sofro, A.; Oktaviarina, A.

    2018-01-01

    Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.

  12. Generation of an optical frequency comb with a Gaussian spectrum using a linear time-to-space mapping system.

    PubMed

    Hisatake, Shintaro; Tada, Keiji; Nagatsuma, Tadao

    2010-03-01

    We demonstrate the generation of an optical frequency comb (OFC) with a Gaussian spectrum using a continuous-wave (CW) laser, based on spatial convolution of a slit and a periodically moving optical beam spot in a linear time-to-space mapping system. A CW optical beam is linearly mapped to a spatial signal using two sinusoidal electro-optic (EO) deflections and an OFC is extracted by inserting a narrow spatial slit in the Fourier-transform plane of a second EO deflector (EOD). The spectral shape of the OFC corresponds to the spatial beam profile in the near-field region of the second EOD, which can be manipulated by a spatial filter without spectral dispersers. In a proof-of-concept experiment, a 16.25-GHz-spaced, 240-GHz-wide Gaussian-envelope OFC (corresponding to 1.8 ps Gaussian pulse generation) was demonstrated.

  13. Revisiting Gaussian Process Regression Modeling for Localization in Wireless Sensor Networks

    PubMed Central

    Richter, Philipp; Toledano-Ayala, Manuel

    2015-01-01

    Signal strength-based positioning in wireless sensor networks is a key technology for seamless, ubiquitous localization, especially in areas where Global Navigation Satellite System (GNSS) signals propagate poorly. To enable wireless local area network (WLAN) location fingerprinting in larger areas while maintaining accuracy, methods to reduce the effort of radio map creation must be consolidated and automatized. Gaussian process regression has been applied to overcome this issue, also with auspicious results, but the fit of the model was never thoroughly assessed. Instead, most studies trained a readily available model, relying on the zero mean and squared exponential covariance function, without further scrutinization. This paper studies the Gaussian process regression model selection for WLAN fingerprinting in indoor and outdoor environments. We train several models for indoor/outdoor- and combined areas; we evaluate them quantitatively and compare them by means of adequate model measures, hence assessing the fit of these models directly. To illuminate the quality of the model fit, the residuals of the proposed model are investigated, as well. Comparative experiments on the positioning performance verify and conclude the model selection. In this way, we show that the standard model is not the most appropriate, discuss alternatives and present our best candidate. PMID:26370996

  14. A model of non-Gaussian diffusion in heterogeneous media

    NASA Astrophysics Data System (ADS)

    Lanoiselée, Yann; Grebenkov, Denis S.

    2018-04-01

    Recent progress in single-particle tracking has shown evidence of the non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. Similar behavior has also been observed in granular materials, turbulent flows, gels and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior and discuss some implications and extensions.

  15. The Gaussian copula model for the joint deficit index for droughts

    NASA Astrophysics Data System (ADS)

    Van de Vyver, H.; Van den Bergh, J.

    2018-06-01

    The characterization of droughts and their impacts is very dependent on the time scale that is involved. In order to obtain an overall drought assessment, the cumulative effects of water deficits over different times need to be examined together. For example, the recently developed joint deficit index (JDI) is based on multivariate probabilities of precipitation over various time scales from 1- to 12-months, and was constructed from empirical copulas. In this paper, we examine the Gaussian copula model for the JDI. We model the covariance across the temporal scales with a two-parameter function that is commonly used in the specific context of spatial statistics or geostatistics. The validity of the covariance models is demonstrated with long-term precipitation series. Bootstrap experiments indicate that the Gaussian copula model has advantages over the empirical copula method in the context of drought severity assessment: (i) it is able to quantify droughts outside the range of the empirical copula, (ii) provides adequate drought quantification, and (iii) provides a better understanding of the uncertainty in the estimation.

  16. Entanglement concentration for two-mode Gaussian states in non-inertial frames

    NASA Astrophysics Data System (ADS)

    Di Noia, Maurizio; Giraldi, Filippo; Petruccione, Francesco

    2017-04-01

    Entanglement creation and concentration by means of a beam splitter (BS) is analysed for a generic two-mode bipartite Gaussian state in a relativistic framework. The total correlations, the purity and the entanglement in terms of logarithmic negativity are analytically studied for observers in an inertial state and in a non-inertial state of uniform acceleration. The dependence of entanglement on the BS transmissivity due to the Unruh effect is analysed in the case when one or both observers undergo uniform acceleration. Due to the Unruh effect, depending on the initial Gaussian state parameters and observed accelerations, the best condition for entanglement generation limited to the two modes of the observers in their regions is not always a balanced beam splitter, as it is for the inertial case.

  17. Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams.

    PubMed

    Li, Jinhong; Wang, Weiwei; Duan, Meiling; Wei, Jinlin

    2016-09-05

    Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function (WDF), the analytical expressions for the propagation factors (M2-factors) and Strehl ratio SR of the Gaussian Schell-model (GSM) vortex beams and GSM non-vortex beams propagation through non-Kolmogorov atmospheric turbulence are derived, and used to study the influence of non-Kolmogorov atmospheric turbulence on beam quality of the GSM vortex beams. It is shown that the smaller the generalized structure constant and the outer scale of turbulence are, and the bigger the inner scale of turbulence is, the smaller the normalized propagation factor is, the bigger the Strehl ratio is, and the better the beam quality of GSM vortex beams in atmospheric turbulence is. The variation of beam quality with the generalized exponent α is nonmonotonic, when α = 3.11, the beam quality of the GSM vortex beams is the poorest through non-Kolmogorov atmospheric turbulence. GSM vortex beams is less affected by turbulence than GSM non-vortex beams under certain condition, and will be useful in long-distance free-space optical communications.

  18. Variational Gaussian approximation for Poisson data

    NASA Astrophysics Data System (ADS)

    Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

    2018-02-01

    The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

  19. Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

    NASA Astrophysics Data System (ADS)

    De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio

    2017-04-01

    We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p →q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

  20. Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels.

    PubMed

    De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio

    2017-04-21

    We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p→q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

  1. Mode-medium instability and its correction with a Gaussian-reflectivity mirror

    NASA Technical Reports Server (NTRS)

    Webster, K. L.; Sung, C. C.

    1992-01-01

    A high-power CO2 laser beam is known to deteriorate after a few microseconds due to a mode-medium instability (MMI) which results from an intensity-dependent heating rate related to the vibrational-to-translational decay of the upper and lower CO2 lasing levels. An iterative numerical technique is developed to model the time evolution of the beam as it is affected by the MMI. The technique is used to study the MMI in an unstable CO2 resonator with a hard-edge output mirror for different parameters like the Fresnel number and the gas density. The results show that the mode of the hard edge unstable resonator deteriorates because of the diffraction ripples in the mode. A Gaussian-reflectivity mirror was used to correct the MMI. This mirror produces a smoother intensity profile which significantly reduces the effects of the MMI. Quantitative results on peak density variation and beam quality are presented.

  2. Mode-medium instability and its correction with a Gaussian reflectivity mirror

    NASA Technical Reports Server (NTRS)

    Webster, K. L.; Sung, C. C.

    1990-01-01

    A high power CO2 laser beam is known to deteriorate after a few microseconds due to a mode-medium instability (MMI) which results from an intensity dependent heating rate related to the vibrational-to-translational decay of the upper and lower CO2 lasing levels. An iterative numerical technique is developed to model the time evolution of the beam as it is affected by the MMI. The technique is used to study the MMI in an unstable CO2 resonator with a hard-edge output mirror for different parameters like the Fresnel number and the gas density. The results show that the mode of the hard edge unstable resonator deteriorates because of the diffraction ripples in the mode. A Gaussian-reflectivity mirror was used to correct the MMI. This mirror produces a smoother intensity profile which significantly reduces the effects of the MMI. Quantitative results on peak density variation and beam quality are presented.

  3. Infrared maritime target detection using a probabilistic single Gaussian model of sea clutter in Fourier domain

    NASA Astrophysics Data System (ADS)

    Zhou, Anran; Xie, Weixin; Pei, Jihong; Chen, Yapei

    2018-02-01

    For ship targets detection in cluttered infrared image sequences, a robust detection method, based on the probabilistic single Gaussian model of sea background in Fourier domain, is put forward. The amplitude spectrum sequences at each frequency point of the pure seawater images in Fourier domain, being more stable than the gray value sequences of each background pixel in the spatial domain, are regarded as a Gaussian model. Next, a probability weighted matrix is built based on the stability of the pure seawater's total energy spectrum in the row direction, to make the Gaussian model more accurate. Then, the foreground frequency points are separated from the background frequency points by the model. Finally, the false-alarm points are removed utilizing ships' shape features. The performance of the proposed method is tested by visual and quantitative comparisons with others.

  4. Generation of vector beams using a double-wedge depolarizer: Non-quantum entanglement

    NASA Astrophysics Data System (ADS)

    Samlan, C. T.; Viswanathan, Nirmal K.

    2016-07-01

    Propagation of horizontally polarized Gaussian beam through a double-wedge depolarizer generates vector beams with spatially varying state of polarization. Jones calculus is used to show that such beams are maximally nonseparable on the basis of even (Gaussian)-odd (Hermite-Gaussian) mode parity and horizontal-vertical polarization state. The maximum nonseparability in the two degrees of freedom of the vector beam at the double wedge depolarizer output is verified experimentally using a modified Sagnac interferometer and linear analyser projected interferograms to measure the concurrence 0.94±0.002 and violation of Clauser-Horne-Shimony-Holt form of Bell-like inequality 2.704±0.024. The investigation is carried out in the context of the use of vector beams for metrological applications.

  5. The elliptical Gaussian wave transformation due to diffraction by an elliptical hologram

    NASA Astrophysics Data System (ADS)

    Janicijevic, L.

    1985-03-01

    Realized as an interferogram of a spherical and a cylindrical wave, the elliptical hologram is treated as a plane diffracting grating which produces Fresnel diffraction of a simple astigmatic Gaussian incident wave. It is shown that if the principal axes of the incident beam coincide with the principal axes of the hologram, the diffracted wave field is composed of three different astigmatic Gaussian waves, with their waists situated in parallel but distinct planes. The diffraction pattern, observed on a transverse screen, is the result of the interference of the three diffracted wave components. It consists of three systems of overlapped second-order curves, whose shape depends on the distance of the observation screen from the hologram, as well as on the parameters of the incident wave beam and the hologram. The results are specialized for gratings in the form of circular and linear holograms and for the case of a stigmatic Gaussian incident wave, as well as for the normal plane-wave incidence on the three mentioned types of hologram.

  6. Scintillation properties of dark hollow beams in a weak turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Chen, Y.; Cai, Y.; Eyyuboğlu, H. T.; Baykal, Y.

    2008-01-01

    The on-axis scintillation index for a circular dark hollow beam (DHB) propagating in a weak turbulent atmosphere is formulated, and the scintillation properties of a DHB are investigated in detail. The scintillation index for a DHB reduces to the scintillation index for a Gaussian beam, an annular beam and a flat-topped beam under certain conditions. It is found that the scintillation index of a DHB is closely related to the beam parameters and can be lower than that of a Gaussian beam, an annular beam and a flat-topped beam in a weak turbulent atmosphere at smaller waist sizes and longer propagation lengths.

  7. Interactive Gaussian Graphical Models for Discovering Depth Trends in ChemCam Data

    NASA Astrophysics Data System (ADS)

    Oyen, D. A.; Komurlu, C.; Lanza, N. L.

    2018-04-01

    Interactive Gaussian graphical models discover surface compositional features on rocks in ChemCam targets. Our approach visualizes shot-to-shot relationships among LIBS observations, and identifies the wavelengths involved in the trend.

  8. Entangling the Whole by Beam Splitting a Part.

    PubMed

    Croal, Callum; Peuntinger, Christian; Chille, Vanessa; Marquardt, Christoph; Leuchs, Gerd; Korolkova, Natalia; Mišta, Ladislav

    2015-11-06

    A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.

  9. Partial-Wave Representations of Laser Beams for Use in Light-Scattering Calculations

    NASA Technical Reports Server (NTRS)

    Gouesbet, Gerard; Lock, James A.; Grehan, Gerard

    1995-01-01

    In the framework of generalized Lorenz-Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.

  10. Experimental study: Underwater propagation of polarized flat top partially coherent laser beams with a varying degree of spatial coherence

    NASA Astrophysics Data System (ADS)

    Avramov-Zamurovic, S.; Nelson, C.

    2018-10-01

    We report on experiments where spatially partially coherent laser beams with flat top intensity profiles were propagated underwater. Two scenarios were explored: still water and mechanically moved entrained salt scatterers. Gaussian, fully spatially coherent beams, and Multi-Gaussian Schell model beams with varying degrees of spatial coherence were used in the experiments. The main objective of our study was the exploration of the scintillation performance of scalar beams, with both vertical and horizontal polarizations, and the comparison with electromagnetic beams that have a randomly varying polarization. The results from our investigation show up to a 50% scintillation index reduction for the case with electromagnetic beams. In addition, we observed that the fully coherent beam performance deteriorates significantly relative to the spatially partially coherent beams when the conditions become more complex, changing from still water conditions to the propagation through mechanically moved entrained salt scatterers.

  11. Evaluation of non-Gaussian diffusion in cardiac MRI.

    PubMed

    McClymont, Darryl; Teh, Irvin; Carruth, Eric; Omens, Jeffrey; McCulloch, Andrew; Whittington, Hannah J; Kohl, Peter; Grau, Vicente; Schneider, Jürgen E

    2017-09-01

    The diffusion tensor model assumes Gaussian diffusion and is widely applied in cardiac diffusion MRI. However, diffusion in biological tissue deviates from a Gaussian profile as a result of hindrance and restriction from cell and tissue microstructure, and may be quantified better by non-Gaussian modeling. The aim of this study was to investigate non-Gaussian diffusion in healthy and hypertrophic hearts. Thirteen rat hearts (five healthy, four sham, four hypertrophic) were imaged ex vivo. Diffusion-weighted images were acquired at b-values up to 10,000 s/mm 2 . Models of diffusion were fit to the data and ranked based on the Akaike information criterion. The diffusion tensor was ranked best at b-values up to 2000 s/mm 2 but reflected the signal poorly in the high b-value regime, in which the best model was a non-Gaussian "beta distribution" model. Although there was considerable overlap in apparent diffusivities between the healthy, sham, and hypertrophic hearts, diffusion kurtosis and skewness in the hypertrophic hearts were more than 20% higher in the sheetlet and sheetlet-normal directions. Non-Gaussian diffusion models have a higher sensitivity for the detection of hypertrophy compared with the Gaussian model. In particular, diffusion kurtosis may serve as a useful biomarker for characterization of disease and remodeling in the heart. Magn Reson Med 78:1174-1186, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

  12. Gaussian random bridges and a geometric model for information equilibrium

    NASA Astrophysics Data System (ADS)

    Mengütürk, Levent Ali

    2018-03-01

    The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.

  13. On the characterization of flowering curves using Gaussian mixture models.

    PubMed

    Proïa, Frédéric; Pernet, Alix; Thouroude, Tatiana; Michel, Gilles; Clotault, Jérémy

    2016-08-07

    In this paper, we develop a statistical methodology applied to the characterization of flowering curves using Gaussian mixture models. Our study relies on a set of rosebushes flowering data, and Gaussian mixture models are mainly used to quantify the reblooming properties of each one. In this regard, we also suggest our own selection criterion to take into account the lack of symmetry of most of the flowering curves. Three classes are created on the basis of a principal component analysis conducted on a set of reblooming indicators, and a subclassification is made using a longitudinal k-means algorithm which also highlights the role played by the precocity of the flowering. In this way, we obtain an overview of the correlations between the features we decided to retain on each curve. In particular, results suggest the lack of correlation between reblooming and flowering precocity. The pertinent indicators obtained in this study will be a first step towards the comprehension of the environmental and genetic control of these biological processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

  14. a Gaussian Process Based Multi-Person Interaction Model

    NASA Astrophysics Data System (ADS)

    Klinger, T.; Rottensteiner, F.; Heipke, C.

    2016-06-01

    Online multi-person tracking in image sequences is commonly guided by recursive filters, whose predictive models define the expected positions of future states. When a predictive model deviates too much from the true motion of a pedestrian, which is often the case in crowded scenes due to unpredicted accelerations, the data association is prone to fail. In this paper we propose a novel predictive model on the basis of Gaussian Process Regression. The model takes into account the motion of every tracked pedestrian in the scene and the prediction is executed with respect to the velocities of all interrelated persons. As shown by the experiments, the model is capable of yielding more plausible predictions even in the presence of mutual occlusions or missing measurements. The approach is evaluated on a publicly available benchmark and outperforms other state-of-the-art trackers.

  15. Non-gaussianity versus nonlinearity of cosmological perturbations.

    PubMed

    Verde, L

    2001-06-01

    Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

  16. Revealing nonclassicality beyond Gaussian states via a single marginal distribution.

    PubMed

    Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul

    2017-01-31

    A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.

  17. Revealing nonclassicality beyond Gaussian states via a single marginal distribution

    PubMed Central

    Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul

    2017-01-01

    A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential—a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis–independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement. PMID:28077456

  18. Gaussian noise and time-reversal symmetry in nonequilibrium Langevin models.

    PubMed

    Vainstein, M H; Rubí, J M

    2007-03-01

    We show that in driven systems the Gaussian nature of the fluctuating force and time reversibility are equivalent properties. This result together with the potential condition of the external force drastically restricts the form of the probability distribution function, which can be shown to satisfy time-independent relations. We have corroborated this feature by explicitly analyzing a model for the stretching of a polymer and a model for a suspension of noninteracting Brownian particles in steady flow.

  19. Distilling Gaussian states with Gaussian operations is impossible.

    PubMed

    Eisert, J; Scheel, S; Plenio, M B

    2002-09-23

    We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.

  20. Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Yuan, Yangsheng; Chen, Yahong; Liang, Chunhao; Cai, Yangjian; Baykal, Yahya

    2013-03-01

    With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.

  1. Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski functionals

    NASA Astrophysics Data System (ADS)

    Buchert, Thomas; France, Martin J.; Steiner, Frank

    2017-05-01

    Despite the wealth of Planck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependences. Aiming at detecting the NGs of the CMB temperature anisotropy δ T , while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function P(δ T) , related to v0, the first Minkowski Functional (MF), and the two other MFs, v1 and v2. From their analytical Gaussian predictions we build the discrepancy functions {{ Δ }k} (k  =  P, 0, 1, 2) which are applied to an ensemble of 105 CMB realization maps of the Λ CDM model and to the Planck CMB maps. In our analysis we use general Hermite expansions of the {{ Δ }k} up to the 12th order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the second order expansions of Matsubara to arbitrary order in the standard deviation {σ0} for P(δ T) and v0, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the Λ CDM map sample and the Planck data. We confirm the weak level of non-Gaussianity (1-2)σ of the foreground corrected masked Planck 2015 maps.

  2. Normal form decomposition for Gaussian-to-Gaussian superoperators

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    De Palma, Giacomo; INFN, Pisa; Mari, Andrea

    2015-05-15

    In this paper, we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non-positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms ofmore » their action on the characteristic function of the inputs. For the special case of one-mode mappings, we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.« less

  3. Investigation of non-Gaussian effects in the Brazilian option market

    NASA Astrophysics Data System (ADS)

    Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

    2018-04-01

    An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

  4. Simulation of laser beam reflection at the sea surface modeling and validation

    NASA Astrophysics Data System (ADS)

    Schwenger, Frédéric; Repasi, Endre

    2013-06-01

    A 3D simulation of the reflection of a Gaussian shaped laser beam on the dynamic sea surface is presented. The simulation is suitable for the pre-calculation of images for cameras operating in different spectral wavebands (visible, short wave infrared) for a bistatic configuration of laser source and receiver for different atmospheric conditions. In the visible waveband the calculated detected total power of reflected laser light from a 660nm laser source is compared with data collected in a field trial. Our computer simulation comprises the 3D simulation of a maritime scene (open sea/clear sky) and the simulation of laser beam reflected at the sea surface. The basic sea surface geometry is modeled by a composition of smooth wind driven gravity waves. To predict the view of a camera the sea surface radiance must be calculated for the specific waveband. Additionally, the radiances of laser light specularly reflected at the wind-roughened sea surface are modeled considering an analytical statistical sea surface BRDF (bidirectional reflectance distribution function). Validation of simulation results is prerequisite before applying the computer simulation to maritime laser applications. For validation purposes data (images and meteorological data) were selected from field measurements, using a 660nm cw-laser diode to produce laser beam reflection at the water surface and recording images by a TV camera. The validation is done by numerical comparison of measured total laser power extracted from recorded images with the corresponding simulation results. The results of the comparison are presented for different incident (zenith/azimuth) angles of the laser beam.

  5. A Method for Determining the Nominal Occular Hazard Zone for Gaussian Beam Laser Rangers with a Firmware Controlled Variable Focal Length

    NASA Technical Reports Server (NTRS)

    Picco, C. E.; Shavers, M. R.; Victor, J. M.; Duron, J. L.; Bowers, W. h.; Gillis, D. B.; VanBaalen, M.

    2009-01-01

    LIDAR systems that maintain a constant beam spot size on a retroreflector in order to increase the accuracy of bearing and ranging data must use a software controlled variable position lens. These systems periodically update the estimated range and set the position of the focusing lens accordingly. In order to precisely calculate the r NOHD for such a system, the software method for setting the variable position lens and gaussian laser propagation can be used to calculate the irradiance at any point given the range estimation. NASA s Space Shuttle LIDAR, called the Trajectory Control Sensor (TCS), uses this configuration. Analytical tools were developed using Excel and VBA to determine the radiant energy to the International Space Station (ISS) crewmembers eyes while viewing the shuttle on approach and departure. Various viewing scenarios are considered including the use of through-the-lens imaging optics and the window transmissivity at the TCS wavelength. The methodology incorporates the TCS system control logic, gaussian laser propagation, potential failure mode end states, and guidance from American National Standard for the Safe Use of Lasers (ANSI Z136.1-2007). This approach can be adapted for laser safety analyses of similar LIDAR systems.

  6. Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.

    PubMed

    Räth, C; Morfill, G E; Rossmanith, G; Banday, A J; Górski, K M

    2009-04-03

    We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

  7. Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

    PubMed

    Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

    2006-07-10

    On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

  8. Theoretical study on second-harmonic generation of focused vortex beams

    NASA Astrophysics Data System (ADS)

    Tang, Daolong; Wang, Jing; Ma, Jingui; Zhou, Bingjie; Yuan, Peng; Xie, Guoqiang; Zhu, Heyuan; Qian, Liejia

    2018-03-01

    Second-harmonic generation (SHG) provides a promising route for generating vortex beams of both short wavelength and large topological charge. Here we theoretically investigate the efficiency optimization and beam characteristics of focused vortex-beam SHG. Owing to the increasing beam divergence, vortex beams have distinct features in SHG optimization compared with a Gaussian beam. We show that, under the noncritical phase-matching condition, the Boyd and Kleinman prediction of the optimal focusing parameter for Gaussian-beam SHG remains valid for vortex-beam SHG. However, under the critical phase-matching condition, which is sensitive to the beam divergence, the Boyd and Kleinman prediction is no longer valid. In contrast, the optimal focusing parameter for maximizing the SHG efficiency strongly depends on the vortex order. We also investigate the effects of focusing and phase-matching conditions on the second-harmonic beam characteristics.

  9. Gaussian vs non-Gaussian turbulence: impact on wind turbine loads

    NASA Astrophysics Data System (ADS)

    Berg, J.; Mann, J.; Natarajan, A.; Patton, E. G.

    2014-12-01

    In wind energy applications the turbulent velocity field of the Atmospheric Boundary Layer (ABL) is often characterised by Gaussian probability density functions. When estimating the dynamical loads on wind turbines this has been the rule more than anything else. From numerous studies in the laboratory, in Direct Numerical Simulations, and from in-situ measurements of the ABL we know, however, that turbulence is not purely Gaussian: the smallest and fastest scales often exhibit extreme behaviour characterised by strong non-Gaussian statistics. In this contribution we want to investigate whether these non-Gaussian effects are important when determining wind turbine loads, and hence of utmost importance to the design criteria and lifetime of a wind turbine. We devise a method based on Principal Orthogonal Decomposition where non-Gaussian velocity fields generated by high-resolution pseudo-spectral Large-Eddy Simulation (LES) of the ABL are transformed so that they maintain the exact same second-order statistics including variations of the statistics with height, but are otherwise Gaussian. In that way we can investigate in isolation the question whether it is important for wind turbine loads to include non-Gaussian properties of atmospheric turbulence. As an illustration the Figure show both a non-Gaussian velocity field (left) from our LES, and its transformed Gaussian Counterpart (right). Whereas the horizontal velocity components (top) look close to identical, the vertical components (bottom) are not: the non-Gaussian case is much more fluid-like (like in a sketch by Michelangelo). The question is then: Does the wind turbine see this? Using the load simulation software HAWC2 with both the non-Gaussian and newly constructed Gaussian fields, respectively, we show that the Fatigue loads and most of the Extreme loads are unaltered when using non-Gaussian velocity fields. The turbine thus acts like a low-pass filter which average out the non-Gaussian behaviour on time

  10. Interference of Multi-Mode Gaussian States and "non Appearance" of Quantum Correlations

    NASA Astrophysics Data System (ADS)

    Olivares, Stefano

    2012-01-01

    We theoretically investigate bilinear, mode-mixing interactions involving two modes of uncorrelated multi-mode Gaussian states. In particular, we introduce the notion of "locally the same states" (LSS) and prove that two uncorrelated LSS modes are invariant under the mode mixing, i.e. the interaction does not lead to the birth of correlations between the outgoing modes. We also study the interference of orthogonally polarized Gaussian states by means of an interferometric scheme based on a beam splitter, rotators of polarization and polarization filters.

  11. Spin-orbit beams for optical chirality measurement

    NASA Astrophysics Data System (ADS)

    Samlan, C. T.; Suna, Rashmi Ranjan; Naik, Dinesh N.; Viswanathan, Nirmal K.

    2018-01-01

    Accurate measurement of chirality is essential for the advancement of natural and pharmaceutical sciences. We report here a method to measure chirality using non-separable states of light with geometric phase-gradient in the circular polarization basis, which we refer to as spin-orbit beams. A modified polarization Sagnac interferometer is used to generate spin-orbit beams wherein the spin and orbital angular momentum of the input Gaussian beam are coupled. The out-of-phase interference between counter-propagating Gaussian beams with orthogonal spin states and lateral-shear or/and linear-phase difference between them results in spin-orbit beams with linear and azimuthal phase gradient. The spin-orbit beams interact efficiently with the chiral medium, inducing a measurable change in the center-of-mass of the beam, using the polarization rotation angle and hence the chirality of the medium are accurately calculated. Tunable dynamic range of measurement and flexibility to introduce large values of orbital angular momentum for the spin-orbit beam, to improve the measurement sensitivity, highlight the techniques' versatility.

  12. Terahertz generation by relativistic ponderomotive focusing of two co-axial Gaussian laser beams propagating in ripple density plasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kumar, Subodh; Singh, Ram Kishor, E-mail: ram007kishor@gmail.com; Sharma, R. P.

    Terahertz (THz) generation by beating of two co-axial Gaussian laser beams, propagating in ripple density plasma, has been studied when both ponderomotive and relativistic nonlinearities are operative. When the two lasers co-propagate in rippled density plasma, electrons acquire a nonlinear velocity at beat frequency in the direction transverse to the direction of propagation. This nonlinear oscillatory velocity couples with the density ripple to generate a nonlinear current, which in turn generates THz radiation at the difference frequency. The necessary phase matching condition is provided by the density ripple. Relativistic ponderomotive focusing of the two lasers and its effects on yieldmore » of the generated THz amplitude have been discussed. Numerical results show that conversion efficiency of the order of 10{sup −3} can be achieved in the terahertz radiation generation with relativistic ponderomotive focusing.« less

  13. Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

    NASA Astrophysics Data System (ADS)

    Wang, Haiyan; Li, Xiangyin

    2010-01-01

    Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.

  14. On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Konomi, Bledar A.; Karagiannis, Georgios; Lin, Guang

    2015-02-01

    The Bayesian treed Gaussian process (BTGP) has gained popularity in recent years because it provides a straightforward mechanism for modeling non-stationary data and can alleviate computational demands by fitting models to less data. The extension of BTGP to the multivariate setting requires us to model the cross-covariance and to propose efficient algorithms that can deal with trans-dimensional MCMC moves. In this paper we extend the cross-covariance of the Bayesian treed multivariate Gaussian process (BTMGP) to that of linear model of Coregionalization (LMC) cross-covariances. Different strategies have been developed to improve the MCMC mixing and invert smaller matrices in the Bayesianmore » inference. Moreover, we compare the proposed BTMGP with existing multiple BTGP and BTMGP in test cases and multiphase flow computer experiment in a full scale regenerator of a carbon capture unit. The use of the BTMGP with LMC cross-covariance helped to predict the computer experiments relatively better than existing competitors. The proposed model has a wide variety of applications, such as computer experiments and environmental data. In the case of computer experiments we also develop an adaptive sampling strategy for the BTMGP with LMC cross-covariance function.« less

  15. Optical levitation of a non-spherical particle in a loosely focused Gaussian beam.

    PubMed

    Chang, Cheong Bong; Huang, Wei-Xi; Lee, Kyung Heon; Sung, Hyung Jin

    2012-10-08

    The optical force on a non-spherical particle subjected to a loosely focused laser beam was calculated using the dynamic ray tracing method. Ellipsoidal particles with different aspect ratios, inclination angles, and positions were modeled, and the effects of these parameters on the optical force were examined. The vertical component of the optical force parallel to the laser beam axis decreased as the aspect ratio decreased, whereas the ellipsoid with a small aspect ratio and a large inclination angle experienced a large vertical optical force. The ellipsoids were pulled toward or repelled away from the laser beam axis, depending on the inclination angle, and they experienced a torque near the focal point. The behavior of the ellipsoids in a viscous fluid was examined by analyzing a dynamic simulation based on the penalty immersed boundary method. As the ellipsoids levitated along the direction of the laser beam propagation, they moved horizontally with rotation. Except for the ellipsoid with a small aspect ratio and a zero inclination angle near the focal point, the ellipsoids rotated until the major axis aligned with the laser beam axis.

  16. A New Non-gaussian Turbulent Wind Field Generator to Estimate Design-Loads of Wind-Turbines

    NASA Astrophysics Data System (ADS)

    Schaffarczyk, A. P.; Gontier, H.; Kleinhans, D.; Friedrich, R.

    Climate change and finite fossil fuel resources make it urgent to turn into electricity generation from mostly renewable energies. One major part will play wind-energy supplied by wind-turbines of rated power up to 10 MW. For their design and development wind field models have to be used. The standard models are based on the empirical spectra, for example by von Karman or Kaimal. From investigation of measured data it is clear that gusts are underrepresented in such models. Based on some fundamental discoveries of the nature of turbulence by Friedrich [1] derived from the Navier-Stokes equation directly, we used the concept of Continuous Time Random Walks to construct three dimensional wind fields obeying non-Gaussian statistics. These wind fields were used to estimate critical fatigue loads necessary within the certification process. Calculations are carried out with an implementation of a beam-model (FLEX5) for two types of state-of-the-art wind turbines The authors considered the edgewise and flapwise blade-root bending moments as well as tilt moment at tower top due to the standard wind field models and our new non-Gaussian wind field model. Clear differences in the loads were found.

  17. Following a trend with an exponential moving average: Analytical results for a Gaussian model

    NASA Astrophysics Data System (ADS)

    Grebenkov, Denis S.; Serror, Jeremy

    2014-01-01

    We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.

  18. Skewness in large-scale structure and non-Gaussian initial conditions

    NASA Technical Reports Server (NTRS)

    Fry, J. N.; Scherrer, Robert J.

    1994-01-01

    We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.

  19. Three dimensional δf simulations of beams in the SSC

    NASA Astrophysics Data System (ADS)

    Koga, J.; Tajima, T.; Machida, S.

    1993-12-01

    A three dimensional δf strong-strong algorithm has been developed to apply to the study of such effects as space charge and beam-beam interaction phenomena in the Superconducting Super Collider (SSC). The algorithm is obtained from the merging of the particle tracking code Simpsons used for 3 dimensional space charge effects and a δf code. The δf method is used to follow the evolution of the non-gaussian part of the beam distribution. The advantages of this method are twofold. First, the Simpsons code utilizes a realistic accelerator model including synchrotron oscillations and energy ramping in 6 dimensional phase space with electromagnetic fields of the beams calculated using a realistic 3 dimensional field solver. Second, the beams are evolving in the fully self-consistent strong-strong sense with finite particle fluctuation noise is greatly reduced as opposed to the weak-strong models where one beam is fixed.

  20. Comparing fixed and variable-width Gaussian networks.

    PubMed

    Kůrková, Věra; Kainen, Paul C

    2014-09-01

    The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is proven that if two Gaussian RBF networks have the same input-output functions, then they must have the same numbers of units with the same centers and widths. Further, it is shown that while sets of input-output functions of Gaussian kernel networks with two different widths are disjoint, each such set is large enough to be a universal approximator. Embedding of RKHSs induced by "flatter" Gaussians into RKHSs induced by "sharper" Gaussians is described and growth of the ratios of norms on these spaces with increasing input dimension is estimated. Finally, large sets of argminima of error functionals in sets of input-output functions of Gaussian RBFs are described. Copyright © 2014 Elsevier Ltd. All rights reserved.

  1. Effects of scale-dependent non-Gaussianity on cosmological structures

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    LoVerde, Marilena; Miller, Amber; Shandera, Sarah

    2008-04-15

    The detection of primordial non-Gaussianity could provide a powerful means to test various inflationary scenarios. Although scale-invariant non-Gaussianity (often described by the f{sub NL} formalism) is currently best constrained by the CMB, single-field models with changing sound speed can have strongly scale-dependent non-Gaussianity. Such models could evade the CMB constraints but still have important effects at scales responsible for the formation of cosmological objects such as clusters and galaxies. We compute the effect of scale-dependent primordial non-Gaussianity on cluster number counts as a function of redshift, using a simple ansatz to model scale-dependent features. We forecast constraints on these modelsmore » achievable with forthcoming datasets. We also examine consequences for the galaxy bispectrum. Our results are relevant for the Dirac-Born-Infeld model of brane inflation, where the scale dependence of the non-Gaussianity is directly related to the geometry of the extra dimensions.« less

  2. Model selection using cosmic chronometers with Gaussian Processes

    NASA Astrophysics Data System (ADS)

    Melia, Fulvio; Yennapureddy, Manoj K.

    2018-02-01

    The use of Gaussian Processes with a measurement of the cosmic expansion rate based solely on the observation of cosmic chronometers provides a completely cosmology-independent reconstruction of the Hubble constant H(z) suitable for testing different models. The corresponding dispersion σH is smaller than ~ 9% over the entire redshift range (lesssim zlesssim 20) of the observations, rivaling many kinds of cosmological measurements available today. We use the reconstructed H(z) function to test six different cosmologies, and show that it favours the Rh=ct universe, which has only one free parameter (i.e., H0) over other models, including Planck ΛCDM . The parameters of the standard model may be re-optimized to improve the fits to the reconstructed H(z) function, but the results have smaller p-values than one finds with Rh=ct.

  3. Integrating a street-canyon model with a regional Gaussian dispersion model for improved characterisation of near-road air pollution

    NASA Astrophysics Data System (ADS)

    Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne

    2017-03-01

    The development and use of dispersion models that simulate traffic-related air pollution in urban areas has risen significantly in support of air pollution exposure research. In order to accurately estimate population exposure, it is important to generate concentration surfaces that take into account near-road concentrations as well as the transport of pollutants throughout an urban region. In this paper, an integrated modelling chain was developed to simulate ambient Nitrogen Dioxide (NO2) in a dense urban neighbourhood while taking into account traffic emissions, the regional background, and the transport of pollutants within the urban canopy. For this purpose, we developed a hybrid configuration including 1) a street canyon model, which simulates pollutant transfer along streets and intersections, taking into account the geometry of buildings and other obstacles, and 2) a Gaussian puff model, which resolves the transport of contaminants at the top of the urban canopy and accounts for regional meteorology. Each dispersion model was validated against measured concentrations and compared against the hybrid configuration. Our results demonstrate that the hybrid approach significantly improves the output of each model on its own. An underestimation appears clearly for the Gaussian model and street-canyon model compared to observed data. This is due to ignoring the building effect by the Gaussian model and undermining the contribution of other roads by the canyon model. The hybrid approach reduced the RMSE (of observed vs. predicted concentrations) by 16%-25% compared to each model on its own, and increased FAC2 (fraction of predictions within a factor of two of the observations) by 10%-34%.

  4. Pre-correction of distorted Bessel-Gauss beams without wavefront detection

    NASA Astrophysics Data System (ADS)

    Fu, Shiyao; Wang, Tonglu; Zhang, Zheyuan; Zhai, Yanwang; Gao, Chunqing

    2017-12-01

    By utilizing the property of the phase's rapid solution of the Gerchberg-Saxton algorithm, we experimentally demonstrate a scheme to correct distorted Bessel-Gauss beams resulting from inhomogeneous media as weak turbulent atmosphere with good performance. A probe Gaussian beam is employed and propagates coaxially with the Bessel-Gauss modes through the turbulence. No wavefront sensor but a matrix detector is used to capture the probe Gaussian beams, and then, the correction phase mask is computed through inputting such probe beam into the Gerchberg-Saxton algorithm. The experimental results indicate that both single and multiplexed BG beams can be corrected well, in terms of the improvement in mode purity and the mitigation of interchannel cross talk.

  5. An Atomic Lens Using a Focusing Hollow Beam

    NASA Astrophysics Data System (ADS)

    Xia, Yong; Yin, Jian-Ping; Wang, Yu-Zhu

    2003-05-01

    We propose a new method to generate a focused hollow laser beam by using an azimuthally distributed 2pi-phase plate and a convergent thin lens, and calculate the intensity distribution of the focused hollow beam in free propagation space. The relationship between the waist wo of the incident collimated Gaussian beam and the dark spot size of the focused hollow beam at the focal point, and the relationship between the focal length f of the thin lens and the dark spot size are studied respectively. The optical potential of the blue-detuned focused hollow beam for 85Rb atoms is calculated. Our study shows that when the larger waist w of the incident Gaussian beam and the shorter focal length f of the lens are chosen, we can obtain an extremely small dark spot size of the focused hollow beam, which can be used to form an atomic lens with a resolution of several angstroms.

  6. Mixed-effects Gaussian process functional regression models with application to dose-response curve prediction.

    PubMed

    Shi, J Q; Wang, B; Will, E J; West, R M

    2012-11-20

    We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime. Copyright © 2012 John Wiley & Sons, Ltd.

  7. Bivariate sub-Gaussian model for stock index returns

    NASA Astrophysics Data System (ADS)

    Jabłońska-Sabuka, Matylda; Teuerle, Marek; Wyłomańska, Agnieszka

    2017-11-01

    Financial time series are commonly modeled with methods assuming data normality. However, the real distribution can be nontrivial, also not having an explicitly formulated probability density function. In this work we introduce novel parameter estimation and high-powered distribution testing methods which do not rely on closed form densities, but use the characteristic functions for comparison. The approach applied to a pair of stock index returns demonstrates that such a bivariate vector can be a sample coming from a bivariate sub-Gaussian distribution. The methods presented here can be applied to any nontrivially distributed financial data, among others.

  8. Accelerated Gaussian mixture model and its application on image segmentation

    NASA Astrophysics Data System (ADS)

    Zhao, Jianhui; Zhang, Yuanyuan; Ding, Yihua; Long, Chengjiang; Yuan, Zhiyong; Zhang, Dengyi

    2013-03-01

    Gaussian mixture model (GMM) has been widely used for image segmentation in recent years due to its superior adaptability and simplicity of implementation. However, traditional GMM has the disadvantage of high computational complexity. In this paper an accelerated GMM is designed, for which the following approaches are adopted: establish the lookup table for Gaussian probability matrix to avoid the repetitive probability calculations on all pixels, employ the blocking detection method on each block of pixels to further decrease the complexity, change the structure of lookup table from 3D to 1D with more simple data type to reduce the space requirement. The accelerated GMM is applied on image segmentation with the help of OTSU method to decide the threshold value automatically. Our algorithm has been tested through image segmenting of flames and faces from a set of real pictures, and the experimental results prove its efficiency in segmentation precision and computational cost.

  9. Childhood malnutrition in Egypt using geoadditive Gaussian and latent variable models.

    PubMed

    Khatab, Khaled

    2010-04-01

    Major progress has been made over the last 30 years in reducing the prevalence of malnutrition amongst children less than 5 years of age in developing countries. However, approximately 27% of children under the age of 5 in these countries are still malnourished. This work focuses on the childhood malnutrition in one of the biggest developing countries, Egypt. This study examined the association between bio-demographic and socioeconomic determinants and the malnutrition problem in children less than 5 years of age using the 2003 Demographic and Health survey data for Egypt. In the first step, we use separate geoadditive Gaussian models with the continuous response variables stunting (height-for-age), underweight (weight-for-age), and wasting (weight-for-height) as indicators of nutritional status in our case study. In a second step, based on the results of the first step, we apply the geoadditive Gaussian latent variable model for continuous indicators in which the 3 measurements of the malnutrition status of children are assumed as indicators for the latent variable "nutritional status".

  10. Terahertz beam propagation measured through three-dimensional amplitude profile determination

    NASA Astrophysics Data System (ADS)

    Reiten, Matthew T.; Harmon, Stacee A.; Cheville, Richard Alan

    2003-10-01

    To determine the spatio-temporal field distribution of freely propagating terahertz bandwidth pulses, we measure the time-resolved electric field in two spatial dimensions with high resolution. The measured, phase-coherent electric-field distributions are compared with an analytic model in which the radiation from a dipole antenna near a dielectric interface is coupled to free space through a spherical lens. The field external to the lens is limited by reflection at the lens-air dielectric interface, which is minimized at Brewster's angle, leading to an annular field pattern. Field measurements compare favorably with theory. Propagation of terahertz beams is determined both by assuming a TEM0,0 Gaussian profile as well as expanding the beam into a superposition of Laguerre-Gauss modes. The Laguerre-Gauss model more accurately describes the beam profile for free-space propagation and after propagating through a simple optical system. The accuracy of both models for predicting far-field beam patterns depend upon accurately measuring complex field amplitudes of terahertz beams.

  11. Generation of dark hollow beams by using a fractional radial Hilbert transform system

    NASA Astrophysics Data System (ADS)

    Xie, Qiansen; Zhao, Daomu

    2007-07-01

    The radial Hilbert transform has been extend to the fractional field, which could be called the fractional radial Hilbert transform (FRHT). Using edge-enhancement characteristics of this transform, we convert a Gaussian light beam into a variety of dark hollow beams (DHBs). Based on the fact that a hard-edged aperture can be expanded approximately as a finite sum of complex Gaussian functions, the analytical expression of a Gaussian beam passing through a FRHT system has been derived. As a numerical example, the properties of the DHBs with different fractional orders are illustrated graphically. The calculation results obtained by use of the analytical method and the integral method are also compared.

  12. Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

    PubMed

    Porras, Miguel A; Ramos, Francisco

    2017-09-01

    The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.

  13. Real-time model learning using Incremental Sparse Spectrum Gaussian Process Regression.

    PubMed

    Gijsberts, Arjan; Metta, Giorgio

    2013-05-01

    Novel applications in unstructured and non-stationary human environments require robots that learn from experience and adapt autonomously to changing conditions. Predictive models therefore not only need to be accurate, but should also be updated incrementally in real-time and require minimal human intervention. Incremental Sparse Spectrum Gaussian Process Regression is an algorithm that is targeted specifically for use in this context. Rather than developing a novel algorithm from the ground up, the method is based on the thoroughly studied Gaussian Process Regression algorithm, therefore ensuring a solid theoretical foundation. Non-linearity and a bounded update complexity are achieved simultaneously by means of a finite dimensional random feature mapping that approximates a kernel function. As a result, the computational cost for each update remains constant over time. Finally, algorithmic simplicity and support for automated hyperparameter optimization ensures convenience when employed in practice. Empirical validation on a number of synthetic and real-life learning problems confirms that the performance of Incremental Sparse Spectrum Gaussian Process Regression is superior with respect to the popular Locally Weighted Projection Regression, while computational requirements are found to be significantly lower. The method is therefore particularly suited for learning with real-time constraints or when computational resources are limited. Copyright © 2012 Elsevier Ltd. All rights reserved.

  14. Commissioning dose computation models for spot scanning proton beams in water for a commercially available treatment planning system

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhu, X. R.; Poenisch, F.; Lii, M.

    2013-04-15

    Purpose: To present our method and experience in commissioning dose models in water for spot scanning proton therapy in a commercial treatment planning system (TPS). Methods: The input data required by the TPS included in-air transverse profiles and integral depth doses (IDDs). All input data were obtained from Monte Carlo (MC) simulations that had been validated by measurements. MC-generated IDDs were converted to units of Gy mm{sup 2}/MU using the measured IDDs at a depth of 2 cm employing the largest commercially available parallel-plate ionization chamber. The sensitive area of the chamber was insufficient to fully encompass the entire lateralmore » dose deposited at depth by a pencil beam (spot). To correct for the detector size, correction factors as a function of proton energy were defined and determined using MC. The fluence of individual spots was initially modeled as a single Gaussian (SG) function and later as a double Gaussian (DG) function. The DG fluence model was introduced to account for the spot fluence due to contributions of large angle scattering from the devices within the scanning nozzle, especially from the spot profile monitor. To validate the DG fluence model, we compared calculations and measurements, including doses at the center of spread out Bragg peaks (SOBPs) as a function of nominal field size, range, and SOBP width, lateral dose profiles, and depth doses for different widths of SOBP. Dose models were validated extensively with patient treatment field-specific measurements. Results: We demonstrated that the DG fluence model is necessary for predicting the field size dependence of dose distributions. With this model, the calculated doses at the center of SOBPs as a function of nominal field size, range, and SOBP width, lateral dose profiles and depth doses for rectangular target volumes agreed well with respective measured values. With the DG fluence model for our scanning proton beam line, we successfully treated more than 500

  15. Commissioning dose computation models for spot scanning proton beams in water for a commercially available treatment planning system

    PubMed Central

    Zhu, X. R.; Poenisch, F.; Lii, M.; Sawakuchi, G. O.; Titt, U.; Bues, M.; Song, X.; Zhang, X.; Li, Y.; Ciangaru, G.; Li, H.; Taylor, M. B.; Suzuki, K.; Mohan, R.; Gillin, M. T.; Sahoo, N.

    2013-01-01

    Purpose: To present our method and experience in commissioning dose models in water for spot scanning proton therapy in a commercial treatment planning system (TPS). Methods: The input data required by the TPS included in-air transverse profiles and integral depth doses (IDDs). All input data were obtained from Monte Carlo (MC) simulations that had been validated by measurements. MC-generated IDDs were converted to units of Gy mm2/MU using the measured IDDs at a depth of 2 cm employing the largest commercially available parallel-plate ionization chamber. The sensitive area of the chamber was insufficient to fully encompass the entire lateral dose deposited at depth by a pencil beam (spot). To correct for the detector size, correction factors as a function of proton energy were defined and determined using MC. The fluence of individual spots was initially modeled as a single Gaussian (SG) function and later as a double Gaussian (DG) function. The DG fluence model was introduced to account for the spot fluence due to contributions of large angle scattering from the devices within the scanning nozzle, especially from the spot profile monitor. To validate the DG fluence model, we compared calculations and measurements, including doses at the center of spread out Bragg peaks (SOBPs) as a function of nominal field size, range, and SOBP width, lateral dose profiles, and depth doses for different widths of SOBP. Dose models were validated extensively with patient treatment field-specific measurements. Results: We demonstrated that the DG fluence model is necessary for predicting the field size dependence of dose distributions. With this model, the calculated doses at the center of SOBPs as a function of nominal field size, range, and SOBP width, lateral dose profiles and depth doses for rectangular target volumes agreed well with respective measured values. With the DG fluence model for our scanning proton beam line, we successfully treated more than 500 patients from

  16. Commissioning dose computation models for spot scanning proton beams in water for a commercially available treatment planning system.

    PubMed

    Zhu, X R; Poenisch, F; Lii, M; Sawakuchi, G O; Titt, U; Bues, M; Song, X; Zhang, X; Li, Y; Ciangaru, G; Li, H; Taylor, M B; Suzuki, K; Mohan, R; Gillin, M T; Sahoo, N

    2013-04-01

    To present our method and experience in commissioning dose models in water for spot scanning proton therapy in a commercial treatment planning system (TPS). The input data required by the TPS included in-air transverse profiles and integral depth doses (IDDs). All input data were obtained from Monte Carlo (MC) simulations that had been validated by measurements. MC-generated IDDs were converted to units of Gy mm(2)/MU using the measured IDDs at a depth of 2 cm employing the largest commercially available parallel-plate ionization chamber. The sensitive area of the chamber was insufficient to fully encompass the entire lateral dose deposited at depth by a pencil beam (spot). To correct for the detector size, correction factors as a function of proton energy were defined and determined using MC. The fluence of individual spots was initially modeled as a single Gaussian (SG) function and later as a double Gaussian (DG) function. The DG fluence model was introduced to account for the spot fluence due to contributions of large angle scattering from the devices within the scanning nozzle, especially from the spot profile monitor. To validate the DG fluence model, we compared calculations and measurements, including doses at the center of spread out Bragg peaks (SOBPs) as a function of nominal field size, range, and SOBP width, lateral dose profiles, and depth doses for different widths of SOBP. Dose models were validated extensively with patient treatment field-specific measurements. We demonstrated that the DG fluence model is necessary for predicting the field size dependence of dose distributions. With this model, the calculated doses at the center of SOBPs as a function of nominal field size, range, and SOBP width, lateral dose profiles and depth doses for rectangular target volumes agreed well with respective measured values. With the DG fluence model for our scanning proton beam line, we successfully treated more than 500 patients from March 2010 through June 2012

  17. Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

    PubMed Central

    Yang, Sejung; Lee, Byung-Uk

    2015-01-01

    In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138

  18. High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.

    PubMed

    Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei

    2017-07-01

    Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.

  19. Acoustic streaming, fluid mixing, and particle transport by a Gaussian ultrasound beam in a cylindrical container

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Marshall, Jeffrey S., E-mail: jeffm@cems.uvm.edu; Wu, Junru

    A computational study is reported of the acoustic streaming flow field generated by a Gaussian ultrasound beam propagating normally toward the end wall of a cylindrical container. Particular focus is given to examining the effectiveness of the acoustic streaming flow for fluid mixing within the container, for deposition of particles in suspension onto the bottom surface, and for particle suspension from the bottom surface back into the flow field. The flow field is assumed to be axisymmetric with the ultrasound transducer oriented parallel to the cylinder axis and normal to the bottom surface of the container, which we refer tomore » as the impingement surface. Reflection of the sound from the impingement surface and sound absorption within the material at the container bottom are both accounted for in the computation. The computation also accounts for thermal buoyancy force due to ultrasonic heating of the impingement surface, but over the time period considered in the current simulations, the flow is found to be dominated by the acoustic streaming force, with only moderate effect of buoyancy force.« less

  20. Acoustic streaming, fluid mixing, and particle transport by a Gaussian ultrasound beam in a cylindrical container

    NASA Astrophysics Data System (ADS)

    Marshall, Jeffrey S.; Wu, Junru

    2015-10-01

    A computational study is reported of the acoustic streaming flow field generated by a Gaussian ultrasound beam propagating normally toward the end wall of a cylindrical container. Particular focus is given to examining the effectiveness of the acoustic streaming flow for fluid mixing within the container, for deposition of particles in suspension onto the bottom surface, and for particle suspension from the bottom surface back into the flow field. The flow field is assumed to be axisymmetric with the ultrasound transducer oriented parallel to the cylinder axis and normal to the bottom surface of the container, which we refer to as the impingement surface. Reflection of the sound from the impingement surface and sound absorption within the material at the container bottom are both accounted for in the computation. The computation also accounts for thermal buoyancy force due to ultrasonic heating of the impingement surface, but over the time period considered in the current simulations, the flow is found to be dominated by the acoustic streaming force, with only moderate effect of buoyancy force.