Twisted Gaussian Schell-model beams
Simon, R. ); Mukunda, N. Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore )
1993-01-01
The authors introduce a new class of partially coherent axially symmetric Gaussian Schell-model (GSM) beams incorporating a new twist phase quadratic in configuration variables. This phase twists the beam about its axis during propagation and is shown to be bounded in strength because of the positive semidefiniteness of the cross-spectral density. Propagation characteristics and invariants for such beams are derived and interpreted, and two different geometric representations are developed. Direct effects of the twist phase on free propagation as well as in parabolic index fibers are demonstrated. Production of such twisted GSM beams, starting with Li-Wolf anisotropic GSM beams, is described. 34 refs., 3 figs.
Multi-Gaussian Schell-model vortex beam
NASA Astrophysics Data System (ADS)
Zhang, Yongtao; Liu, Lin; Zhao, Chengliang; Cai, Yangjian
2014-02-01
Multi-Gaussian Schell-model (MGSM) beam was introduced recently (Sahin and Korotkova, 2012 [34], and Korotkova et al., 2012 [35]). In this paper, multi-Gaussian Schell-model vortex (MGSMV) beam is introduced as a natural extension of MGSM beam. The explicit expression for the cross-spectral density of a MGSMV beam propagating through a stigmatic ABCD optical system is derived and the focusing properties of a MGSMV beam are studied in detail. It is found that we can shape the focused beam profile by varying the initial beam parameters, which will be useful in material thermal processing and particle trapping.
Ghost imaging with twisted Gaussian Schell-model beam.
Cai, Yangjian; Lin, Qiang; Korotkova, Olga
2009-02-16
Based on the classical optical coherence theory, ghost imaging with twisted Gaussian Schell-model (GSM) beams is analyzed. It is found that the twist phase of the GSM beam has strong influence on ghost imaging. As the absolute value of the twist factor increases, the ghost image disappears gradually, but its visibility increases. This phenomenon is caused by the fact that the twist phase enhances the transverse spatial coherence of the twisted GSM beam on propagation.
Elliptical Laguerre-Gaussian correlated Schell-model beam.
Chen, Yahong; Liu, Lin; Wang, Fei; Zhao, Chengliang; Cai, Yangjian
2014-06-02
A new kind of partially coherent beam with non-conventional correlation function named elliptical Laguerre-Gaussian correlated Schell-model (LGCSM) beam is introduced. Analytical propagation formula for an elliptical LGCSM beam passing through a stigmatic ABCD optical system is derived. The elliptical LGCSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays an elliptical ring-shaped beam profile, being qualitatively different from the circular ring-shaped beam profile of the circular LGCSM beam. Furthermore, we carry out experimental generation of an elliptical LGCSM beam with controllable ellipticity, and measure its focusing properties. Our experimental results are consistent with the theoretical predictions. The elliptical LGCSM beam will be useful in atomic optics.
Gaussian Schell-model beams propagating through polarization gratings.
Piquero, G; Borghi, R; Santarsiero, M
2001-06-01
The effects of polarization gratings on partially coherent beams are investigated by studying a Gaussian Schell-model beam impinging on a linear polarizer whose transmission axis varies periodically along one transverse direction. Analytical expressions for the beam polarization-coherence matrix after the grating are obtained. In particular, the evolution of the degree of polarization upon propagation is analyzed. Different behaviors of the output beam, depending on the beam parameters and on the period of the grating, are exhibited. In particular, it is shown that, by suitably choosing the latter quantities, it is possible to obtain not only any desirable value of the degree of polarization of the output beam but also particular distributions of such parameters across the transverse sections of the beam.
Diffraction of cosine-Gaussian-correlated Schell-model beams.
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.
Vector Hermite-Gaussian correlated Schell-model beam.
Chen, Yahong; Wang, Fang; Yu, Jiayi; Liu, Lin; Cai, Yangjian
2016-07-11
A new kind of partially coherent vector beam named vector Hermite-Gaussian correlated Schell-model (HGCSM) beam is introduced as a natural extension of recently introduced scalar HGCSM beam. The realizability and beam conditions for a vector HGCSM beam with uniform state of polarization (SOP) or non-uniform SOP are derived, respectively. Furthermore, analytical formulae for a vector HGCSM beam propagating in free space are derived, and the propagation properties of a vector HGCSM beam with uniform SOP or non-uniform SOP in free space are studied and analyzed in detail. We find that the behaviors of a vector HGCSM beam on propagation are quite different from those of a conventional vector partially coherent beam with uniform SOP or non-uniform SOP, and modulating the structures of the correlation functions cannot only modulate the intensity distribution, but also the state of polarization, the degree of polarization and the polarization singularities of a partially coherent vector beam on propagation. Furthermore, we report experimental generation of a radially polarized HGCSM beam for the first time. Our results provide a novel way for polarization modulation.
Modeling the interferometric radius measurement using Gaussian beam propagation
Medicus, Katherine M.; Snyder, James J.; Davies, Angela
2006-12-01
We model the interferometric radius measurement using Gaussian beam propagation to identify biases in the measurement due to using a simple geometric ray-trace model instead of the more complex Gaussian model. The radius measurement is based on using an interferometer to identify the test part's position when it is at two null locations, and the distance between the positions is an estimate of the part's radius. The null condition is observed when there is no difference in curvature between the reflected reference and the test wavefronts, and a Gaussian model will provide a first-order estimate of curvature changes due to wave propagation and therefore changes to the radius measurement. We show that the geometric ray assumption leads to radius biases (errors) that are a strong function of the test part radius and increase as the radius of the part decreases. We tested for a bias for both microscaled(<1 mm) and macroscaled parts. The bias is of the order of parts in 105 for micro-optics with radii a small fraction of a millimeter and much smaller for macroscaled optics. The amount of bias depends on the interferometer configuration (numerical aperture, etc.), the nominal radius of the test part, and the distances in the interferometer.
Modeling the radiation of ultrasonic phased-array transducers with Gaussian beams.
Huang, Ruiju; Schmerr, Lester W; Sedov, Alexander
2008-12-01
A new transducer beam model, called a multi-Gaussian array beam model, is developed to simulate the wave fields radiated by ultrasonic phased-array transducers. This new model overcomes the restrictions on using ordinary multi-Gaussian beam models developed for large single-element transducers in phased-array applications. It is demonstrated that this new beam model can effectively model the steered and focused beams of a linear phased-array transducer.
Nonparaxial multi-Gaussian beam models and measurement models for phased array transducers.
Zhao, Xinyu; Gang, Tie
2009-01-01
A nonparaxial multi-Gaussian beam model is proposed in order to overcome the limitation that paraxial Gaussian beam models lose accuracy in simulating the beam steering behavior of phased array transducers. Using this nonparaxial multi-Gaussian beam model, the focusing and steering sound fields generated by an ultrasonic linear phased array transducer are calculated and compared with the corresponding results obtained by paraxial multi-Gaussian beam model and more exact Rayleigh-Sommerfeld integral model. In addition, with help of this novel nonparaxial method, an ultrasonic measurement model is provided to investigate the sensitivity of linear phased array transducers versus steering angles. Also the comparisons of model predictions with experimental results are presented to certify the accuracy of this provided measurement model.
Gaussian-Schell-model beams propagating through rough gratings.
Torcal-Milla, Francisco Jose; Sanchez-Brea, Luis Miguel
2011-03-01
In this work we analyze the near-field intensity distribution produced by a rough grating illuminated with a Gaussian-Schell-model beam. This kind of grating is formed by rough and smooth slits. Statistical techniques are used to describe the grating, and the Fresnel approach is used to perform the propagation of light. Two kinds of coherence affect the light propagation. One of them comes from the light beam, since it is not totally coherent. The other one comes from the rough topography of the grating surface. We have found that the Talbot effect is not present just after the grating, but it gradually increases. In addition, the contrast of the self-images decreases from a certain distance due to the coherence properties of the illumination beam. Then, the self-imaging process is only present between two specific distances from the grating. To corroborate the analytical results, we have performed numerical simulations for the mean intensity distribution based on the Sommerfeld-Rayleigh approach, showing their validity.
Twisted Gaussian Schell-model beams as series of partially coherent modified Bessel-Gauss beams.
Gori, F; Santarsiero, M
2015-04-01
We show that twisted Gaussian Schell-model (TGSM) beams can be represented through an incoherent superposition of partially coherent beams carrying optical vortices and whose cross-spectral densities are expressed in terms of modified Bessel functions. Moreover, starting from this result, we show that the modal expansion of the cross-spectral density of a TGSM source can be directly obtained through simple mathematics.
Zhou, Yuan; Yuan, Yangsheng; Qu, Jun; Huang, Wei
2016-05-16
Analytical formulas are derived for the average intensity, the root-mean-square (rms) angular width, and the M^{2}-factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in non-Kolmogorov turbulence. The influence of the beam and turbulence parameters on the LGCSM beam is numerically calculated. It is shown that the quality of the LGCSM beam can be improved by choosing appropriate beam or turbulence parameter values. It is also found that the LGCSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation. Our results will have some theoretical reference value for optical communications.
Simulation of ultrasonic surface waves with multi-Gaussian and point source beam models
Zhao, Xinyu; Schmerr, Lester W. Jr.; Li, Xiongbing; Sedov, Alexander
2014-02-18
In the past decade, multi-Gaussian beam models have been developed to solve many complicated bulk wave propagation problems. However, to date those models have not been extended to simulate the generation of Rayleigh waves. Here we will combine Gaussian beams with an explicit high frequency expression for the Rayleigh wave Green function to produce a three-dimensional multi-Gaussian beam model for the fields radiated from an angle beam transducer mounted on a solid wedge. Simulation results obtained with this model are compared to those of a point source model. It is shown that the multi-Gaussian surface wave beam model agrees well with the point source model while being computationally much more efficient.
An efficient simplified analysis model of a partially coherent Gaussian vortex beam
NASA Astrophysics Data System (ADS)
Nie, Jianye; Xiao, Qianyi; Liu, Guodong; Zhang, Rongzhu
2017-08-01
Based on the Gaussian-Schell model, analytical expression of the axial light intensity of a partially coherent Gaussian vortex beam (PCGVB) is deduced. The transformation law of axial light intensity is analyzed and a comparison to a partially coherent fundamental-mode Gaussian beam is made. The results show that for a low coherent Gaussian vortex beam, the light intensity distribution can be expressed as a common Gaussian beam with the same coherence length instead. The substitution result is more accurate, especially when the coherence is lower or the value of topological charge is smaller. Moreover, based on axial light intensity, a convenient analytical model of the light intensity distribution of a PCGVB is presented.
Experimental determination of the radius of curvature of an isotropic Gaussian Schell-model beam.
Zhu, Shijun; Chen, Yahong; Cai, Yangjian
2013-02-01
We propose a method to determine the radius of curvature of an isotropic Gaussian Schell-model (GSM) beam by measuring the transverse beam widths and the transverse coherence widths at two different planes. Furthermore, we carry out experimental determination of the radius of curvature of a GSM beam. Using the measured beam parameters, we carry out a comparative study of the propagation properties of a GSM beam both theoretically and experimentally. Our experimental results agree well with theoretical predictions.
Born modeling for heterogeneous media using the Gaussian beam summation based Green's function
NASA Astrophysics Data System (ADS)
Huang, Xingguo; Sun, Hui; Sun, Jianguo
2016-08-01
Born approximation is a commonly used approximation in the simulation of seismic wave propagation. Calculation of the Green's function in Born approximation integral is essential for Born modeling. We derive a new Born formula based on the Gaussian beam representations of Green's functions. This procedure can be used to mitigate the problems like the caustic, shadow region, and multivalued traveltime caused by multipathing that traditional geometric ray theory cannot deal with. However, due to the characteristic of complex traveltime in the Gaussian beam, we present a new isochronous stack method for Gaussian beam based Born modeling. Additionally, two basic issues, background velocity and integral region selection, are discussed. Numerical results demonstrate the accuracy and efficiency of the Gaussian beam based Born theory and implementation.
Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams.
Lin, Qiang; Cai, Yangjian
2002-02-15
A 4 x 4 complex curvature tensor M>(-1) is introduced to describe partially coherent anisotropic Gaussian-Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M(-1) that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases.
Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry.
Liang, Chunhao; Wang, Fei; Liu, Xianlong; Cai, Yangjian; Korotkova, Olga
2014-02-15
Cosine-Gaussian-correlated Schell-model sources whose degree of coherence (DOC) is of circular symmetry have been introduced just recently [Opt. Lett. 38, 2578 (2013)]. In this Letter, we propose a model for a source whose DOC is the superposition of two 1D cosine-Gaussian-correlated Schell-model sources, i.e., possesses rectangular symmetry. The novel model sources and beams they generate are termed rectangular cosine-Gaussian Schell-model (RCGSM). The RCGSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays a four-beamlet array profile, being qualitatively different from the ring-shaped profile of the CGSM beam whose DOC is of circular symmetry. Furthermore, we have carried out experimental generation of the proposed beam and measured its focusing properties. Our experimental results are consistent with the theoretical predictions.
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.
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.
Cosine-Gaussian correlated Schell-model pulsed beams.
Ding, Chaoliang; Korotkova, Olga; Zhang, Yongtao; Pan, Liuzhan
2014-01-13
A new class of partially coherent pulses of Schell type with cosine-Gaussian temporal degree of coherence is introduced. Such waves are termed the Cosine-Gaussian Schell-model (CGSM) pulses. The analytic expression for the temporal mutual coherence function of the CGSM pulse in dispersive media is derived and used to study the evolution of its intensity distribution and its temporal degree of coherence. Further, the numerical calculations are performed in order to show the dependence of the intensity profile and the temporal degree of coherence of the CGSM pulse on the incident pulse duration, the initial temporal coherence length, the order-parameter n and the dispersion of the medium. The most important feature of the novel pulsed wave is its ability to split into two pulses on passage in a dispersive medium at some critical propagation distance. Such critical distance and the subsequent evolution of the split pulses are shown to depend on the source parameters and on the properties of the medium in which the pulse travels.
Fast Pencil Beam Dose Calculation for Proton Therapy Using a Double-Gaussian Beam Model
da Silva, Joakim; Ansorge, Richard; Jena, Rajesh
2015-01-01
The highly conformal dose distributions produced by scanned proton pencil beams (PBs) are more sensitive to motion and anatomical changes than those produced by conventional radiotherapy. The ability to calculate the dose in real-time as it is being delivered would enable, for example, online dose monitoring, and is therefore highly desirable. We have previously described an implementation of a PB algorithm running on graphics processing units (GPUs) intended specifically for online dose calculation. Here, we present an extension to the dose calculation engine employing a double-Gaussian beam model to better account for the low-dose halo. To the best of our knowledge, it is the first such PB algorithm for proton therapy running on a GPU. We employ two different parameterizations for the halo dose, one describing the distribution of secondary particles from nuclear interactions found in the literature and one relying on directly fitting the model to Monte Carlo simulations of PBs in water. Despite the large width of the halo contribution, we show how in either case the second Gaussian can be included while prolonging the calculation of the investigated plans by no more than 16%, or the calculation of the most time-consuming energy layers by about 25%. Furthermore, the calculation time is relatively unaffected by the parameterization used, which suggests that these results should hold also for different systems. Finally, since the implementation is based on an algorithm employed by a commercial treatment planning system, it is expected that with adequate tuning, it should be able to reproduce the halo dose from a general beam line with sufficient accuracy. PMID:26734567
Fast Pencil Beam Dose Calculation for Proton Therapy Using a Double-Gaussian Beam Model.
da Silva, Joakim; Ansorge, Richard; Jena, Rajesh
2015-01-01
The highly conformal dose distributions produced by scanned proton pencil beams (PBs) are more sensitive to motion and anatomical changes than those produced by conventional radiotherapy. The ability to calculate the dose in real-time as it is being delivered would enable, for example, online dose monitoring, and is therefore highly desirable. We have previously described an implementation of a PB algorithm running on graphics processing units (GPUs) intended specifically for online dose calculation. Here, we present an extension to the dose calculation engine employing a double-Gaussian beam model to better account for the low-dose halo. To the best of our knowledge, it is the first such PB algorithm for proton therapy running on a GPU. We employ two different parameterizations for the halo dose, one describing the distribution of secondary particles from nuclear interactions found in the literature and one relying on directly fitting the model to Monte Carlo simulations of PBs in water. Despite the large width of the halo contribution, we show how in either case the second Gaussian can be included while prolonging the calculation of the investigated plans by no more than 16%, or the calculation of the most time-consuming energy layers by about 25%. Furthermore, the calculation time is relatively unaffected by the parameterization used, which suggests that these results should hold also for different systems. Finally, since the implementation is based on an algorithm employed by a commercial treatment planning system, it is expected that with adequate tuning, it should be able to reproduce the halo dose from a general beam line with sufficient accuracy.
Scintillation index of a multi-Gaussian Schell-model beam in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Yuan, Yangsheng; Liu, Xianlong; Wang, Fei; Chen, Yahong; Cai, Yangjian; Qu, Jun; Eyyuboğlu, Halil T.
2013-09-01
Multi-Gaussian Schell-model (MGSM) beam was introduced recently [Sahin and Korotkova, Opt. Lett. 37 (2012) 2970; Korotkova et al., J. Opt. Soc. Am. A 29 (2012) 2159]. In this paper, an explicit expression for the scintillation index of a multi-Gaussian Schell-model (MGSM) beam in weakly or extremely strong turbulent atmosphere is derived with the help of a tensor method. Applying the derived formulae, the scintillation properties of a MGSM beam and a GSM beam in weakly or extremely strong turbulent atmosphere are studied numerically and comparatively. Our results show that a MGSM beam has advantage over a GSM beam for reducing turbulence-induced scintillation, which will be useful for long-distance free-space optical communications.
A reciprocity inequality for Gaussian Schell-model beams and some of its consequences
Friberg, Ari T.; Visser, Taco D.; Wolf, Emil
2000-03-15
A reciprocity inequality is derived, involving the effective size of a planar, secondary, Gaussian Schell-model source and the effective angular spread of the beam that the source generates. The analysis is shown to imply that a fully spatially coherent source of that class (which generates the lowest-order Hermite-Gaussian laser mode) has certain minimal properties. (c) 2000 Optical Society of America.
NASA Astrophysics Data System (ADS)
Trofimov, M. Yu.; Zakharenko, A. D.; Kozitskiy, S. B.
2016-10-01
A mode parabolic equation in the ray centered coordinates for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the ASA wedge benchmark and proved an excellent agreement with the source images method in the case of cross-slope propagation. But in the cases of wave propagation at some angles to the cross-slope direction an account of mode interaction becomes necessary.
Modeling of scattering intensity of spheroid particles with a Gaussian beam
NASA Astrophysics Data System (ADS)
Tang, Hong; Zheng, Wenbin
2017-04-01
Based on the Generalized Lorenz Mie Theory (GLMT), the scattering intensity of spheroid particles is investigated within the Gaussian beam. The spheroid model is applied to represent the real non-spherical particles, and the scattering intensity of particles is deduced according to the GLMT. On the other hand, the sphere of the same volume for the spheroid is used for calculating the scattering intensity of the spheroid within the Gaussian beam. For a comparison, the scattering intensity of the spheroid with the pane wave is also calculated. Simulation data results indicate that fairly reasonable results of the scattering intensity for the spheroids can be obtained with this model, and it can provide a reliable and efficient approach to research the scattering intensity of the non-spherical particles by the Gaussian beam.
Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal.
Shen, Yan; Liu, Lin; Zhao, Chengliang; Yuan, Yangsheng; Cai, Yangjian
2014-02-01
We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.
Propagation factors of cosine-Gaussian-correlated Schell-model beams in non-Kolmogorov turbulence.
Xu, Hua-Feng; Zhang, Zhou; Qu, Jun; Huang, Wei
2014-09-22
Based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function (WDF), we have studied the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. It has been found that the CGSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation, and this advantage will be more obvious for the beams with larger parameter n and spatial coherence δ or under the condition of stronger fluctuation of turbulence. The CGSM beam with larger parameter n or smaller spatial coherence δ will be less affected by the turbulence. In addition, the effects of the slope-parameter α, inner and outer scale and the refractive-index structure constant of the non-Kolmogorov's power spectrum on the propagation factor are also analyzed in detailed.
Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam.
Chen, Yahong; Wang, Fei; Zhao, Chengliang; Cai, Yangjian
2014-03-10
Laguerre-Gaussian correlated Schell-model (LGCSM) vortex beam is introduced as an extension of LGCSM beam which was proposed [Opt. Lett.38, 91 (2013)Opt. Lett.38, 1814 (2013)] just recently. Explicit formula for a LGCSM vortex beam propagating through a stigmatic ABCD optical system is derived, and the propagation properties of such beam in free space and the focusing properties of such beam are studied numerically. Furthermore, we carry out experimental generation of a LGCSM vortex beam, and studied its focusing properties. It is found that the propagation and focusing properties of a LGCSM vortex beam are different from that of a LGCSM beam, and we can shape the beam profile of a LGCSM vortex at the focal plane (or in the far field) by varying its initial spatial coherence. Our experimental results are consistent with the theoretical predictions, and our results will be useful for particle trapping.
Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Qiu, Yunli; Chen, Zhaoxi; He, Yingji
2017-04-01
Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.
Propagation of Gaussian Schell-model Array beams in free space and atmospheric turbulence
NASA Astrophysics Data System (ADS)
Mao, Yonghua; Mei, Zhangrong; Gu, Juguan
2016-12-01
Based on the extended Huygens-Fresnel principle, the evolution behavior of the spectral density and the spectral degree of coherence of the beam produced by a recently introduced novel class of Gaussian Schell-model Arrays (GSMA) source in free space and turbulence atmospheric are explored and comparatively analyzed. And the influence of the fractal constant of the atmospheric power spectrum and refractive-index structure constant on the spectral density and the spectral degree of coherence of beams are analyzed. It is shown that the optical lattice profile is stable when beams propagate in free space, but the spectral density eventually is suppressed and transformed into a Gaussian profiles when it passes at sufficiently large distances through the turbulent atmosphere. The distributions of the spectral degree of coherence in far field eventually transformed into a shrink Gaussian profile relative to free space which means that the degree of spatial coherence turns worse.
Evolution properties of Bessel-Gaussian Schell-model beams in non-Kolmogorov turbulence.
Wang, Xiaoyang; Yao, Mingwu; Qiu, Zhiliang; Yi, Xiang; Liu, Zengji
2015-05-18
The analytical expressions for the spectral degree of coherence, the effective radius of curvature and the propagation factor of the Bessel-Gaussian Schell-model (BGSM) beam in turbulent atmosphere are derived based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF). The evolution properties of BGSM beams propagating in non-Kolmogorov turbulence are investigated by a set of numerical examples. It is demonstrated that the spectral degree of coherence of the BGSM beam evolves into Gaussian profile twice with the increasing of the propagation distance. The turbulence-induced degradation can be remarkably reduced by using the BGSM beam with the proper source parameters. The effects that the generalized refractive-index structure constant, outer and inner scales, and the spectral index of spatial power spectrum of atmospheric turbulence have on the evolution properties of BGSM beams are also discussed in detail.
Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere.
Zhu, Yingbin; Zhao, Daomu; Du, Xinyue
2008-10-27
Analytical formulas for the elements of the 2x2 cross-spectral density matrix of a kind of stochastic electromagnetic array beam propagating through the turbulent atmosphere are derived with the help of vector integration. Two types of superposition (i.e. the correlated superposition and the uncorrelated superposition) are considered. The changes in the spectral density and in the spectral degree of polarization of such an array beam generated by isotropic or anisotropic electromagnetic Gaussian Schell-model sources on propagation are determined by the use of the analytical formulas. It is shown by numerical calculations that for the array beam composed by isotropic Gaussian-Schell model sources, the spectral degree of polarization in the sufficiently far field returns to the value of the array source; for the array beam composed by anisotropic sources, the spectral degree of polarization in the far field approaches a fixed value that is different from the source.
Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal.
Zhang, Lina; Cai, Yangjian
2011-07-04
Nonparaxial propagation theory of coherent beams in a uniaxial crystal is extended to the partially coherent case. An analytical formula for the 3×3 cross-spectral density matrix of a nonparaxial Gaussian Schell-model (GSM) beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. Statistical properties, such as the spectral intensity and the degree of polarization, of a nonparaxial GSM beam in a uniaxial crystal are studied numerically. It is found that the statistical properties of a nonparaxial GSM beam are closely determined by its initial beam parameters and the parameters of the crystal. Uniaxial crystal can be used to modulate the spectral density and degree of polarization of a nonparaxial partially coherent beam. Our results may be useful in some applications, such as optical trapping and nonlinear optics, where a light beam with special beam profile and polarization is required.
Spreading and wandering of Gaussian-Schell model laser beams in an anisotropic turbulent ocean
NASA Astrophysics Data System (ADS)
Wu, Yuqian; Zhang, Yixin; Zhu, Yun; Hu, Zhengda
2016-09-01
The effect of anisotropic turbulence on the spreading and wandering of Gaussian-Schell model (GSM) laser beams propagating in an ocean is studied. The long-term spreading of a GSM beam propagating through the paraxial channel of a turbulent ocean is also developed. Expressions of random wander for such laser beams are derived in an anisotropic turbulent ocean based on the extended Huygens-Fresnel principle. We investigate the influence of parameters in a turbulent ocean on the beam wander and spreading. Our results indicate that beam spreading and random beam wandering are smaller without considering the anisotropy of turbulence in the oceanic channel. Salinity fluctuation has a greater contribution to both the beam spreading and beam wander than that of temperature fluctuations in a turbulent ocean. Our results could be helpful for designing a free-space optical wireless communication system in an oceanic environment.
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).
Experimental Method of Generating Electromagnetic Gaussian Schell-model Beams
2015-03-26
pain, having patience with me, and keeping me on track throughout my Master’s program and research process. Matthew J. Gridley v Table of Contents...ISOLATION OF SPECKLE FOR TARGET-IN-THE-LOOP COHERENT BEAM COMBINING. Thesis, Air Force Institute of Technology, 2014. [11] Korotkova, Olga. Random Light Beams
Cai, Yangjian; Lin, Qiang; Ge, Di
2002-10-01
By adopting a new tensor method, we derived an analytical propagation formula for the cross-spectral density of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams through dispersive and absorbing media. Using the derived formula, we studied the evolution properties and spectrum properties of twisted anisotropic GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media have strong influences on the propagation properties of twisted anisotropic GSM beams and their spectrum evolution. Our method provides a simple and convenient way to study the propagation of twisted anisotropic GSM beams in media with complex refractive index.
Shape-invariant difference between two Gaussian Schell-model beams.
Borghi, R; Gori, F; Guattari, G; Santarsiero, M
2015-05-01
The difference between two Gaussian Schell-model cross-spectral densities can give a new genuine correlation function if suitable conditions are met. Generally speaking, the structure of such cross-spectral density changes in a complicated way upon propagation. We consider here the notable exception of shape-invariant beams, and we investigate their intensity and coherence properties. The modal analysis of this class of cross-spectral densities is exploited to devise a synthesis scheme for this type of beam.
Propagation of a Laguerre-Gaussian correlated Schell-model beam beyond the paraxial approximation
NASA Astrophysics Data System (ADS)
Guo, Lina; Chen, Yahong; Liu, Lin; Cai, Yangjian
2015-10-01
Recently, Laguerre-Gaussian correlated Schell-model (LGCSM) beam was introduced theoretically [Mei and Korotkova, Opt. Lett. 38(2), (2013), 91-93] and generated experimentally [Wang et al., Opt. Lett. 38(11), (2013), 1814-1816]. In this paper, we treat the propagation of a LGCSM beam beyond the paraxial approximation. Based on the generalized Rayleigh-Sommerfeld diffraction integral, analytical expressions for the intensity and spectral degree of coherence of a nonparaxial LGCSM beam propagating in free space are obtained, and the corresponding results of a paraxial LGCSM beam are also derived as a special case. Our numerical results show that the nonparaxial propagation properties of a LGCSM beam are closely related to the initial beam parameters, such as the beam waist width, the coherence width and the mode order. Furthermore, in the far field, flat-topped, hollow intensity profiles can be formed through varying the initial beam parameters, which is different from that of a nonparaxial Gaussian Schell-model beam.
Waveform model of a laser altimeter for an elliptical Gaussian beam.
Yue, Ma; Mingwei, Wang; Guoyuan, Li; Xiushan, Lu; Fanlin, Yang
2016-03-10
The current waveform model of a laser altimeter is based on the Gaussian laser beam of the fundamental mode, whose cross section is a circular spot, whereas some of the cross sections of Geoscience Laser Altimeter System lasers are closer to elliptical spots. Based on the expression of the elliptical Gaussian beam and the waveform theory of laser altimeters, the primary parameters of an echo waveform were derived. In order to examine the deduced expressions, a laser altimetry waveform simulator and waveform processing software were programmed and improved under the circumstance of an elliptical Gaussian beam. The result shows that all the biases between the theoretical and simulated waveforms were less than 0.5%, and the derived model of an elliptical spot is universal and can also be used for the conventional circular spot. The shape of the waveforms is influenced by the ellipticity of the laser spot, the target slope, and the "azimuth angle" between the major axis and the slope direction. This article provides the waveform theoretical basis of a laser altimeter under an elliptical Gaussian beam.
Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere.
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.
Orbital angular moment of an electromagnetic Gaussian Schell-model beam with a twist phase.
Liu, Lin; Huang, Yusheng; Chen, Yahong; Guo, Lina; Cai, Yangjian
2015-11-16
We derive the analytical formula for the orbital angular momentum (OAM) flux of a stochastic electromagnetic beam carrying twist phase [i.e., twisted electromagnetic Gaussian Schell-model (TEGSM) beam] in the source plane with the help of the Wigner distribution function. Furthermore, we derive the general expression of the OAM flux of a TEGSM beam on propagation with the help of a tensor method. As numerical examples, we explore the evolution properties of the OAM flux of a TEGSM beam propagating through a cylindrical thin lens or a uniaxial crystal. It is found that the OAM flux of a TEGSM beam closely depends on its twist factors and degree of polarization in the source plane, and one can modulate the OAM flux of a TEGSM beam by a cylindrical thin lens or a uniaxial crystal. Our results may be useful in some applications, such as particle manipulation and free-space optical communications, where light beam with OAM is preferred.
Twisted Gaussian Schell-model beams. II. Spectrum analysis and propagation characteristics
Sundar, K.; Simon, R. ); Mukunda, N. )
1993-09-01
Extending the work of part I of this series, the authors analyze the structure of the eigenvalue spectrum as well as the propagation characteristics of the twisted Gaussian Schell-model beams. The manner in which the twist phase affects the spectrum, and hence the positivity property of the cross-spectral density, is brought out. Propagation characteristics of these beams are simply deduced from the elementary properties of their modes. It is shown that the twist phase lifts the degeneracy in the eigenvalue spectrum on the one hand and acts as incoherence in disguise on the other. An abstract Hilbert-space operator bringing out the cross-spectral density of the twisted Gaussian Schell-model beam is explicitly constructed, bringing out the useful similarity between these cross-spectral densities and quantum-mechanical thermal-state-density operators of isotropic two-dimensional oscillators, with a term proportional to the angular momentum added to the Hamiltonian. 10 refs.
Optical trapping Rayleigh particles by using focused multi-Gaussian Schell-model beams.
Liu, Xiayin; Zhao, Daomu
2014-06-20
We numerically investigate the radiation forces of multi-Gaussian Schell-model (MGSM) beams, in which the degree of coherence is modeled by the multi-Gaussian function, exerted on the Rayleigh dielectric sphere. By simulation of the forces calculation it is found that the steepness of the edge of the intensity profile (i.e., the summation index M) and the initial coherence width of the MGSM beams play important roles in the trapping range and stability. We can increase the trapping range at the focal plane by increasing the value of M or decreasing the initial coherence of the MGSM beams. It is also found that the trapping stability becomes lower due to the increase of the value of M or the decrease of coherence. Furthermore, the trapping stability under different conditions is explicitly analyzed. The results presented here are helpful for some possible applications.
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.
Lu, Chuanyi; Zhao, Daomu
2016-10-10
An analytical expression for the elements of the cross-spectral density matrix of electromagnetic multi-Gaussian Schell-model beams with astigmatic aberration propagating through the turbulent ocean is derived. We investigate the statistical characteristics of the beams on propagation in great detail. It is found that, due to astigmatism, the circular symmetry of such beams suffers a certain degree of damage in the near field. In addition, astigmatism also destroys the attractive far-field flat profiles in free space. Meanwhile, we also show that astigmatism and oceanic turbulence both have certain effects on the spectral degree of polarization.
Focusing properties of radially polarized multi-cosine Gaussian correlated Schell-model beams
NASA Astrophysics Data System (ADS)
Tang, Miaomiao; Zhao, Daomu; Li, Xinzhong; Li, Hehe
2017-08-01
Scalar partially coherent beams with multi-cosine Gaussian Schell-model correlations were introduced recently (Mei et al., 2015) [9]. In this paper, we introduce a new class of vector multi-cosine Gaussian correlated sources with radial polarization. The realizability conditions for such sources and corresponding beam conditions are established. Analytical formulas for the cross-spectral density matrix of such beam propagating through a stigmatic ABCD optical system are derived and used to examine their focusing properties in detail. The results demonstrate the novel vector sources can generate lattice-like intensity patterns in the focal plane, and possess periodic distribution of the degree of polarization. It is also shown that the initial polarization structure is broken due to the special source coherence and the state of polarization displays in a more complex way in the focal plane. Besides, such characteristics can be flexible modulated by varying the source coherence parameters.
Wang, Fei; Cai, Yangjian; Lin, Qiang
2008-08-01
The truncated fractional Fourier transform (FRT) is applied to a partially coherent Gaussian Schell-model (GSM) beam. The analytical propagation formula for a partially coherent GSM beam propagating through a truncated FRT optical system is derived by using a tensor method. Furthermore, we report the experimental observation of the truncated FRT for a partially coherent GSM beam. The experimental results are consistent with the theoretical results. Our results show that initial source coherence, fractional order, and aperture width (i.e., truncation parameter) have strong influences on the intensity and coherence properties of the partially coherent beam in the FRT plane. When the aperture width is large, both the intensity and the spectral degree of coherence in the FRT plane are of Gaussian distribution. As the aperture width decreases, the diffraction pattern gradually appears in the FRT plane, and the spectral degree of coherence becomes of non-Gaussian distribution. As the coherence of the initial GSM beam decreases, the diffraction pattern for the case of small aperture widths gradually disappears.
Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model.
Chu, Xiuxiang; Qiao, Chunhong; Feng, Xiaoxing; Chen, Ruipin
2011-07-20
We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian-Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.
Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum
Simon, R.; Sundar, K. ); Mukunda, N. )
1993-09-01
The authors present a comprehensive normal-mode decomposition analysis for the recently introduced class of twisted Gaussian Schell-model fields in partially coherent beam optics. The formal analogies to quantum mechanics in two dimensions are exploited. The authors also make effective use of a dynamical SU(2) symmetry of these fields to achieve the mode decomposition and to determine the spectrum. The twist phase is nonseparable in nature, rendering it nontrivially two dimensional. The consequences of this, resulting in the need to use Laguerre-Gaussian functions rather than products of Hermite-Gaussians, are carefully analyzed. An important identity involving these sets of special functions is established and is used in deriving the spectrum. 10 refs.
Generation and propagation of an electromagnetic Gaussian Schell-model vortex beam.
Liu, Xianlong; Wang, Fei; Liu, Lin; Zhao, Chengliang; Cai, Yangjian
2015-11-01
We outline the propagation of an electromagnetic Gaussian Schell-model (EGSM) vortex beam through a paraxial ABCD optical system and analyze the vortex phase-induced changes of the statistical properties, such as average intensity, state of polarization, and degree of polarization (DOP), of a focused EGSM beam. It is found that one can shape the beam profile of an EGSM vortex beam in the focal plane through varying its initial topological charge, DOP, and coherence widths. Furthermore, we first report experimental generation of an EGSM vortex beam and measure its focusing properties in experiments. Our experimental results are consistent with the numerical results and may be useful in material thermal processing and particle trapping.
Effects of coherence on anisotropic electromagnetic Gaussian-Schell model beams on propagation.
Wang, Hua; Wang, Xiangzhao; Zeng, Aijun; Yang, Kun
2007-08-01
An analytical formula for the cross-spectral density matrix of the electric field of anisotropic electromagnetic Gaussian-Schell model beams propagating in free space is derived by using a tensor method. The effects of coherence on those beams are studied. It is shown that two anisotropic stochastic electromagnetic beams that propagate from the source plane z=0 into the half-space z>0 may have different beam shapes (i.e., spectral density) and states of polarization in the half-space, even though they have the same beam shape and states of polarization in the source plane. This fact is due to a difference in the coherence properties of the field in the source plane.
Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam.
Zheng, Chongwei
2006-09-01
The fractional Fourier transform (FRT) is applied to a partially coherent off-axis Gaussian Schell-model (GSM) beam, and an analytical formula is derived for the FRT of a partially coherent off-axis GSM beam. The corresponding tensor ABCD law for performing the FRT of a partially coherent off-axis GSM beam is also obtained. As an application example, the FRT of a partially coherent linear laser array that is expanded as a sum of off-axis GSM beams is studied. The derived formulas are used to provide numerical examples. The formulas provide a convenient way to analyze and calculate the FRT of a partially coherent off-axis GSM beam.
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.
Gaussian beam tracing for ocean acoustics
NASA Astrophysics Data System (ADS)
Porter, Michael B.; Hursky, Paul
2010-09-01
Gaussian beam tracing methods have emerged as a standard approach for modeling sound propagation in the ocean. The first implementations were developed in the 1970's by Bucker and evolved significantly. Today there are actually some four different types of Gaussian beam algorithms. They are quite different in terms of both the beam characteristics and their performance. This paper will review the development of the methods and their application to typical ocean acoustic problems.
Mao, Haidan; Du, Xinyue; Chen, Linfei; Zhao, Daomu
2011-06-01
On the basis of the fact that a hard-edged aperture function can be expressed as finite matrices with different weighting coefficients, we obtain the analytical formula for the propagation of the broadband gaussian Schell-model (BGSM) beam through the apertured fractional Fourier transformation (AFrFT) system. It is shown by numerical examples that the intensity distribution in the plane of a small fractional order is obviously influenced by the bandwidth when the BGSM beams propagate through the AFrFT system. Further extensions are also pointed out.
Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence.
Huang, Yongping; Zhang, Bin; Gao, Zenghui; Zhao, Guangpu; Duan, Zhichun
2014-07-28
The analytical expressions for the cross-spectral density and average intensity of Gaussian Schell-model (GSM) vortex beams propagating through oceanic turbulence are obtained by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of ocean water. The evolution behavior of GSM vortex beams through oceanic turbulence is studied in detail by numerical simulation. It is shown that the evolution behavior of coherent vortices and average intensity depends on the oceanic turbulence including the rate of dissipation of turbulent kinetic energy per unit mass of fluid, rate of dissipation of mean-square temperature, relative strength of temperature salinity fluctuations, and beam parameters including the spatial correlation length and topological charge of the beams, as well as the propagation distance.
NASA Astrophysics Data System (ADS)
Wang, Xun; Liu, Zhirong; Huang, Kelin; Sun, Jingbo
2017-03-01
According to the theory of first-order Born approximation, analytical expressions for Gaussian Schell-model arrays (GSMA) beam scattered on a deterministic medium in the far-zone are derived. In terms of the analytical formula obtained, shifts of GSMA beam's scattered spectrum are numerically investigated. Results show that the scattering directions sx and sy, effective radius σ of the scattering medium, the initial beam transverse width σ0, correlation widths δx and δy of the source, and line width Γ0 of the incident spectrum closely influence the distributions of normalized scattered spectrum in the far-zone. These features of GSMA beam scattered spectrum could be used to obtain information about the structure of a deterministic medium.
NASA Astrophysics Data System (ADS)
Ji, Xiaoling; Pu, Zhengcai; Jia, Xinhong
2009-07-01
The spatial correlation properties and the spectral intensity distributions of focused Gaussian Schell-model (GSM) array beams are studied in detail. The closed-form expressions for the spectral degree of coherence and the spectral intensity of focused GSM array beams are derived. It is shown that the spectral degree of coherence of focused GSM array beams is the same as that of focused GSM beams in the focal plane. On the other hand, it is found that, in the focal plane the spectral intensity distribution of focused GSM array beams is the fringe pattern when the value of the coherence length is small. However, it becomes one peak located at the center as the value of the coherence length is large enough. In the focal plane, the spectral intensity maximum increases and the width of the normalized spectral intensity distribution decreases as the beam number increases. In general, for GSM array beams, the width of the modulus of the spectral degree of coherence in the focal plane always exceeds that of the normalized spectral intensity distribution, which is different from the behavior of focused GSM beams. In addition, the power in the bucket (PIB) and the beam propagation factor ( M2 factor) are also discussed. The main results are explained physically.
Du, Xinyue; Zhao, Daomu
2008-09-29
The cross-spectral density matrixes of electromagnetic Gaussian Schell-model sources that are completely unpolarized or completely polarized are derived. We find that both the completely unpolarized stochastic electromagnetic Gaussian Schell-model beam and the completely polarized stochastic electromagnetic Gaussian Schell-model beam will keep their spectral degree of polarization or become partially polarized under different constraint conditions during their propagation in free space or through turbulent atmosphere. We give necessary theoretical explanation to the physical phenomena. They are considered as coherence-induced polarization changes and spectral density-induced polarization changes.
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.
Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam.
Zhu, Shijun; Cai, Yangjian; Korotkova, Olga
2010-06-07
Analytical formula is derived for the propagation factor (known asM(2)-factor) of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in free space and in turbulent atmosphere. In free space, the M(2)-factor of an EGSM beam is mainly determined by its initial degree of polarization, r.m.s. widths of the spectral densities and correlation coefficients, and its value remains invariant on propagation. In turbulent atmosphere, the M(2)-factor of an EGSM beam is also determined by the parameters of the turbulent atmosphere, and its value increases on propagation. The relative M(2)-factor of an EGSM beam with lower correlation factors, larger r.m.s. widths of the spectral densities and longer wavelength is less affected by the atmospheric turbulence. Under suitable conditions, an EGSM beam is less affected by the atmospheric turbulence than a scalar GSM beam (i.e. fully polarized GSM beam). Our results will be useful in long-distance free-space optical communications.
BEAM-BEAM SIMULATIONS FOR DOUBLE-GAUSSIAN BEAMS.
MONTAG, C.; MALITSKY, N.; BEN-ZVI, I.; LITVINENKO, V.
2005-05-16
Electron cooling together with intra-beam scattering results in a transverse distribution that can best be described by a sum of two gaussians, one for the high-density core and one for the tails of the distribution. Simulation studies are being performed to understand the beam-beam interaction of these double-gaussian beams. Here we report the effect of low-frequency random tune modulations on diffusion in double-gaussian beams and compare the effects to those in beam-beam interactions with regular gaussian beams and identical tune shift parameters.
Second-order statistics of a twisted gaussian Schell-model beam in turbulent atmosphere.
Wang, Fei; Cai, Yangjian
2010-11-22
We present a detailed investigation of the second-order statistics of a twisted gaussian Schell-model (TGSM) beam propagating in turbulent atmosphere. Based on the extended Huygens-Fresnel integral, analytical expressions for the second-order moments of the Wigner distribution function of a TGSM beam in turbulent atmosphere are derived. Evolution properties of the second-order statistics, such as the propagation factor, the effective radius of curvature (ERC) and the Rayleigh range, of a TGSM beam in turbulent atmosphere are explored in detail. Our results show that a TGSM beam is less affected by the turbulence than a GSM beam without twist phase. In turbulent atmosphere the Rayleigh range doesn't equal to the distance where the ERC takes a minimum value, which is much different from the result in free space. The second-order statistics are closely determined by the parameters of the turbulent atmosphere and the initial beam parameters. Our results will be useful in long-distance free-space optical communications.
Propagation of multi-Gaussian Schell-model vortex beams in isotropic random media.
Tang, Miaomiao; Zhao, Daomu
2015-12-14
The effect of isotropic and homogeneous random media on propagation characteristics of recently introduced multi-Gaussian Schell-model (MGSM) vortex beams is investigated. The analytical formula for the cross-spectral density function of such a beam propagating in random turbulent media is derived and used to explore the evolution of the spectral density, the degree of coherence and the turbulence-induced spreading. An example illustrates the fact that, at sufficiently large distance from the source, the source correlations modulation of the spectral distribution in free space is shown to be suppressed by the uniformly correlated turbulence. The impacts, arising from the index M, the correlation width of the source and the properties of the medium on such characteristics are analyzed in depth.
Z-scan experiment with anisotropic Gaussian Schell-model beams.
Liu, Yongxin; Pu, Jixiong; Qi, Hongqun
2009-09-01
We analyze the z-scan experiment with anisotropic Gaussian Schell-model (AGSM) beams. The expression for the cross-spectral density of the AGSM beam passing through the lens and onto the nonlinear thin sample is derived. Based on the expression, we simulate the results of the z-scan experiment theoretically and analyze the effects of the e factor (e=w(0x)/w(0y)) and the spatial degree of coherence in the x and y orientations on the on-axis z-scan transmittance. It is found that DeltaTp(-v) becomes larger with an increment of the e factor and the spatial degree of coherence. So we can improve the sensitivity of the z-scan experiment by increasing the e factor and the spatial degree of coherence. The results are helpful for improving the sensitivity of the z-scan experiment.
Modeling of Gaussian-to-annular beam shaping by geometrical optics for optical trepanning
NASA Astrophysics Data System (ADS)
Zeng, Danyong; Latham, William P.; Kar, Aravinda
2004-09-01
Laser drilling is very important in many industries such as automotive, aerospace, electronics and materials processing. It can be used to produce critical components with novel hole geometry for advanced systems. Percussion drilling and trepanning are two laser drilling methods. In the conventional trepanning method, a laser beam in scanned along a circular or spiral orbit to remove material to achieve a desired hole shape. These orbits generally trace a circular path at the inner wall of the holes. This suggests that an annular beam can be used to accomplish trepanning, which we referred to as optical trepanning. The ray tracing technique of geometrical optics will be employed in this paper to design the necessary optics to transform a Gaussian laser beam into an annular beam of different intensity profiles. Such profiles include half Gaussian with maximum intensities at the inner and outer surfaces of the annulus, respectively, and full Gaussian with maximum intensity within the annulus.
An analysis of a non-Gaussian, Gaussian laser beam
NASA Astrophysics Data System (ADS)
Ross, T. Sean
2006-02-01
It is possible to construct summations of Laguerre-Gaussian modes which have the appearance of a zero order fundamental Gaussian but which, in fact, have no zero order content. These examples have circulated informally as a warning against trusting a single beam profile measurement as to the indication of the modal content of a given beam. These 'non-Gaussian' Gaussian beams also turn out to be extremely revealing of the fundamental assumptions upon which all modal decompositions and modal-based beam quality measures are based upon. Due to the contrived nature of these beams, they are also subject to some very subtle but important theoretical errors. This paper will rigorously examine a 'non-Gaussian', Gaussian beam in terms of its amplitude and phase characteristics, propagation behavior, M2 and what it reveals about modal decompositions and modal beam quality measures in general.
Hirayama, S; Takayanagi, T; Fujii, Y; Fujimoto, R; Fujitaka, S; Umezawa, M; Nagamine, Y; Hosaka, M; Yasui, K; Toshito, T
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 distribution 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.
Description and characterization of plasmonic Gaussian beams
NASA Astrophysics Data System (ADS)
Garcia-Ortiz, Cesar E.; Pisano, Eduardo; Coello, Victor
2017-08-01
In this work, we present for the first time a detailed description and experimental characterization of plasmonic Gaussian beams (PGBs), as well as the analytical expression to describe their field and intensity distributions. The propagation parameters of the PGBs, such as the divergence angle, Rayleigh range, beam width function, and the beam waist are determined experimentally in accordance to the proposed model. The radius of curvature of the wavefront and the Gouy phase shift of PGBs can also be predicted using this method.
Qian, Xianmei; Zhu, Wenyue; Rao, Ruizhong
2009-03-02
The propagation effects of spatially pseudo-partially coherent Gaussian Schell-model beams in atmosphere are investigated numerically. The characteristics of beam spreading, beam wandering and intensity scintillation are analyzed respectively. It is found that the degradation of degree of source coherence may cause reductions of relative beam spreading and scintillation index, which indicates that partially coherent beams are more resistant to atmospheric turbulence than fully coherent beams. And beam wandering is not much sensitive to the change of source coherence. However, a partially coherent beam have a larger spreading than the fully coherent beam both in free space and in atmospheric turbulence. The influences of changing frequency of random phase screen which models the source coherence on the final intensity pattern are also discussed.
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.
Ding, Guilin; Lü, Baida
2002-03-01
The generalized Huygens-Fresnel diffraction integral for misaligned asymmetric first-order optical systems is derived by using the canonical operator method, which enables us to study propagation properties of anisotropic Gaussian Schell-model (AGSM) beams through misaligned asymmetric first-order optical systems. It is shown that under the action of misaligned asymmetric first-order optical systems AGSM beams do not preserve the closed property. Therefore generalized partially coherent anisotropic Gaussian Schell-model beams called decentered anisotropic Gaussian Schell-model (DAGSM) beams are introduced, and AGSM beams can be regarded as a special case of DAGSM beams.
Verma, Manish; Senthilkumaran, P; Joseph, Joby; Kandpal, H C
2013-07-01
The effect on the Stokes parameters of a Gaussian Schell model beam on propagation in free space is studied experimentally and results are matched with the theory [X. H. Zhao, et al. Opt. Express 17, 17888 (2009)] that in general the degree of polarization of a Gaussian Schell model beam doesn't change on propagation if the three spectral correlation widths δ xx, δ yy, δ xy are equal and the beam width parameters σ x =σ y. It is experimentally shown that all the four Stokes parameters at the center of the beam decrease on propagation while the magnitudes of the normalized Stokes parameters and the spectral degree of polarization at the center of the beam remain constant for different propagation distances.
NASA Astrophysics Data System (ADS)
Xu, Hua-Feng; Huang, Lin-Mu; Sheng, Zong-Qiang; Tang, Xu-Dong; Qu, Jun
2017-08-01
The analytical expressions for an orthogonal cosine-Gaussian Schell-model (OCGSM) beam propagating in uniaxial crystals orthogonal to the optical axis are derived. Based on the formulas derived, the propagation properties, such as the normalized spectral density, the spectral degree of coherence (SDOC), and the effective beam width of an OCGSM beam in uniaxial crystals are illustrated. Numerical results show that, by changing the beam mode order n and m, the OCGSM beam can split into two- or four-beamlet elliptical beams and keep invariant in uniaxial crystals during propagation, which is different from the conventional Gaussian Schell-model beam. The SDOC of the OCGSM beam will evolve into an elliptical shape and the effective beam width of the OCGSM beam will spread faster along the x direction than the y direction in uniaxial crystals. In addition, the significant influence of the beam mode order, the spatial coherence length and the ratio of the extraordinary refractive index to the ordinary refractive index of the uniaxial crystals on the evolution properties of an OCGSM beam is discussed in detail.
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.
Coherence properties of a source array derived from a Gaussian Schell-model beam.
Yoshimura, H; Iwai, T
1995-11-10
The spatial coherence properties of a source array derived from a quasi-monochromatic Gaussian Schell-model (GSM) beam are analyzed. The method for realizing the source array by use of a GSM source and a Gaussian amplitude grating was originally proposed in our preceding paper [J. Opt. Soc. Am. A 11, 2112 (1994)], in which the intensity distribution was analyzed. One result that we obtain is that the degree of spatial coherence of each element in the source array is the same as that at the other elements. In particular, each element becomes equivalent to the GSM source and has a high degree of spatial coherence with the other elements if three conditions are satisfied simultaneously: (1) the spatial-coherence length of the GSM source is larger than the GSM source size, (2) the GSM source size normalized by a period of the grating is 0.3 to 0.5, and (3) each aperture size of the grating normalized by the period is 0.05 or less.
Cai, Yangjian; Hu, Li
2006-03-15
By expanding the hard-aperture function into a finite sum of complex Gaussian functions, we derived an approximate analytical formula for a partially coherent twisted anisotropic Gaussian Schell-model (AGSM) beam propagating through an apertured paraxial general astigmatic (GA) optical system by use of a tensor method. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. Our formulas avoid time-consuming numerical integration and provide a convenient and effective way for studying the propagation and transformation of a partially coherent twisted AGSM beam through an apertured paraxial GA optical system.
Reflection and transmission of Gaussian beam by a chiral slab
NASA Astrophysics Data System (ADS)
Yan, Bing; Zhang, Huayong; Zhang, Jianyong
2016-06-01
Based on the generalized Lorenz-Mie theory framework, the reflection and transmission of an incident Gaussian beam by a chiral slab were investigated, by expanding the incident Gaussian beam, reflected beam, internal beam as well as transmitted beam in terms of cylindrical vector wave functions. The unknown expansion coefficients were determined by virtue of the boundary conditions. For a localized beam model, numerical results of the normalized field intensity distributions are presented, and the propagation characteristics are discussed concisely in this paper.
Cylindrical quasi-Gaussian beams.
Mitri, F G
2013-11-15
Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w(0) satisfying both the Helmholtz and Maxwell's equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell's vectorial equations and Lorenz's gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures.
Propagation of cosine-Gaussian-correlated Schell-model beams in atmospheric turbulence.
Mei, Zhangrong; Schchepakina, Elena; Korotkova, Olga
2013-07-29
A stochastic beam generated by a recently introduced source of Schell type with cosine-Gaussian spectral degree of coherence is shown to possess interesting novel features on propagation in isotropic and homogeneous atmospheric turbulence with general non-Kolmogorov power spectrum. It is shown that while at small distances from the source the beam's intensity exhibits annular profile with adjustable area of the dark region, the center disappears at sufficiently large distances and the beam's intensity tends to Gaussian form. Hence the 3D bottle beam is produced by the cumulative effect of the random source and the atmosphere. The distances at which the on-axis beam intensity has local minima and maxima are shown to have analytic dependence on the source and the atmospheric parameters. And the influence of the fractal constant of the atmospheric power spectrum and refractive-index structure constant on beam characteristics is analyzed in depth. The novel double-cycle qualitative change in the degree of coherence is shown to occur on atmospheric propagation which was not previously known for any other beams.
Asymmetric Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-06-01
We introduce a family of asymmetric Laguerre-Gaussian (aLG) laser beams. The beams have been derived via a complex-valued shift of conventional LG beams in the Cartesian plane. While propagating in a uniform medium, the first bright ring of the aLG beam becomes less asymmetric and the energy is redistributed toward peripheral diffraction rings. The projection of the orbital angular momentum (OAM) onto the optical axis is calculated. The OAM is shown to grow quadratically with increasing asymmetry parameter of the aLG beam, which equals the ratio of the shift to the waist radius. Conditions for the OAM becoming equal to the topological charge have been derived. For aLG beams with zero radial index, we have deduced an expression to define the intensity maximum coordinates and shown the crescent-shaped intensity pattern to rotate during propagation. Results of the experimental generation and rotation of aLG beams agree well with theoretical predictions.
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.
Elegant Gaussian beams for enhanced optical manipulation
Alpmann, Christina 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 function is relevant.
Yu, Jiayi; Chen, Yahong; Liu, Lin; Liu, Xianlong; Cai, Yangjian
2015-05-18
Elegant Hermite-Gaussian correlated Schell-model (EHGCSM) beam was introduced in theory and generated in experiment just recently [Phys. Rev. A 91, 013823 (2015)]. In this paper, we study the propagation properties of an EHGCSM beam in turbulent atmosphere with the help of the extended Huygens-Fresnel integral. Analytical expressions for the cross-spectral density and the propagation factors of an EHGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence and the propagation factors, of an EHGCSM beam in Kolmogorov and non-Kolmogorov turbulence are illustrated numerically. It is found that an EHGCSM beam exhibits splitting and combing properties in turbulent atmosphere, and an EHGCSM beam with large mode orders is less affected by turbulence than an EHGCSM beam with small mode orders or a Gaussian Schell-model beam or a Gaussian beam, which will be useful in free-space optical communications.
Quasi-Gaussian electromagnetic beams
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2013-03-01
A class of Maxwellian beams, which is an exact solution of the vector wave equation (Helmholtz equation) and Maxwell's equations, is introduced. The solution, termed a quasi-Gaussian electromagnetic (EM) beam, is formed from a superposition of sources and sinks with complex coordinates, and is characterized by an arbitrary waist w0 and a diffraction convergence length known as the Rayleigh range zR. An attractive feature of this beam is the description of strongly focused (or strongly divergent) EM-optical wave fields for kw0≤1, where k is the wave number. A vector wave analysis is developed to determine and compute the spatial Cartesian components of the electric and magnetic fields (valid in the near field and the far field) stemming from Maxwell's vector equations and the Lorenz gauge condition, with particular emphasis on the parameter kw0 and the polarization states of the vector potentials used to derive the EM field's components. The results are potentially useful in the study of the axial and/or arbitrary wave scattering, radiation force, and torque in lasers operating with strongly focused (or strongly divergent) beams for particle manipulation in optical tweezers and imaging applications.
Least-squares Gaussian beam migration
NASA Astrophysics Data System (ADS)
Yuan, Maolin; Huang, Jianping; Liao, Wenyuan; Jiang, Fuyou
2017-02-01
A theory of least-squares Gaussian beam migration (LSGBM) is presented to optimally estimate a subsurface reflectivity. In the iterative inversion scheme, a Gaussian beam (GB) propagator is used as the kernel of linearized forward modeling (demigration) and its adjoint (migration). Born approximation based GB demigration relies on the calculation of Green’s function by a Gaussian-beam summation for the downward and upward wavefields. The adjoint operator of GB demigration accounts for GB prestack depth migration under the cross-correlation imaging condition, where seismic traces are processed one by one for each shot. A numerical test on the point diffractors model suggests that GB demigration can successfully simulate primary scattered data, while migration (adjoint) can yield a corresponding image. The GB demigration/migration algorithms are used for the least-squares migration scheme to deblur conventional migrated images. The proposed LSGBM is illustrated with two synthetic data for a four-layer model and the Marmousi2 model. Numerical results show that LSGBM, compared to migration (adjoint) with GBs, produces images with more balanced amplitude, higher resolution and even fewer artifacts. Additionally, the LSGBM shows a robust convergence rate.
Avramov-Zamurovic, S; Nelson, C; Guth, S; Korotkova, O
2016-05-01
Reduction in the scintillation index of multi-Gaussian Schell-model beams propagating in turbulent air is demonstrated as a function of two source parameters: the r.m.s. coherence width and the summation index. The beams were generated with the help of a nematic phase-only, reflective spatial light modulator at a cycling rate of 333 frames per second and recorded after propagating through a weakly turbulent air channel over a distance of 70 m. Experimental results are in good agreement with theory.
NASA Astrophysics Data System (ADS)
Gao, Ming; Li, Yan; Lv, Hong; Gong, Lei
2014-11-01
This paper is based on the unified theory of coherence and polarization of stochastic electromagnetic beams and the extended Huygens-Fresnel principle, combined with the quadratic approximation of Rytov's phase structure function and the generalized Stokes parameters. We have derived the novel expressions for the cross-spectral density matrix elements and the degree of cross-polarization of a class of elliptically polarized spatially and spectrally partially coherent Electromagnetic Gaussian-Schell model pulse (EGSMP) beams propagating through atmospheric turbulence along a slant path. Additionally, we calculate and analyze the effects of the turbulent intensity, the initial pulse duration, waist width of the beam, the spatial coherence length and temporal coherence length et al. on the polarization properties of fully polarized and partially coherent EGSMP beams. Finally, a comparison of the impact of those factors on the partially polarization beams is made. The results show that the influences of the turbulent intensity, the initial pulse duration, waist width of the beam, the spatial coherence length and temporal coherence length et al. on the polarization properties of fully polarized and partially coherent EGSMP beams are larger. While the effects of those parameters on the partially polarization and partially coherent EGSMP beams are smaller. It is noted that the results of this paper have established sound theoretical basis on the topic of improving performance of the laser system propagating through the atmospheric turbulence.
NASA Astrophysics Data System (ADS)
Wang, Xiaoyang; Yao, Mingwu; Yi, Xiang; Qiu, Zhiliang; Liu, Zengji
2017-01-01
The explicit closed-form expressions for the beam width and angular spread of multi-Gaussian Schell-model vortex (MGSMV) beams propagating through atmospheric turbulence are derived in this paper. The spreading and evolution behavior of coherent vortices of MGSMV beams in non-Kolmogorov turbulence are investigated quantitatively by some typical numerical examples, where the evolution behavior of coherent vortices is stressed in particular. It is illustrated that MGSMV beams are more resistant to atmospheric turbulence than multi-Gaussian Schell-model (MGSM) non-vortex beams. By increasing the beam index of MGSMV beams, the deleterious turbulence effects can be reduced gradually. As MGSMV beams propagate in non-Kolmogorov turbulence, the position and number of coherent vortices are changeable. The impact of the beam index and fluctuations of atmospheric turbulence on the conservation distance of the topological charge is also explored in depth.
Zhao, Xinhui; Yao, Yong; Sun, Yunxu; Liu, Chao
2009-09-28
In the free space optical communication system with circle polarization shift keying (CPolSK) modulation, the changes of polarization state of light beam have significant influence on the system performance. Keeping the state of polarization (SOP) unchanged on propagation can reduce the bit error rate. Based on the unified theory of coherence and polarization, we derive the sufficient condition for Gaussian Schell-model (GSM) beam to keep the SOP unchanged. We found that when the three spectral correlation widths (delta(xx), delta(yy) and delta(xy)) equal to each other and sigma(x) = sigma(y), the GSM beam maintains the SOP on propagation. This conclusion can be helpful for the design of the transmitter in the CPolSK system.
Li, Ye; Zhang, Yixin; Zhu, Yun; Chen, Minyu
2016-07-01
Based on the spatial power spectrum of the refractive index of anisotropic turbulence, the average polarizability of the Gaussian Schell-model quantized beams and lateral coherence length of the spherical wave propagating through the ocean water channel are derived. Numerical results show that, in strong temperature fluctuation, the depolarization effects of anisotropic turbulence are inferior to isotropic turbulence, as the other parameters of two links are the same. The depolarization effects of salinity fluctuation are less than the effects of the temperature fluctuation; the average polarizability of beams increases when increasing the inner scale of turbulence and the source's transverse size; and the larger rate of dissipation of kinetic energy per unit mass of fluid enhances the average polarizability of beams. The region of the receiving radius is smaller than the characteristic radius and the average polarizability of beams in isotropy turbulence is smaller than that of beams in anisotropy turbulence. However, the receiving radius region is larger than a characteristic radius and the average polarizability of beams in isotropy turbulence is larger than that of beams in anisotropy turbulence.
NASA Astrophysics Data System (ADS)
Haghighatzadeh, A.; Golnabi, H.
2013-05-01
Both theoretical and experimental results of an optical beam shaping system are investigated in this report. The described system is a two-stage beam shaping device including a fiber-bundle and a prism-duct. A source light is used to illuminate the fiber-bundle and the image of output beam is captured by a CCD camera. The fiber-bundle output beam shape shows a linear arrangement of circular spots lights, which are placed in a rectangular cross section of about 21.37 mm×2.44 mm. In another study, the photograph picture of the prism output beam is taken by a digital camera. The prism output beam cross section is a square shape with a dimension of about 4×4 mm2. According to the experimental results, the prism duct converted a Gaussian beam profile with multiple-peak distribution to a hat-top beam profile with the uniform intensity distribution. For theoretical investigations, using ZEMAX software a simulation is performed to analyze the beam shaping design. By proper modeling the output beam shape and radiance profiles in position space and angle space of the fiber-bundle and the prism duct are investigated. Theoretical radiance profiles are obtained by using simulated images and results are in agreement with the experimental results.
Scalar field of nonparaxial Gaussian beams.
Ulanowski, Z; Ludlow, I K
2000-12-15
A family of closed-form expressions for the scalar field of strongly focused Gaussian beams in oblate spheroidal coordinates is given. The solutions satisfy the wave equation and are free from singularities. The lowest-order solution in the far field closely matches the energy density produced by a sine-condition, high-aperture lens illuminated by a paraxial Gaussian beam. At the large waist limit the solution reduces to the paraxial Gaussian beam form. The solution is equivalent to the spherical wave of a combined complex point source and sink but has the advantage of being more directly interpretatable.
Ma, Jing; Wu, Jiajie; Tan, Liying; Yu, Siyuan
2017-02-20
Based on the extended Huygens-Fresnel principle, the element expression of a cross-spectral matrix of Gaussian-Schell-model (GSM) laser beams propagating in a space-to-ground optical communication downlink is derived analytically. With full consideration of both the source parameters and the zenith angle, the changes in the degree of polarization (DOP) and the state of polarization (SOP) are investigated. The simulation results indicate that the source parameters play a crucial role in determining both DOP and SOP in space-to-ground optical communication downlinks. Compared to the source parameters, the zenith angle has no obvious influence on the polarization properties when it is smaller than 88°. The results of this work provide a design basis for a polarization shift keying optical communication system with a GSM laser beam.
Modeling focusing Gaussian beams in a turbid medium with Monte Carlo simulations.
Hokr, Brett H; Bixler, Joel N; Elpers, Gabriel; Zollars, Byron; Thomas, Robert J; Yakovlev, Vladislav V; Scully, Marlan O
2015-04-06
Monte Carlo techniques are the gold standard for studying light propagation in turbid media. Traditional Monte Carlo techniques are unable to include wave effects, such as diffraction; thus, these methods are unsuitable for exploring focusing geometries where a significant ballistic component remains at the focal plane. Here, a method is presented for accurately simulating photon propagation at the focal plane, in the context of a traditional Monte Carlo simulation. This is accomplished by propagating ballistic photons along trajectories predicted by Gaussian optics until they undergo an initial scattering event, after which, they are propagated through the medium by a traditional Monte Carlo technique. Solving a known problem by building upon an existing Monte Carlo implementation allows this method to be easily implemented in a wide variety of existing Monte Carlo simulations, greatly improving the accuracy of those models for studying dynamics in a focusing geometry.
Gaussian Multipole Model (GMM)
Elking, Dennis M.; Cisneros, G. Andrés; Piquemal, Jean-Philip; Darden, Thomas A.; Pedersen, Lee G.
2009-01-01
An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer energies, inter-molecular density overlap integrals, and permanent molecular multipole moments with their respective ab initio values. For the case of water, the atomic Gaussian multipole moments Qlm are shown to be a smooth function of internal geometry (bond length and bond angle), which can be approximated by a truncated linear Taylor series. In addition, results are given when the Gaussian multipole charge density is applied to a model for exchange-repulsion energy based on the inter-molecular density overlap. PMID:20209077
Optimization of Gaussian beam widths in acoustic propagation
NASA Astrophysics Data System (ADS)
Gordon, D. F.
1989-10-01
The use of Gaussian beams to compute wave propagation phenomena is a field of current interest and activity. Porter and Bucker (1987) supply an extensive list of references. More recent references can be found in Benites and Aki (1989). Gaussian beams can be traced as rays in range-dependent media providing not only propagation loss, but travel times, multipath structure, and frequency dependence. The well-known ray theory problems of caustics and shadow zones are treated automatically. A beam width minimization technique applied to a Gaussian beam model developed by Dr. H. P. Bucker, is outlined. Porter and Bucker (1987) gives the formulation upon which the techniques is built. A free parameter E is usually determined in a heuristic manner. Here, it is shown that the minimization of beam width assigns a precise value to E. Examples are given showing that the minimized beams give good propagation losses in some cases. A case also shown in the standard Gaussian beams give poor results and the minimized beams give even worse results. The problem appears to arise in beams that pass near boundaries. This problem will have to be corrected before a final judgment can be made on the validity of minimum-width beams.
Gaussian Process Morphable Models.
Luthi, Marcel; Gerig, Thomas; Jud, Christoph; Vetter, Thomas
2017-08-14
Models of shape variations have become a central component for the automated analysis of images. An important class of shape models are point distribution models (PDMs). These models represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of PDMs, which we refer to as Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loève expansion. To compute the expansion, we make use of an approximation scheme based on the Nyström method. The resulting model can be seen as a continuous analog of a standard PDM. However, while for PDMs the shape variation is restricted to the linear span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, a PDM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics but is flexible enough to explain shapes that cannot be represented by the PDM.
Temperature modes for nonlinear Gaussian beams.
Myers, Matthew R; Soneson, Joshua E
2009-07-01
In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions.
Beam tracing description of non-Gaussian wave beams
NASA Astrophysics Data System (ADS)
Tsironis, Christos; Poli, Emanuele; Pereverzev, Grigory V.
2006-11-01
In experiments involving electron-cyclotron waves, beams with a non-Gaussian amplitude profile can be generated by the launching system or during the propagation in the plasma. The propagation and absorption of non-Gaussian beams is formulated in terms of the beam tracing asymptotic technique. The proper sequence for tracing arbitrary beams has been established, which involves the formulation of the decomposition of arbitrary electric field profiles into Gaussian-Hermite modes, the generalization of the beam width parameter, and the damping of higher-order modes. The effect of the phase-shift of the modes (with respect to the beam axis) is analyzed within beam tracing and included in the description of the beam. As an application, we consider the propagation and absorption of multimode beams in a simplified plasma geometry, where a comparison with an exact solution is possible. Also, the properties of the propagation of a non-Gaussian beam in the transmission line of an EC launching system are analyzed.
Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams.
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.
Propagation of modified Bessel-Gaussian beams in turbulence
NASA Astrophysics Data System (ADS)
Eyyuboğlu, Halil Tanyer; Hardalaç, Fırat
2008-03-01
We investigate the propagation characteristics of modified Bessel-Gaussian beams traveling in a turbulent atmosphere. The source beam formulation comprises a Gaussian exponential and the summation of modified Bessel functions. Based on an extended Huygens-Fresnel principle, the receiver plane intensity is formulated and solved down to a double integral stage. Source beam illustrations show that modified Bessel-Gaussian beams, except the lowest order case, will have well-like shapes. Modified Bessel-Gaussian beams with summations will experience lobe slicing and will display more or less the same profile regardless of order content. After propagating in turbulent atmosphere, it is observed that a modified Bessel-Gaussian beam will transform into a Bessel-Gaussian beam. Furthermore it is seen that modified Bessel-Gaussian beams with different Bessel function combinations, but possessing nearly the same profile, will differentiate during propagation. Increasing turbulence strength is found to accelerate the beam transformation toward the eventual Gaussian shape.
Modulation depth of Michelson interferometer with Gaussian beam.
Välikylä, Tuomas; Kauppinen, Jyrki
2011-12-20
Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.
Zhu, Ziren; Liu, Lin; Wang, Fei; Cai, Yangjian
2015-03-01
Analytical expressions for the cross-spectral density function and the second-order moments of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in uniaxial crystals orthogonal to the optical axis are derived. Based on the formulas derived, we study the propagation properties, such as beam irradiance, beam diameters, and the spectral degree of coherence, of a LGCSM beam inside uniaxial crystals in detail. The effect of the initial beam parameters (mode order and spatial coherence length) and the parameters of the uniaxial crystals on the evolution properties of a LGCSM beam is revealed through numerical examples. The uniaxial crystals provide one way to modulate the properties of a LGCSM beam.
Shen, Jiajian; Liu, Wei; Stoker, Joshua; Ding, Xiaoning; Anand, Aman; Hu, Yanle; Herman, Michael G; Bues, Martin
2016-12-01
To find an efficient method to configure the proton fluence for a commercial proton pencil beam scanning (PBS) treatment planning system (TPS). An in-water dose kernel was developed to mimic the dose kernel of the pencil beam convolution superposition algorithm, which is part of the commercial proton beam therapy planning software, eclipse™ (Varian Medical Systems, Palo Alto, CA). The field size factor (FSF) was calculated based on the spot profile reconstructed by the in-house dose kernel. The workflow of using FSFs to find the desirable proton fluence is presented. The in-house derived spot profile and FSF were validated by a direct comparison with those calculated by the eclipse TPS. The validation included 420 comparisons of the FSFs from 14 proton energies, various field sizes from 2 to 20 cm and various depths from 20% to 80% of proton range. The relative in-water lateral profiles between the in-house calculation and the eclipse TPS agree very well even at the level of 10(-4). The FSFs between the in-house calculation and the eclipse TPS also agree well. The maximum deviation is within 0.5%, and the standard deviation is less than 0.1%. The authors' method significantly reduced the time to find the desirable proton fluences of the clinical energies. The method is extensively validated and can be applied to any proton centers using PBS and the eclipse TPS.
Entanglement Rate for Gaussian Continuous Variable Beams
2016-08-24
entangledGaussian beamswith arbitrary correlators . This expression is especially useful for situationswhere the source emits an arbitrary frequency spectrum...However, such a naive approach fails if there are correlations between subsequent pairs, or if we consider entangled beams of radiation that cannot be...frequency integral over what we call a ‘spectral density of entanglement’.We showhow to obtain this from the two-point time correlators of the entangled
Production and propagation of Hermite-sinusoidal-Gaussian laser beams.
Tovar, A A; Casperson, L W
1998-09-01
Hermite-sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the limit of large Hermite-Gaussian beam size, the sinusoidal factors are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar Hermite-Gaussian form. The propagation of these beams is examined in detail, and resonators are designed that will produce them. As an example, a special resonator is designed to produce hyperbolic-sine-Gaussian beams. This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. The beam mode has finite energy and is perturbation stable.
NASA Astrophysics Data System (ADS)
Rohani, A.; Shishegar, A. A.; Safavi-Naeini, S.
2004-03-01
A fast Gaussian beam tracing method for general vectorial astigmatic Gaussian beams based on phase matching has been formulated. Given the parameters of a vectorial Gaussian beam in its principal coordinate system the parameters of the reflected and refracted beams from a general curved surface (with general constitutive parameters) are found. The reflection and transmission of such beams from and through passive photonic structures such as lenses, mirrors and prisms can then be found by considering multiple reflections and transmissions.
Correlation singularities of partially coherent beams with multi-Gaussian correlation function
NASA Astrophysics Data System (ADS)
Zhang, Yongtao; Wang, Haixia; Ding, Chaoliang; Pan, Liuzhan
2017-08-01
Correlation singularities of partially coherent beams with multi-Gaussian correlation function (i.e., multi-Gaussian Schell-model beams) are studied. It is shown that there exist correlation singularities for scalar multi-Gaussian Schell-model (MGSM) beams, both in the source plane and in the output plane. We find the simple relation between the correlation singularities and the beam index M of MGSM beams, i.e., the number of ring dislocations equals M - 1, which may be used to determine the beam index M.
Higher order annular Gaussian laser beam propagation in free space
NASA Astrophysics Data System (ADS)
Eyyuboglu, Halil T.; Yenice, Yusuf E.; Baykal, Yahya K.
2006-03-01
Propagation of higher order annular Gaussian (HOAG) laser beams in free space is examined. HOAG beams are defined as the difference of two Hermite-Gaussian (HG) beams; thus, they can be produced by subtracting a smaller beam from a larger beam, that are cocentered and both possess HG mode field distributions. Such beams can be considered as a generalization of the well-known annular Gaussian beams. We formulate the source and receiver plane characteristics and kurtosis parameter of HOAG beams propagating in free space and evaluate them numerically. In comparison to HG beams, HOAG beams have a broader beam size with outer lobes of kidney shape. The amount of received power within the same receiver aperture size, that is, power in bucket, is generally lower for higher order beams. The convergence of the kurtosis parameter to an asymptotic value for higher order beams takes much longer propagation distances compared to zero-order beams.
High-order pseudo-Gaussian scalar acoustical beams.
Mitri, Farid
2014-01-01
Exact solutions of the scalar Helmholtz equation describing tightly spherically-focused beams are introduced without any approximations using the complex source point method in spherical coordinates. The generalized solutions, valid for any integer degree n and order m, describe high-order pseudo-Gaussian vortex, intermediate (vortex), hollow (nonvortex), and trigonometric (non-vortex) beams having an arbitrary beam waist w0. A very useful property of these beams is the efficient and fast computational modeling of tightly focused or quasi-collimated wave-fronts depending on the dimensionless waist parameter kw0, where k is the wave number of the acoustical radiation. Examples that illustrate hollow vortex and non-vortex beams are provided, and numerical simulations for the magnitude, isosurface, and phase plots of the pressure wave field of higher-order quasi-Gaussian beams are evaluated with particular emphasis on kw0 for strongly (kw0 = 3) to weakly focused (i.e., quasi-collimated) beams (kw0 = 7). Potential applications are in beam-forming design, imaging, particle sizing and manipulation in acoustical tweezers, and phenomena related to scattering, radiation force, and torque.
NASA Astrophysics Data System (ADS)
Inaniwa, T.; Kanematsu, N.; Hara, Y.; Furukawa, T.; Fukahori, M.; Nakao, M.; Shirai, T.
2014-09-01
Challenging issues in treatment planning for scanned carbon-ion (C-ion) therapy are (i) accurate calculation of dose distribution, including the contribution of large angle-scattered fragments, (ii) reduction in the memory space required to store the dose kernel of individual pencil beams and (iii) shortening of computation time for dose optimization and calculation. To calculate the dose contribution from fragments, we modeled the transverse dose profile of the scanned C-ion beam with the superposition of three Gaussian distributions. The development of pencil beams belonging to the first Gaussian component was calculated analytically based on the Fermi-Eyges theory, while those belonging to the second and third components were transported empirically using the measured beam widths in a water phantom. To reduce the memory space for the kernels, we stored doses only in the regions of interest considered in the dose optimization. For the final dose calculation within the patient’s whole body, we applied a pencil beam redefinition algorithm. With these techniques, the triple Gaussian beam model can be applied not only to final dose calculation but also to dose optimization in treatment planning for scanned C-ion therapy. To verify the model, we made treatment plans for a homogeneous water phantom and a heterogeneous head phantom. The planned doses agreed with the measurements within ±2% of the target dose in both phantoms, except for the doses at the periphery of the target with a high dose gradient. To estimate the memory space and computation time reduction with these techniques, we made a treatment plan for a bone sarcoma case with a target volume of 1.94 l. The memory space for the kernel and the computation time for final dose calculation were reduced to 1/22 and 1/100 of those without the techniques, respectively. Computation with the triple Gaussian beam model using the proposed techniques is rapid, accurate and applicable to dose optimization and
Propagation of sharply autofocused ring Airy Gaussian vortex beams.
Chen, Bo; Chen, Chidao; Peng, Xi; Peng, Yulian; Zhou, Meiling; Deng, Dongmei
2015-07-27
Controlling the focal length and the intensity of the optical focus in the media is an important task. Here we investigate the propagation properties of the sharply autofocused ring Airy Gaussian vortex beams numerically and some numerical experiments are performed. We introduce the distribution factor b into the initial beams, and discuss the influences for the beams. With controlling the factor b, the beams that tend to a ring Airy vortex beam with the smaller value, or a hollow Gaussian vortex beam with the larger one. By a choice of initial launch condition, we find that the number of topological charge of the incident beams, as well as its size, greatly affect the focal intensity and the focal length of the autofocused ring Airy Gaussian vortex beams. Furthermore, we show that the off-axis autofocused ring Airy Gaussian beams with vortex pairs can be implemented.
Zhang, Rong; Wang, Xiangzhao; Cheng, Xin; Qiu, Zicheng
2010-11-01
When propagating in free space, the transversal distribution of the degree of polarization of an anisotropic electromagnetic Gaussian-Schell model (AEGSM) beam will generally undergo a complex evolution process. We find that this transversal distribution of the degree of polarization of an AEGSM beam can be controlled by exploiting the partial correlation properties of the source. The main research of our paper falls into two parts. First, the concept of analogical propagation of the transversal distribution of the degree of polarization is proposed, and the condition for an AEGSM beam having an analogical propagation is obtained. When an AEGSM beam is on analogical propagation, the distribution of the degree of polarization on any cross section of the beam is always similar to that on the source plane, except that the size of the distribution pattern will expand continuously as the propagation distance increases. Second, the far-field transversal distribution of the degree of polarization is considered, and the condition for the far-field transversal polarization distribution of an AEGSM beam to be always of circularly symmetric shape, no matter how complicated it is on the source, is obtained. Our research is expected to find applications in areas that make use of the polarization properties of random electromagnetic beams.
Electron acceleration by a tightly focused cylindrical vector Gaussian beam
NASA Astrophysics Data System (ADS)
Xu, Jian; Yang, Zhen-Jun; Li, Jian-Xing; Zang, Wei-Ping
2017-02-01
We have studied the electron acceleration by a tightly focused cylindrical vector Gaussian beam. Different from the Lax series field, cylindrical vector Gaussian beams are vector-beam solutions of Maxwell’s equations and its focusing property can be numerically analyzed by the Richards-Wolf vectorial diffraction theory. Field differences exist between the cylindrical vector Gaussian beam and the Lax series field. The cylindrical vector Gaussian beam increases the asymmetry of the electromagnetic fields, which is more beneficial to the electron acceleration. When the beam waist falls down to the order of the wavelength, the high laser intensity zone is more proper to define the reflection, capture and transmission conditions of the electrons. The injection energy and the injected angle of the electron and the initial phase of the laser beam play important roles for the electron to enter and be trapped by the high laser intensity zone.
Comparison of Gaussian and super Gaussian laser beams for addressing atomic qubits
NASA Astrophysics Data System (ADS)
Gillen-Christandl, Katharina; Gillen, Glen D.; Piotrowicz, M. J.; Saffman, M.
2016-05-01
We study the fidelity of single-qubit quantum gates performed with two-frequency laser fields that have a Gaussian or super Gaussian spatial mode. Numerical simulations are used to account for imperfections arising from atomic motion in an optical trap, spatially varying Stark shifts of the trapping and control beams, and transverse and axial misalignment of the control beams. Numerical results that account for the three-dimensional distribution of control light show that a super Gaussian mode with intensity I˜ e^{-2(r/w_0)^n} provides reduced sensitivity to atomic motion and beam misalignment. Choosing a super Gaussian with n=6 the decay time of finite temperature Rabi oscillations can be increased by a factor of 60 compared to an n=2 Gaussian beam, while reducing crosstalk to neighboring qubit sites.
Gaussian entanglement generation from coherence using beam-splitters
NASA Astrophysics Data System (ADS)
Wang, Zhong-Xiao; Wang, Shuhao; Ma, Teng; Wang, Tie-Jun; Wang, Chuan
2016-11-01
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.
The symmetry properties of stable polynomial Gaussian beam profiles
NASA Astrophysics Data System (ADS)
Roux, Filippus S.
2006-12-01
We consider the symmetry properties of polynomial Gaussian beam profiles (intensity distributions) that remain stable during propagation, apart from being scaled and possibly rotated. These beams are expressed as special linear combinations of the Laguerre-Gaussian modes. Two kinds of symmetries are present: discreet rotational symmetries and mirror symmetries. The symmetry properties are shown to depend on the particular subset of Laguerre-Gaussian modes that is used to construct the stable beam. We demonstrate the symmetry properties of a few examples of stable beams through numerical simulations.
Yang, Ailin; Zhang, Entao; Ji, Xiaoling; Lü, Baida
2008-06-09
The propagation of partially coherent Hermite-cosh-Gaussian (H-ChG)beams through atmospheric turbulence is studied in detail. The analytical expression for the angular spread of partially coherent H-ChG beams in turbulence is derived. It is shown that the angular spread of partially coherent H-ChG beams with smaller spatial correlation length sigma0, smaller waist width w0, smaller beam parameter Omega0, and larger beam orders m, n is less affected by turbulence than that of partially coherent H-ChG beams with larger sigma0, w0, Omega0, and smaller m, n. Under a certain condition partially coherent H-ChG beams may generate the same angular spread as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The angular spread of partially coherent Hermite-Gaussian (H-G), cosh-Gaussian (ChG), Gaussian Schell-model (GSM) beams, and fully coherent H-ChG, H-G, ChG, Gaussian beams is studied and treated as special cases of partially coherent H-ChG beams. The results are interpreted physically.
Optical rogue waves generated on Gaussian background beam.
Liu, Chong; Yang, Zhan-Ying; Zhao, Li-Chen; Xin, Guo-Guo; Yang, Wen-Li
2014-02-15
We study optical rogue waves (RWs) in a nonlinear graded-index waveguide with variable coefficients. An exact RW solution on Gaussian background beam is presented, in contrast to the previous studies about RWs, on plane wave background. It is shown that the characteristics of RWs are maintained on Gaussian background beam and that the beam's width is even a bit smaller than the RWs scale. These results may raise the possibility of related experiments and potential applications in nonlinear optics.
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.
BER of flat-topped Gaussian beam in slant path turbulent atmosphere
NASA Astrophysics Data System (ADS)
Lu, Fang; Han, Yanyan; Han, Xiang-e.; Yang, Rui-ke
2013-08-01
Based on the theory of optical wave propagation in the slant path and the ITU-R turbulence structure constant model which is dependent on altitude, the on-axis scintillation index of the flat-topped Gaussian beam at the receiver plane in slant path turbulence was given by using Kolmogorov atmospheric turbulence power spectrum model. The influences of the link altitudes, atmospheric refractive index structure constant C0 at the ground，the source size and the beam order on scintillation index of the flat-topped Gaussian beam are discussed in detail. The result shows that the scintillation index increased first and then decreased with the increase of the beam order. The advantage of a flat-topped Gaussian beam over a single Gaussian beam is restricted to small source sizes, which is consistent with the case of the horizontal path. To find the average bit error rate under weak slant path turbulence, the log-normal distribution model of the intensity fluctuation was used. The influence of beam order and source size on BER was discussed. The result indicates that the smaller sized flat-topped Gaussian beam will bring average bit error rate advantage over the same size Gaussian beam. Our results correctly reduce to the result of the horizontal path with atmospheric structure constant fixed.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
Kotlyar, V. V.; Kovalev, A. A. Porfirev, A. P.
2016-07-14
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.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
NASA Astrophysics Data System (ADS)
Kotlyar, V. V.; Kovalev, A. A.; Porfirev, A. P.
2016-07-01
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.
Fractionalization of optical beams: II. Elegant Laguerre Gaussian modes
NASA Astrophysics Data System (ADS)
Gutiérrez-Vega, Julio C.
2007-05-01
We apply the tools of fractional calculus to introduce new fractional-order solutions of the paraxial wave equation that smoothly connect the elegant Laguerre-Gaussian beams of integral-order. The solutions are characterized in general by two fractional indices and are obtained by fractionalizing the creation operators used to create elegant Laguerre-Gauss beams from the fundamental Gaussian beam. The physical and mathematical properties of the circular fractional beams are discussed in detail. The orbital angular momentum carried by the fractional beam is a continuous function of the angular mode index and it is not restricted to take only discrete values.
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.
Photonic bandgap under irradiation of a Gaussian beam
NASA Astrophysics Data System (ADS)
Jamshidi-Ghaleh, Kazem; Abdi-Ghaleh, Reza
2011-01-01
The transfer matrix of a dielectric slab under propagation of a Gaussian beam was formulated. The derived matrix was applied for a one-dimensional photonic crystal (1DPC) structure and the transmittance spectrum and photonic bandgap (PBG) properties were investigated. An r-dependent (r is the radial coordinate of the Gaussian beam) PBG was obtained. With the increase of r, a redshift and a decrease in the PBG are observed. Higher PBGs experience more shift. Also properties of the photonic crystal (PC) structure with defect layer were investigated and displacement to red and decrease of the defect mode peak height, with an increase of r, were observed. The extra optical path that the outer rays travel due to the oblique propagation compared to the central ray in a Gaussian beam is responsible for these effects. For long Rayleigh ranges our results for the Gaussian beam were the same as that for plane wave.
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.
Generation and propagation of a vector cosine-Gaussian correlated beam with radial polarization.
Zhu, Shijun; Chen, Yahong; Wang, Jing; Wang, Haiyan; Li, Zhenhua; Cai, Yangjian
2015-12-28
Scalar cosine-Gaussian-correlated Schell-model (CGCSM) beams of circular or rectangular symmetry were introduced just recently. In this paper, a new kind of partially coherent vector beam named vector CGCSM beam with radial polarization (i.e., radially polarized CGCSM beam) is introduced. The realizability conditions for a radially polarized CGCSM source and the beam condition for radiation generated by such source are derived. The statistical properties, such as the average intensity, the degree of coherence, the degree of polarization and the state of polarization, of a radially polarized CGCSM beam focused by a thin lens are analyzed in detail. It is found that the statistical properties of a radially polarized CGCSM beam are quite different from those of a conventional radial polarized partially coherent beam with Gaussian correlated Schell-model function. Furthermore, we first report experimental generation of a radially polarized CGCSM beam and measure its focusing properties. Our experimental results are consistent with the theoretical predictions.
Trap split with Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Hamideh Kazemi, Seyedeh; Ghanbari, Saeed; Mahmoudi, Mohammad
2017-08-01
We present a convenient and effective way to generate a novel phenomenon of trapping, named ‘trap split’, in a conventional four-level double-Λ atomic system, driven by four femtosecond Laguerre-Gaussian laser pulses. We find that trap split can always be achieved when atoms are trapped by such laser pulses, as compared to Gaussian ones. This feature is enabled by the interaction of the atomic system and the Laguerre-Gaussian laser pulses with zero intensity in the center. A further advantage of using Laguerre-Gaussian laser pulses is the insensitivity to fluctuation in the intensity of the lasers in such a way that the separation between the traps remains constant. Moreover, it is demonstrated that the suggested scheme with Laguerre-Gaussian laser pulses can form optical traps with spatial sizes that are not limited by the wavelength of the laser, and can, in principle, become smaller than the wavelength of light. This work would greatly facilitate the trapping and manipulating of particles and the generation of trap split. It may also suggest the possibility of extension into new research fields, such as micro-machining and biophysics.
Radiation pressure acceleration of corrugated thin foils by Gaussian and super-Gaussian beams
Adusumilli, K.; Goyal, D.; Tripathi, V. K.
2012-01-15
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 ripple 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.
Quantitative comparison of self-healing ability between Bessel–Gaussian beam and Airy beam
Wen, Wei; Chu, Xiuxiang
2015-09-15
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 Airy beam. To confirm this result, the intensity profiles of Bessel–Gaussian beam and Airy beam with different similarities are numerically calculated and compared.
Gaussian entanglement generation from coherence using beam-splitters
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
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.
NASA Astrophysics Data System (ADS)
Swain, Prasad Kumar; Goswami, Nabamita; Saha, Ardhendu
2017-01-01
A new theoretical approach towards the composite effect of spatial and angular Goos-Hanchen (GH) shift and Imbert-Fedorov (IF) shift for the Gaussian beam, Laguerre-Gaussian beam and Bessel beam with long range surface plasmon (LRSP) resonance is observed, designed and simulated through the variation of incident angle at a wavelength of 1550 nm where the four layered Kreschmann-Rather geometry comprises a ZnSe prism, a liquid crystal layer of E44 and two metal layers of silver. To the best of our knowledge several articles have been devoted, separately considering the Gaussian beam, Laguerre-Gaussian beam and Bessel beam without considering the effect of spatial and angular GH shift and IF shift whereas the exact output beam position can only be identified with the composite effect of these shifts. The investigation of these spatial and angular shifts for Gaussian beam and different orders of Laguerre-Gaussian beam are calculated and represented where these lateral shifts increase with the increment of the modes and further these lateral shifts for Bessel beam have also been analyzed. With this new approach various avenues expedite the way of futuristic applications in the field of fine tuning in optical switching with the accurate beam position using different beams.
Diffraction of Gaussian beams on intracavity Bragg gratings
NASA Astrophysics Data System (ADS)
Bitauld, David; Menez, Ludivine; Zaquine, Isabelle; Maruani, Alain; Frey, Robert
2005-06-01
The diffraction of Gaussian beams on intracavity Bragg gratings is analyzed theoretically. For reasonable waists the associated beam divergence does not significantly influence the diffraction efficiency of such devices. Nevertheless, the tilt angle of the incident beam, imposed by the Bragg resonance condition, strongly reduces the diffraction efficiency at short grating periods. However, the angular selectivity can be maintained if the Fabry-Perot cavity is tuned to the incident beam direction, which allows the use of small-volume holograms together with a dense angular multiplex. This theoretical analysis can be applied to the optimization of the diffraction properties of Gaussian beams on any intracavity Bragg grating, which could then be used for free-space parallel signal processing.
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.
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.
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.
Gaussian beam scattering by a gyrotropic anisotropic object
NASA Astrophysics Data System (ADS)
Chen, Zhenzhen; Zhang, Huayong; Wu, Xianliang; Huang, Zhixiang
2016-09-01
An exact semi-analytical solution is presented to the scattering of an on-axis Gaussian beam incident on a gyrotropic anisotropic object. The on-axis incident Gaussian beam, scattered fields as well as internal fields are expanded in terms of appropriate spherical vector wave functions, and the unknown expansion coefficients of the scattered fields are determined by virtue of Schelkunoff's equivalence theorem and electromagnetic boundary conditions. Numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.
BRIEF COMMUNICATIONS: Transformation of Gaussian beams using a spatially inhomogeneous beam splitter
NASA Astrophysics Data System (ADS)
Sakyan, A. S.
1989-03-01
A spatially inhomogeneous beam splitter was developed for transformation of the profiles of Gaussian laser beams in a wide range of wavelengths. An experimental investigation of an He-Ne laser showed that a flat-topped beam could be produced in which the relative variation of the distribution of the power density across the beam did not exceed 3%.
Propagation of Airy-Gaussian beams in a chiral medium
NASA Astrophysics Data System (ADS)
Deng, Fu; Yu, Weihao; Huang, Jiayao; Zhao, Ruihuang; Lin, Jiong; Deng, Dongmei
2016-04-01
We have expressed and investigated the propagation of Airy-Gaussian beams (AiGBs) in a chiral medium analytically. It is shown that AiGBs split into two components, i.e., the left circularly polarized (LCP) beams and the right circularly polarized (RCP) beams, which have a different propagation trajectory and are affected by the chiral parameter γ and the distribution factor χ 0. It is found that the LCP beams accelerate faster than the RCP beams during propagation, and are influenced by the chiral parameter. With an increase in the chiral parameter, the acceleration of the LCP beams increases, but that of the RCP beams decreases. So, it is significant that we can control the self-acceleration of AiGBs by varying the chiral parameter and the distribution factor.
Hermite-Gaussian modal laser beams with orbital angular momentum.
Kotlyar, V V; Kovalev, A A
2014-02-01
A relationship for the complex amplitude of generalized paraxial Hermite-Gaussian (HG) beams is deduced. We show that under certain parameters, these beams transform into the familiar HG modes and elegant HG beams. The orbital angular momentum (OAM) of a linear combination of two generalized HG beams with a phase shift of π/2, with their double indices composed of adjacent integer numbers taken in direct and inverse order, is calculated. The modulus of the OAM is shown to be an integer number for the combination of two HG modes, always equal to unity for the superposition of two elegant HG beams, and a fractional number for two hybrid HG beams. Interestingly, a linear combination of two such HG modes also presents a mode that is characterized by a nonzero OAM and the lack of radial symmetry but does not rotate during propagation.
Multi-photon resonance phenomena using Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Hamideh Kazemi, Seyedeh; Mahmoudi, Mohammad
2016-12-01
We study the influence of laser profile on the linewidth of the optical spectrum of multi-photon resonance phenomena. First, we investigate the dependence of the absorption spectrum on the laser profile in a two-level system. Thanks to the Laguerre-Gaussian field, the linewidth of the one-photon optical pumping and two-photon absorption peaks are explicitly narrower than that obtained with a Gaussian field. In the next section, it is shown that, compared to the Gaussian fields, the Laguerre-Gaussian ones reduce the linewidth of the optical spectrum in the coherent population trapping. Interestingly, it turns out that the use of a Laguerre-Gaussian beam makes the linewidth of the spectrum narrower as compared with a Gaussian one in Doppler-broadened electromagnetically induced transparency. Moreover, we study the effect of the laser profile on the Autler-Townes doublet structure in the absorption spectrum for a laser-driven four-level atomic system. We also consider the different values of the Laguerre-Gaussian mode beam waist, and, perhaps more remarkably, we find that for the small waist values, the Autler-Townes doublet can be removed and a prominent narrow central peak appears in the absorption spectrum. Finally, we investigate the effect of the laser profile on the linewidth of the sub-natural three-photon absorption peak of double dark resonance. The differences in the linewidth are quite large, offering potential applications in metrology and isotope separation methods. Our results can be used for super ultra-high resolution laser spectroscopy and to improve the resolution of the technology of isotope/isomer separation and photo-biology even at essential overlap of the spectra of the different particles.
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).
Focal shift in tightly focused Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Ren, Zhi-Cheng; Qian, Sheng-Xia; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2015-01-01
We study the nonparaxial propagation behavior of Laguerre-Gaussian (LG) beams under the tight focusing condition by using the Rayleigh-Sommerfeld integrals. We obtain an analytical formula and show the focal shift with respect to the geometric focus of a high numerical-aperture objective. An analytical expression for the focal shift of a tightly focused LG beam increases with the focal length while decreases with the beam waist. This approach can be extended to deal with the tight focusing field and the focal shift of LG vector fields with space-variant polarization distributions or other focusing behaviors such as the 4π focusing and the Fresnel zone plates.
Propagation properties of elliptical Gaussian beam in uniaxial crystals along the optical axis
NASA Astrophysics Data System (ADS)
Liu, Dajun; Wang, He; Wang, Yaochuan; Yin, Hongming
2015-10-01
Based on the paraxial vectorial theory of beams propagating in uniaxial anisotropic crystal, we have derived the analytical propagation equations of elliptical Gaussian beam in uniaxial crystal along the optical axis, and given the typical numerical example to illustrate our analytical results. It is found that the x-polarized Gaussian beams split into an ordinary beam and an extraordinary beam, which independently propagate along the optical axis, and the elliptical Gaussian beam loses its initial profile with the propagation distance increasing.
Prestack Gaussian-beam Depth Migration for Common Offset Gathers
NASA Astrophysics Data System (ADS)
Xiao, P.
2016-12-01
The purpose of depth migration is to form subsurface images where rapid lateral variations in the earth's velocities cause significant refraction of seismic energy. Problems that require depth migration are imaging beneath salt masses, near fault shadows, and in thrust belts. Since the earth's velocity variations most often can be realistically represented only in three dimensions, the depth migration program should operate efficiently in three dimensions. Also, the depth migration often must be prestack because the assumptions of poststack processing—that a stack is the same as a zero-offset section and that the subsurface is adequately illuminated at zero offset—break down when there are rapid velocity variations. Imaging that requires depth migration often requires it to be both three dimensional and prestack. Accurate depth migrations could best be achieved by full waveform methods, such as finite-difference migration, because these methods best extrapolate the wave field where there are rapidly varying seismic velocities. Unfortunately, full waveform migration is not currently practical for prestack. Kirchhoff migration is the most popular method of three-dimensional prestack depth migration because of its flexibility and efficiency. Its effectiveness can become limited, however, when complex velocity structure causes multipathing of seismic energy. An alternative is Gaussian beam migration, which is an extension of Kirchhoff migration that overcomes many of the problems caused by multipathing. Unlike first-arrival and most-energetic-arrival methods, which retain only one travel time, this alternative method retains most arrivals by the superposition of Gaussian beams. This paper presents a prestack Gaussian beam migration method that operates on common-offset gathers. The method is efficient because the computation of beam superposition isolates summations that do not depend on the seismic data and evaluates these integrals by considering their saddle
Scintillation analysis for multiple uplink Gaussian beams in the presence of beam wander
NASA Astrophysics Data System (ADS)
Wu, Wu-ming; Ning, Yu; Zhang, Peng-fei; Feng, Xiao-xing; Qiao, Chun-hong
2014-02-01
For a beam from ground to space, the main optical turbulence effects are scintillation and beam wander. Multiple incoherent beams can reduce the scintillation. The scintillation is determined by the number of the beams, the beam separation and the size of the beam wander variance. A wave optics simulation was applied to study the scintillation index of 1-, 3, 6 collimated uplink Gaussian beams, where a hexagonal close-pack spacing is used. Based on the results of simulations, we propose an approximation to average spatial correlation in terms of the beam separation in the tracked and untracked cases. The relation between scintillation index and beam separation is different in the weak and moderately-strong fluctuation regimes when the number of beams is the same. And the average spatial correlation is determined by the beam waist radius, beam separation and beam wander variance.
Non-Gaussian beam dynamics in low energy antiproton storage rings
NASA Astrophysics Data System (ADS)
Resta-López, J.; Hunt, J. R.; Welsch, C. P.
2016-10-01
In low energy antiproton facilities, where electron cooling is fundamental, the cooling forces together with heating phenomena causing emittance blow-up, such as Intra Beam Scattering (IBS), result in highly non-Gaussian beam distributions. In these cases, a precise simulation of IBS effects is essential to realistically evaluate the long term beam evolution, taking into account the non-Gaussian characteristics of the beam. Here, we analyse the beam dynamics in the Extra Low ENergy Antiproton ring (ELENA), which is a new small synchrotron currently being constructed at CERN to decelerate antiprotons to energies as low as 100 keV. Simulations are performed using the code BETACOOL, comparing different models of IBS.
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.
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.
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.
Fractional Fourier transform for off-axis elliptical Gaussian beams
NASA Astrophysics Data System (ADS)
Zheng, Chongwei
2006-03-01
The fractional Fourier transform (FRT) is applied to off-axis elliptical Gaussian beam (EGB). An analytical formula is derived for the FRT of off-axis EGB in terms of the tensor method. The corresponding tensor ABCD law for performing the FRT of off-axis EGB is also obtained. By using the derived formulae, numerical examples are given. The derived formulae provide a convenient way for analyzing and calculating the FRT of off-axis EGB.
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-05
This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs.
Ramirez, E V Garcia; Carrasco, M L Arroyo; Otero, M M Mendez; Cerda, S Chavez; Castillo, M D Iturbe
2010-10-11
In this work we present a simple model that can be used to calculate the far field intensity distributions when a Gaussian beam cross a thin sample of nonlinear media but the response can be nonlocal.
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.
Reflection of a Gaussian beam from a nonlinear interface.
Marcuse, D
1980-09-15
A numerical analysis of the reflection of a two dimensional Gaussian beam from the interface between a linear and a nonlinear medium is presented. The refractive index of the nonlinear medium is a function of the intensity of the radiation field, having a smaller value than the linear refractive index for zero field intensity. The Gaussian beam is incident from the linear medium and suffers total reflection at low intensity. At sufficiently high intensity nonlinear effects are observed. Above a threshold value the incident beam breaks up into a reflected wave and a surface wave. Once the beam is sufficiently strong for a surface wave to form, its interaction with the boundary becomes surprisingly independent of field intensity; but for very strong fields the reflectivity is increased at the expense of the surface wave. A very different behavior is observed when the refractive index is constrained to remain below a certain maximum value. Now the field detaches itself from the surface and penetrates into the nonlinear medium forming one or more distinct beams. The plane wave theory predicts the existence of hysteresis so that two different solutions should exist for the same physical parameters. A second solution was indeed found in one case with constrained refractive index, but its validity is somewhat uncertain at this time.
Dimensional properties of Laguerre-Gaussian vortex beams.
Zhang, Jie; Huang, Su-Juan; Zhu, Fu-Quan; Shao, Wei; Chen, Mu-Sheng
2017-04-20
We derive and analyze the dimensional properties of Laguerre-Gaussian vortex beams theoretically and numerically. The analytical expressions of inner and outer radii are given out and proved to be proportional to the transverse beam size, when the topological charge remains. The ratio of the outer and inner radius only depends on the topological charge, having nothing to do with the waist radius and the propagation distance, and the ratio decreases as the topological charge increases. Using a spatial light modulator loaded with computer-generated holograms, we generate vortex beams. The experimental results are in good agreement with our numerical simulations. This research may provide useful insights into the study of the optical vortex beam and its further applications.
2011-09-01
N00014-09-C-0425 http://hlsresearch.com LONG-TERM GOALS Long-term goals of this research are: • provide the underwater acoustic research ...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) HLS Research ,3366 North Torrey Pines Court, Suite 310,La Jolla,CA,92037 8. PERFORMING ORGANIZATION...the Matlab version of Bellhop and the VirTEX channel simulator that was developed at HLS Research by Martin Siderius and Michael Porter. Bellhop
Mei, Zhangrong; Zhao, Daomu; Korotkova, Olga; Mao, Yonghua
2015-12-01
We introduce a novel class of planar, quasi-homogeneous Schell-model source for producing far fields with optical lattice average intensity patterns and derive the corresponding beam conditions. The array dimension, lobes intensity profile, and periodicity of the optical lattice can be flexibly tuned by changing the correlation parameters of the source field. It is also found that, with an appropriate choice of the source parameters, the radiant intensity may possess flat-topped intensity patterns.
Wu, Zhen-Sen; Li, Ya-Qing
2011-07-01
On the basis of the extended Huygens-Fresnel principle, the scattering of partially coherent Gaussian-Schell-model (GSM) beams from a diffuse target in slant double-passage atmospheric turbulence is studied and compared with that of fully coherent Gaussian beams. Using the cross-spectral density function of the GSM beams, we derive the expressions of the mutual coherence function, angle-of-arrival fluctuation, and covariance and variance of the intensity of the scattered field, taking into account the fluctuations of both the log-amplitude and phase. The numerical results are presented, and the influences of the wavelength, propagation distance, and waist radius on scattering properties are discussed. The perturbation region of the normalized intensity variance of the partially coherent GSM beam is smaller than that of the fully coherent Gaussian beam at the middle turbulence level. The normalized intensity variance of long-distance beam propagation is smaller than that of beam propagation along a short distance.
Scintillation index of flat-topped Gaussian laser beam in strongly turbulent medium.
Gerçekcioğlu, Hamza; Baykal, Yahya
2011-08-01
In a strongly turbulent medium, the scintillation index of flat-topped Gaussian beams is derived and evaluated. In the formulation, unified solution of Rytov method is utilized. Our results correctly reduce to the existing strong turbulence scintillation index of the Gaussian beam, and naturally to spherical and plane wave scintillations. Another checkpoint of our result is the scintillation index of flat-topped Gaussian beams in weak turbulence. Regardless of the order of flatness, scintillations of flat-topped Gaussian beams in strong turbulence are found to be determined mainly by the small-scale effects. For large-sized beams in moderate and strongly turbulent medium, flatter beams exhibit smaller scintillations.
Gaussian beam profile shaping apparatus, method therefor and evaluation thereof
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.
Gaussian beam profile shaping apparatus, method therefore and evaluation thereof
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.
Fast multiscale Gaussian beam methods for wave equations in bounded convex domains
Bao, Gang; Lai, Jun; Qian, Jianliang
2014-03-15
Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, we have to take into account reflecting multiscale Gaussian beams, which are accomplished by enforcing reflecting boundary conditions during beam propagation and carrying out suitable reflecting beam summation. To propagate multiscale beams efficiently, we prove that the ratio of the squared magnitude of beam amplitude and the beam width is roughly conserved, and accordingly we propose an effective indicator to identify significant beams. We also prove that the resulting multiscale Gaussian beam methods converge asymptotically. Numerical examples demonstrate the accuracy and efficiency of the method.
Optimal focusing conditions of lenses using Gaussian beams
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
Optimal focusing conditions of lenses using Gaussian beams
Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; Mourad, Idir
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 in 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.
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.
NASA Astrophysics Data System (ADS)
Suvorov, A. A.
2010-10-01
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 the beam characteristics (power, radius, etc.) on the active medium properties and the resonator parameters is obtained.
Propagation of a cosh-Gaussian beam through an optical system in turbulent atmosphere.
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.
Radiant exposure level comparison between Gaussian and top hat beams in various scanning patterns.
U-Thainual, Paweena; Yang, Yi; Le, Hanh N D; Kim, Do-Hyun
2014-12-20
The radiant exposure of optical irradiation beams with different scanning parameters has been theoretically studied. We analyzed the difference in radiant exposure introduced by Gaussian and top hat beams. Various parameters such as scanning pattern, aperture position, beam size and scan spacing were also introduced in this study. We found that Gaussian beams introduce higher calculated radiant exposure to the aperture than top hat beams for certain beam size to aperture size ratios. However, as the scan spacing decreases, the radiant exposure difference calculated from Gaussian and top hat beams diminishes.
Second and third harmonic waves excited by focused Gaussian beams.
Levy, Uri; Silberberg, Yaron
2015-10-19
Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region. However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on quite an extended region of the material away from the focal plane. Here we solve analytically the amplitude integral for second harmonic and third harmonic waves and study the generated harmonic intensities vs. focal-plane position within the material. We find that maximum intensity for positive wave-vector mismatch values, for both second harmonic and third harmonic waves, is achieved when the fundamental Gaussian is focused few Rayleigh lengths beyond the front surface. Harmonic-generation theory predicts strong intensity oscillations with thickness if the material is very thin. We reproduced these intensity oscillations in glass slabs pumped at 1550nm. From the oscillations of the 517nm third-harmonic waves with slab thickness we estimate the wave-vector mismatch in a Soda-lime glass as Δk(H)= -0.249μm(-1).
Vortex and anti-vortex compositions of exact elegant Laguerre-Gaussian vector beams
NASA Astrophysics Data System (ADS)
Nasalski, W.
2014-05-01
Reformulation of conventional beam definitions into their bidirectional versions and use of Hertz potentials make beam fields exact vector solutions to Maxwell's equations. This procedure is applied to higher-order elegant Laguerre-Gaussian beams of transverse magnetic and transverse electric polarization. Their vortex and anti-vortex co-axial compositions of equal and opposite topological charges are given in a closed analytic form. Polarization components of the composed beams are specified by their radial and azimuthal indices. The longitudinal components are common for beam compositions of both types; meanwhile, their transverse components are different and comprise two—nonparaxial and paraxial—separate parts distinguished by a paraxial parameter and its inverse, respectively. The new solutions may appear useful in modeling and tailoring of arbitrary vector beams.
Numerical calculation of beam shifts for higher-order Laguerre-Gaussian beams upon transmission
NASA Astrophysics Data System (ADS)
Prajapati, Chandravati
2017-04-01
We study numerically the spatial and angular contributions to Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts for higher-order (| l | ≥ 1) Laguerre-Gaussian (LG) beams upon transmission from a planar interface separating two media. Two kinds of spin-orbit interaction and their role in beam shifts are discussed. Firstly, the interaction between the spin and intrinsic orbital angular momentum (OAM) of the LG beam that produces polarization dependent angular shift which is further coupled to the angular momentum structure of the beam and gives rise to spatial shift in orthogonal direction. Secondly, the interaction between the intrinsic and extrinsic OAM of the beam which produces polarization independent transverse shift, called orbital-Hall effect (OHE). Since the angular and spatial shifts are coupled and the angular shift is dependent on the beam waist, the beam shifts can be tuned to maximize or reduce the resultant shifts for LG beams.
Double pulse laser induced breakdown spectroscopy with Gaussian and multimode beams
NASA Astrophysics Data System (ADS)
Lednev, V. N.; Pershin, S. M.; Bunkin, A. F.; Samokhvalov, A. A.; Veiko, V. P.; Kudryashov, S. I.; Ionin, A. A.
2016-10-01
Single vs multimode laser beams were compared for double pulse laser ablation, plasma properties and laser induced breakdown spectroscopy (LIBS) analytical capabilities. Laser beams with Gaussian and multimode profiles were generated within the same Nd:YAG laser in single and double pulse regimes. Gaussian beam produced a small and deep crater while multimode beam formed a wide shallow crater. Greater double pulse enhancement of ablated material and plasma volume were observed for Gaussian beam sampling. The higher intensity for atomic/ionic lines in the plasma spectra was observed for multimode beam sampling due to greater laser pulse energy and larger ablated mass. Interestingly, spectra line intensity enhancement for double pulse ablation was 2-3 times greater for Gaussian than for multimode beam ablation. Background emission decreased for plasma induced by multimode beam when using double pulse mode while for Gaussian beam an opposite dependence was observed. Surprisingly, higher peak fluence at sample surface for Gaussian beam didn't provide higher plasma temperature and electron density for double pulse ablation. Analytical capabilities of LIBS method were compared for double pulse plasma induced by Gaussian and multimode beam in terms of precision, sensitivity and linearity of calibration curves. It was observed that Gaussian beam sampling leads to improvement of analysis precision while sensitivity was element dependent.
Propagation of an Airy-Gaussian beam in uniaxial crystals
NASA Astrophysics Data System (ADS)
Zhou, Mei-Ling; Chen, Chi-Dao; Chen, Bo; Peng, Xi; Peng, Yu-Lian; Deng, Dong-Mei
2015-12-01
Under the paraxial approximation, the analytical propagation expression of an Airy-Gaussian beam (AiGB) in uniaxial crystals orthogonal to the optical axis is investigated. The propagation dynamics of the AiGB is given for different ratios of the extraordinary index to the ordinary refractive index. It has been found that the continuity and the self-bending effect of AiGB become weaker when the ratio increases. From the figure of the maximum intensity of AiGB, one can see that the maximum intensity is not monotone decreasing due to the anisotropic effect of the crystals. The intensity distribution of AiGB in different distribution factors is shown. The AiGB converges toward a Gaussian beam as the distribution factor increases. 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, China (Grant No. SYBZZXM201227), the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province in China, and the Fund from the Key Laboratory of Geospace Environment, University of Science and Technology of China, Chinese Academy of Sciences.
Composite vortex beams by coaxial superposition of Laguerre-Gaussian beams
NASA Astrophysics Data System (ADS)
Huang, Sujuan; Miao, Zhuang; He, Chao; Pang, Fufei; Li, Yingchun; Wang, Tingyun
2016-03-01
We propose the generation of novel composite vortex beams by coaxial superposition of Laguerre-Gaussian (LG) beams with common waist position and waist parameter. Computer-generated holography by conjugate-symmetric extension is applied to produce the holograms of several composite vortex beams. Utilizing the holograms, fantastic light modes including optical ring lattice, double dark-ring and double bright-ring composite vortex beams etc. are numerically reconstructed. The generated composite vortex beams show diffraction broadening with some of them showing dynamic rotation around beam centers while propagating. Optical experiments based on a computer-controlled spatial light modulator (SLM) verify the numerical results. These novel composite vortex beams possess more complicated distribution and more controllable parameters for their potential application in comparison to conventional optical ring lattice.
LASER BEAMS: Laser heterodyning of Gaussian beams with partial spatial coherence
NASA Astrophysics Data System (ADS)
Kozin, G. I.; Kuznetsov, A. P.; Lebedinskii, M. O.
2005-05-01
The characteristics of Gaussian beams with partial spatial coherence are considered theoretically. The conditions for efficient recording of laser radiation reflected from scattering surfaces upon laser heterodyning and intracavity radiation reception are analysed. Recommendations on the use of projecting telescopic systems are given. Theoretical conclusions are confirmed experimentally.
Leung Shingyu; Qian Jianliang
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 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.
Abd El-Maksoud, Rania H
2016-02-20
In this paper, a methodology is developed to model and analyze the effect of undesired (ghost) reflections of Gaussian beams that are produced by anamorphic optical systems. The superposition of these beams with the nominal beam modulates the nominal power distribution at the recording plane. This modulation may cause contrast reduction, veiling parts of the nominal image, and/or the formation of spurious interference fringes. The developed methodology is based on synthesizing the beam optical paths into nominal and ghost optical beam paths. Similar to the nominal beam, we present the concept that each ghost beam is characterized by a beam size, wavefront radius of curvature, and Gouy phase in the paraxial regime. The nominal and ghost beams are sequentially traced through the system and formulas for estimating the electric field magnitude and phase of each ghost beam at the recording plane are presented. The effective electric field is the addition of the individual nominal and ghost electric fields. Formulas for estimating Gouy phase, the shape of the interference fringes, and the central interference order are introduced. As an application, the theory of the formation of the interference fringes by Michelson interferometer is presented. This theory takes into consideration the ghost reflections that are formed by the beam splitter. To illustrate the theory and to show its wide applicability, simulation examples that include a Mangin mirror, a Michelson interferometer, and a black box optical system are provided.
Scale factor correction for Gaussian beam truncation in second moment beam radius measurements
NASA Astrophysics Data System (ADS)
Hofer, Lucas R.; Dragone, Rocco V.; MacGregor, Andrew D.
2017-04-01
Charged-couple devices (CCD) and complementary metal oxide semiconductor (CMOS) image sensors, in conjunction with the second moment radius analysis method, are effective tools for determining the radius of a laser beam. However, the second moment method heavily weights sensor noise, which must be dealt with using a thresholding algorithm and a software aperture. While these noise reduction methods lower the random error due to noise, they simultaneously generate systematic error by truncating the Gaussian beam's edges. A scale factor that is invariant to beam ellipticity and corrects for the truncation of the Gaussian beam due to thresholding and the software aperture has been derived. In particular, simulations showed an order of magnitude reduction in measured beam radius error when using the scale factor-irrespective of beam ellipticity-and further testing with real beam data demonstrated that radii corrected by the scale factor are independent of the noise reduction parameters. Thus, through use of the scale factor, the accuracy of beam radius measurements made with a CCD or CMOS sensor and the second moment are significantly improved.
Electron beam dose planning using Gaussian beams. Improved radial dose profiles.
Lax, I; Brahme, A; Andreo, P
1983-01-01
The Gaussian solution of the transport equation for electrons in a medium omits the large angle single scattering events. These events have been included by using Monte Carlo calculated radial dose profiles for point monodirectional beams. A sum of three Gaussian functions with different relative weights and widths have been fitted to the Monte Carlo calculated radial dose profiles. These profiles have been confirmed by measurements in an almost point monodirectional beam, and the importance of an adequate experimental set-up for determination of radial dose profiles is discussed. The analytic treatment when using three different functions in the Gaussian formalism is presented. Central axis depth dose curves for 10 MeV and 20 MeV have finally been calculated and compared with depth dose curves calculated using Monte Carlo technique and a single Gaussian function. Considerable errors (20-30%) result with the single Gaussian function at small field sizes whereas three components give good agreement with the Monte Carlo method.
Gaussian beam measurement for HIFI instrument: Herschel Space Observatory
NASA Astrophysics Data System (ADS)
Pantaleev, Miroslav G.; Ermisch, Karsten; Fredrixon, Mathias; Svensson, Magnus; Belitsky, Victor
2004-09-01
The Heterodyne Instrument (HIFI) is part of the ESA Herschel Space Observatory Project. The instrument is intended for high-resolution spectroscopy and has a frequency coverage from 480 to 1250 GHz band in five receiver bands and 1410 to 1910 GHz in two additional bands. HIFI is built based on a modular principle: the mixers together with their respective optics are integrated into Mixer Sub-Assemblies (MSA). Each frequency band has two MSAs allocated for horizontal and vertical polarization. In this paper, we present the work done on the design and construction of a Gaussian beam measurement range. One of the unique features of the developed method is a possibility to measure the beam parameters of the MSAs in the absolute coordinate system referred to the device under test. This along with other methods should allow integration of the entire HIFI with the best possible coupling of the antenna beam to the receivers and achieving ultimate performance in such a complicated optical system. The range houses the measured MSA, which is at 4 K ambient temperature, and a continuous wave source placed on a precise scanner entirely under vacuum. Developed triangulation system provides mechanical reference data on the MSA, in-situ, after the entire system is evacuated and the cooling is finished. We adopted a scalar measurement approach where the test source scans the receiver input beam and the mixer IF power is measured. The data collected from 3-4 planar scans are used to calculate the orientation and position of the optical axis. We present results from the first beam measurements for MSA HIFI bands 1 and 2 (480 and 640 GHz), the measurement system performance and accuracy analysis.
LASER BEAMS: On the reconstruction of parameters of quasi-Gaussian pump beams during transient SBS
NASA Astrophysics Data System (ADS)
Dementjev, Aleksandr S.; Kosenko, E. K.; Murauskas, E.; Girdauskas, V.
2006-08-01
The radii and radii of curvature of Stokes stimulated Brillouin scattering (SBS) beams are measured by the method of moments for smooth nearly Gaussian focused pump beams with the propagation ratio M2σp<=1.2. It is shown that in the case of sufficiently deeply focused pump radiation, the propagation ratio M2σS of Stokes beams near the threshold of the transient SBS is smaller than M2σp and approaches it with increasing the pump pulse energy. It is also found that the radii of Stokes beams at the output from a nonlinear medium are smaller than the radii of pump beams, while the radii of wave-front curvature are close (in modulus) to the radii of wave-front curvature for pump beams.
Evolution of a Gaussian laser beam in warm collisional magnetoplasma
NASA Astrophysics Data System (ADS)
Jafari, M. J.; Jafari Milani, M. R.; Niknam, A. R.
2016-07-01
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. It 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).
Evolution of a Gaussian laser beam in warm collisional magnetoplasma
Jafari, M. J.; Jafari Milani, M. R.; 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. It 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).
Santarsiero, M; Gori, F; Borghi, R; Guattari, G
1999-09-01
A new, to our knowledge, technique for determining the modal content of partially coherent beams that are made up of an incoherent superposition of Hermite-Gaussian modes is studied. The algorithm makes use of the intensity profile of the beam at an arbitrarily chosen transverse plane. Analytical derivations are presented for a Gaussian Schell-model source and flat-topped beams, as well as an analysis of their performances in the presence of experimental errors and noise. Numerical simulations are performed to test the accuracy and the stability of the recovery algorithm.
Wang, Xun; Liu, Zhirong; Zhao, Daomu
2014-10-01
Analytical expressions for the three components of nonparaxial propagation of a polarized elliptical Gaussian vortex beam in uniaxial crystal orthogonal to the optical axis are derived. Intensity and phase distributions of the three components of a polarized elliptical Gaussian vortex beam propagating in a uniaxial crystal orthogonal to the optical axis are illustrated by numerical examples. The influences of the initial beam's parameters and the parameters of the uniaxial crystal on the evolution of the beam's intensity and phase distributions in the uniaxial crystal are examined in detail. Results show that the statistical properties of an elliptical Gaussian vortex beam nonparaxially propagating in uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal. The beam waist width ω_{0} not only affects the size of the beam profile in uniaxial crystal but also determines the nonparaxial effect of an elliptical Gaussian vortex beam. The profile of an elliptical Gaussian vortex beam in the uniaxial crystal becomes twisted and tilted, whether the elliptical factor α is greater or smaller than unity. The beam profile is tilted to the left in positive crystal. In contrast, it is inclined to the right in negative crystal. The results indicate that uniaxial crystal provides a convenient method to modulate the intensity and phase distributions of an elliptical Gaussian vortex beam, which is beneficial to optical manipulation of microscopic particles and nonlinear optics involving a specific beam profile and phase.
NASA Astrophysics Data System (ADS)
Xiang, NingJing; Wu, ZhenSen; Wang, MingJun
2014-10-01
The extended Huygens-Fresnel principle and Goodman model was utilized for target surface to derive the mutual coherence function (MCF) of a Gaussian beam reflected from an arbitrary rough target in atmospheric turbulence. According to the MCF, expressions of the mean irradiance and average speckle size at the receiver were obtained. The analysis indicated that the mean intensity is closely related to the ratio of root mean square (rms) height to the lateral correlation length. In addition, the speckle size at the receiver is associated with turbulence strength, propagation distance and roughness of the target. The results can be reduced to the result of a Gaussian beam illuminating rough target and scattering from a target in free space.
NASA Astrophysics Data System (ADS)
Liu, Dajun; Wang, Yaochuan; Yin, Hongming
2016-04-01
The partially coherent four-petal Gaussian vortex beam is introduced and described by analytical expressions. The analytical propagation equation for partially coherent four-petal Gaussian vortex beam in turbulent atmosphere is derived by using the extended Huygens-Fresnel diffraction integral formula. The influences of refraction index structure, beam order n, topological charge M and the coherence length on the average intensity distributions of beam are investigated by numerical examples.
Microwave Gaussian beam splitting with a variable split angle by using a chiral lens
NASA Astrophysics Data System (ADS)
Tariq, Salim; Mahmoud, Samir F.; Laghari, Mohammad S.
1999-01-01
In this paper we present analysis and design of a chiral lens that is used to split a linearly polarized Gaussian beam into right-circularly and left-circularly polarized beams traveling in different directions. It will be shown that split beams remain Gaussian if the curvature of the lens is large in comparison with the beam width. Moreover, the split angle can be varied by changing the point of beam incidence on the curved surface of the lens. Parameters like the beam width and cross-polarization ratio for the split beams are derived and computed.
Transformation of a high-order mode-intensity distribution to a nearly Gaussian beam
NASA Astrophysics Data System (ADS)
Machavariani, G.; Davidson, Nir; Ishaaya, Amiel A.; Friesem, Asher A.; Hasman, Erez
2003-11-01
A simple method for obtaining a nearly Gaussian laser beam from a high order Hermite-Gaussian mode is presented. The method is based on separating the equal lobes of the high order mode and combining them together coherently. The method was experimentally verified with an arrangement of three mirrors, a 50% beam splitter and a phase tuning plate. The beam quality factor calculated in x-direction for the resulting output beam is 1.045, being very close to that of ideal Gaussian beam. The calculated power leakage is only 1.5%. The experimental near-field and far-field intensity distributions of the output beam have nearly Gaussian cross sections in both the x and y directions, with M2x=1.34 and M2y=1.32. With some modifications, it is possible to obtain an output beam with M2x=1.15 and no power leakage.
Terahertz generation by two cross focused Gaussian laser beams in magnetized plasma
Singh, Ram Kishor Sharma, R. P.
2014-11-15
This paper presents a theoretical model for terahertz (THz) radiation generation by two cross-focused Gaussian laser beams in a collisionless magnetoplasma. The plasma is redistributed due to the ponderomotive nonlinearity which leads to the cross focusing of the laser beams. The focusing of the copropagating laser beams increases with increasing the externally applied static magnetic field which is perpendicular to the wave propagation direction. The nonlinear current at THz frequency arises on account of nonlinear ponderomotive force as a result of beating of the two lasers. The generated THz radiation amplitude increases significantly with increasing magnetic field. The cross focusing of two laser beams enhances the THz yield. Optimization of laser-plasma parameters gives the radiated normalized THz power of the order of 10 kW.
Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma
Patil, S. D.; Takale, M. V.
2013-07-15
In the present paper, we have employed the quantum dielectric response in thermal quantum plasma to model relativistic self-focusing of Gaussian laser beam in a plasma. We have presented an extensive parametric investigation of the dependence of beam-width parameter on distance of propagation in relativistic thermal quantum plasma. We have studied the role of Fermi temperature in the phenomenon of self-focusing. It is found that the quantum effects cause much higher oscillations of beam-width parameter and better relativistic focusing of laser beam in thermal quantum plasma in comparison with that in the relativistic cold quantum plasma and classical relativistic plasma. Our computations show more reliable results in comparison to the previous works.
Variational learning for Gaussian mixture models.
Nasios, Nikolaos; Bors, Adrian G
2006-08-01
This paper proposes a joint maximum likelihood and Bayesian methodology for estimating Gaussian mixture models. In Bayesian inference, the distributions of parameters are modeled, characterized by hyperparameters. In the case of Gaussian mixtures, the distributions of parameters are considered as Gaussian for the mean, Wishart for the covariance, and Dirichlet for the mixing probability. The learning task consists of estimating the hyperparameters characterizing these distributions. The integration in the parameter space is decoupled using an unsupervised variational methodology entitled variational expectation-maximization (VEM). This paper introduces a hyperparameter initialization procedure for the training algorithm. In the first stage, distributions of parameters resulting from successive runs of the expectation-maximization algorithm are formed. Afterward, maximum-likelihood estimators are applied to find appropriate initial values for the hyperparameters. The proposed initialization provides faster convergence, more accurate hyperparameter estimates, and better generalization for the VEM training algorithm. The proposed methodology is applied in blind signal detection and in color image segmentation.
Determination of the beam centroid of an obstructed focused Gaussian laser beam
Doyle St John, W.
2009-08-01
Diffraction of an obstructed focused Gaussian laser beam has been treated theoretically using the Huygens-Fresnel diffraction integral and was found to be in good agreement with experimental measurements. The obstruction is a vertically oriented opaque cylinder treated as a flat hard aperture. Measurements and calculations are compared for the diffracted irradiance profile and the beam centroid as a function of cylinder diameter and lateral and longitudinal placement along the optic axis. The cylinders used were gauge pins and/or wires with diameters from 0.5 to 100 mil.
Optical Gaussian beam interaction with one-dimensional thermal wave in the Raman-Nath configuration.
Bukowski, Roman J
2009-03-01
Optical Gaussian beam interaction with a one-dimensional temperature field in the form of a thermal wave in the Raman-Nath configuration is analyzed. For the description of the Gaussian beam propagation through the nonstationary temperature field the complex geometric optics method was used. The influence of the refractive coefficient modulation by thermal wave on the complex ray phase, path, and amplitude was taken into account. It was assumed that for detection of the modulated Gaussian beam parameters two types of detector can be used: quadrant photodiodes or centroidal photodiodes. The influence of such parameters as the size and position of the Gaussian beam waist, the laser-screen (detector) distance, the thermal wave beam position and width, as well as thermal wave frequency and the distance between the probing optical beam axis and source of thermal waves on the so-called normal signal was taken into account.
Generation of radially polarized Bessel-Gaussian beams from c-cut Nd:YVO₄ laser.
Vyas, Sunil; Kozawa, Yuichi; Sato, Shunichi
2014-02-15
We experimentally demonstrate the generation of radially polarized Bessel-Gaussian beams from a c-cut Nd:YVO₄ laser with a hemispherical cavity configuration by proper mode control. The output beam has an annular-shaped intensity distribution with radial polarization. When the beam is focused, the intensity pattern changes to a multi-ring, which is a typical characteristic of the lowest transverse mode of vector Bessel-Gaussian beam. Higher-order modes of vector Bessel-Gaussian beam are also observed from the same cavity by slightly changing the cavity alignment. The experimental results show a good agreement with the simulation results for both focal and far fields. The present method is a simple and direct way for generating vector Bessel-Gaussian beams.
Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam
NASA Astrophysics Data System (ADS)
Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu
2016-07-01
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.
Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam
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
Generation and propagation of a sine-azimuthal wavefront modulated Gaussian beam.
Lao, Guanming; Zhang, Zhaohui; Luo, Meilan; Zhao, Daomu
2016-07-21
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.
Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures.
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.
Gaussian laser beam transformation into an optical vortex beam by helical lens
NASA Astrophysics Data System (ADS)
Janicijevic, Ljiljana; Topuzoski, Suzana
2016-01-01
In this article, we investigate the Fresnel diffraction characteristics of the hybrid optical element which is a combination of a spiral phase plate (SPP) with topological charge p and a thin lens with focal length f, named the helical lens (HL). As incident a Gaussian laser beam is treated, having its waist a distance ζ from the HL plane and its axis passing through the centre of the HL. It is shown that the SPP introduces a phase singularity of pth order to the incident beam, while the lens transforms the beam characteristic parameters. The output light beam is analyzed in detail: its characteristic parameters and focusing properties, amplitude and intensity distributions and the vortex rings profiles, and radii, at any z distance behind the HL plane, as well as in the near and far field.
Anupriya, J.; Ram, Nibedita; Pattabiraman, M.
2010-04-15
We describe a computational and experimental study on Hanle electromagnetically induced transparency and absorption resonance line shapes with a Laguerre Gaussian (LG) beam. It is seen that the LG beam profile brings about a significant narrowing in the line shape of the Hanle resonance and ground-state Zeeman coherence in comparison to a Gaussian beam. This narrowing is attributed to the azimuthal mode index of the LG field.
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'.
Speech Enhancement Using Gaussian Scale Mixture Models.
Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J
2010-08-11
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.
Efficient Matrix Completion with Gaussian Models
2010-10-01
Sapiro and Mallat have recently reported excellent results in a number of inverse problems [16]. In particular, for inpainting , which is an analogue...been shown to bring dramatic improvements over single Gaussian models in image inpaint - ing [16], are expected to better capture different characteris
Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.
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.
NASA Astrophysics Data System (ADS)
Bakhtiari, Farhad; Golmohammady, Shole; Yousefi, Masoud; Ghafary, Bijan
2016-12-01
In the present paper, a scheme for generation of terahertz (THz) radiation in electron-neutral collisional plasma based on beating of two Gaussian laser array beams has been proposed. It is shown that the efficiency of THz radiation based on the Gaussian laser array beams can be enhanced drastically in comparison with the efficiency of THz radiation based on the Gaussian one. Furthermore, the producing THz radiation by the Gaussian laser array beams, which has an exclusive field profile, is affected by some array structure parameters. It can also be used to overcome the negative consequences of electron neutral collisions in plasma, which may be occurring in the THz radiation generation process. Optimizing the collisional plasma, laser beams and array structure parameters, THz radiation efficiency up to 0.07% can be obtained in our scheme which is about three times greater than the maximum efficiency obtained for standard (single) Gaussian laser beam. Also, considering the electrostatic energy channel in solving the THz wave equation, and reduction of THz radiation efficiency to 0.054%, in this assumption, the ratio between the efficiency of Gaussian laser array beams and standard Gaussian laser beam remained unchanged.
Kamiya, Ryo; Ogawa, Koichi
2013-08-01
The aim of the study is to improve the spatial resolution of SPECT images acquired with a fan-beam collimator. The aperture angle of a hole in the fan-beam collimator depends on the position of the collimator. To correct the aperture effect in an iterative image reconstruction, an asymmetrically trimmed Gaussian weight was used for a model. To confirm the validity of our method, point source phantoms and brain phantom were used in the simulation, and we applied the method to the clinical data. The results of the simulation showed that the spatial resolution of point sources improved from about 6 to 2 pixels full width at half maximum, and the corrected point sources were isotropic. The results of the simulation with the brain phantom showed that our proposed method could improve the spatial resolution of the phantom, and our method was effective for different fan-beam collimators with different focal lengths. The results of clinical data showed that the quality of the reconstructed image was improved with our proposed method. Our proposed aperture correction method with the asymmetrically trimmed Gaussian weighting function was effective in improving the spatial resolution of SPECT images acquired with the fan-beam collimator.
Propagation of a general multi-Gaussian beam in turbulent atmosphere in a slant path.
Chu, Xiuxiang; Liu, Zejin; Wu, Yi
2008-01-01
The propagation of a multi-Gaussian beam in turbulent atmosphere in a slant path is studied. The analytical expression for the average intensity of a general multi-Gaussian beam is derived. As special cases the average intensities of a two- and a four-Gaussian beam are investigated and numerically calculated. The investigation reveals that at lower altitude and with large sigma the intensity distribution at the receiver plane can have a shape (multiple peaks) similar to that at the source plane. But with increase in altitude or decrease in sigma, the multiple peaks gradually disappear and evolve into the profile of a fundamental Gaussian beam. From the comparisons between the different propagations we can see that the beam spreading due to wavelength and initial waist width in a slant path is much slower than that in a horizontal path.
Propagation properties of the pulsed hollow Gaussian beam through a circular aperture
NASA Astrophysics Data System (ADS)
Lu, Shizhuan; You, Kaiming; Chen, Liezun; Dai, Zhiping; Yang, Hui
2015-03-01
Based on the angular spectrum representation of the Maxwell equations and the method of stationary phase, this paper presents the far-field analytical expression of a pulsed hollow Gaussian beam with constant waist width diffracted by the circular aperture, and the result can be simplified for the case of the paraxial propagation of pulsed Gaussian beam in the free space. Based on the analytical result, the influences of truncation parameter on the transverse intensity distribution of the pulsed beam are analyzed. Comparisons of normalized temporal intensity between the pulsed Gaussian beam and the fourth order pulsed hollow Gaussian beam are presented. We find that the spatial mode can induce the temporal shape changing.
Propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere.
Zhou, Guoquan
2011-02-28
The propagation of a higher-order cosh-Gaussian beam through a paraxial and real ABCD optical system in turbulent atmosphere has been investigated. The analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of a higher-order cosh-Gaussian beam through a paraxial and real ABCD optical system are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a higher-order cosh-Gaussian in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a higher-order cosh-Gaussian beam in turbulent atmosphere are also examined in detail.
ATOMIC AND MOLECULAR PHYSICS: A Novel Mirror for Cold Molecules with a Semi-Gaussian Beam
NASA Astrophysics Data System (ADS)
Yin, Ya-Ling; Zhou, Qi; Xia, Yong; Yin, Jian-Ping
2008-09-01
We propose a novel mirror for cold molecules with a blue-detuned semi-Gaussian beam and study the dynamic reflection process of cold molecules by Monte Carlo simulation. Our study shows that this mirror can realize a specular reflection of cold iodine molecular beam with a temperature of 30 mK by a reflectivity of 58.2% when the semi-Gaussian laser power is 1.0kW. When a semi-Gaussian CO2 laser beam with a power of 5.8 kW is used, the reflectivity of this mirror can reach about 100%.
Self-focusing of a Gaussian electromagnetic beam in a complex plasma
Mishra, S. K.; Misra, Shikha; Sodha, M. S.
2011-04-15
This paper analyzes the propagation of a Gaussian electromagnetic beam in a complex plasma; the paraxial approach has been invoked for the study of the propagation characteristics. The analytical model emphasizes the open nature of complex plasmas and incorporates the charge, number density, and energy balance of the plasma constituents along with the plasma neutrality. Diffusion due to the density and temperature gradients, thermal conduction, Ohmic heating, and energy exchange in collisions/accretion have also been taken into account. For a numerical appreciation of the results, the critical curves for the propagation of the beam in dark plasmas have been discussed. The dependence of the beam width parameter on distance of propagation has been evaluated for three typical cases viz., of steady divergence, oscillatory divergence, and self-focusing. The equality of electron and ion density, an assumption inherent in the earlier analysis, has been discarded on account of the presence of charged dust particles.
Acoustic radiation force of a Gaussian beam incident on spherical particles in water.
Zhang, Xiaofeng; Zhang, Guangbin
2012-11-01
Based on the finite series method, the Gaussian beam is expanded as spherical functions and the beam coefficient of a Gaussian beam is obtained. A new expression for the acoustic radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface area for a sphere in a Gaussian beam, is presented in this paper. Numerical results for the radiation force function of a Gaussian beam incident upon the spherical particles are presented for rigid spheres, liquid spheres and elastic spheres immersed in water to illustrate the theory. The radiation force function vs. ka curve, ka being the radius times the wavenumber in the surrounding medium, is discussed for different beam widths. The acoustic radiation force function is determined by the parameters of the particles, with liquid spheres having smaller values than those for rigid and elastic spheres. The beam width also affects the acoustic radiation force function. When the radius of the sphere is larger than the beam width, the beam width has greater effects on the radiation force. This analysis helps analyzing and understanding the effects of the acoustic Gaussian beams on spherical objects. Copyright © 2012 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
Propagation of elegant vortex Hermite-Gaussian beams in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Zhu, Xuanxuan; Wu, Guohua; Luo, Bin
2016-10-01
Based on the extended Huygens-Fresnel principle, the propagation of the elegant vortex Hermite-Gaussian (vHG) beam through the atmospheric turbulence is analyzed numerically. The intensity of the vortex beam will changes from the hollow distribution to the Gauss distribution with the increase of the turbulent atmosphere or transmission distance. The topological charge, beam size and wavelength all are associated with that process. The result obtained is similar with the propagation of the Laguerre-Gaussian beam in turbulent atmosphere. Finally, the beam spreading of the elegant vHG beam traveling through the atmospheric turbulence is considered. The influence of the beam parameters (topological charge, beam waist radius and wavelength), transmission distance and atmospheric turbulence on the beam spreading of the elegant vHG beam is explored in detail. The results have great potential applied values for the free space communication.
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.
NASA Astrophysics Data System (ADS)
Kanematsu, Nobuyuki; Komori, Masataka; Yonai, Shunsuke; Ishizaki, Azusa
2009-04-01
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.
Xiao, A.; Borland, M.
2015-01-01
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 for the proposed hybrid seven-bend-achromat (H7BA) upgrade lattice [2] for the Advanced Photon Source.
Chen, Ye; Liu, Jonathan T.C.
2015-01-01
Bessel beams have recently been investigated as a means of improving deep-tissue microscopy in highly scattering and heterogeneous media. It has been suggested that the long depth-of-field and self-reconstructing property of a Bessel beam enables an increased penetration depth of the focused beam in tissues compared to a conventional Gaussian beam. However, a study is needed to better quantify the magnitude of the beam steering as well as the distortion of focused Gaussian and Bessel beams in tissues with microscopic heterogeneities. Here, we have developed an imaging method and quantitative metrics to evaluate the motion and distortion of low-numerical-aperture (NA) Gaussian and Bessel beams focused in water, heterogeneous phantoms, and fresh mouse esophagus tissues. Our results indicate that low-NA Bessel beams exhibit reduced beam-steering artifacts and distortions compared to Gaussian beams, and are therefore potentially useful for microscopy applications in which pointing accuracy and beam quality are critical, such as dual-axis confocal (DAC) microscopy. PMID:25909015
Chen, Ye; Liu, Jonathan T C
2015-04-01
Bessel beams have recently been investigated as a means of improving deep-tissue microscopy in highly scattering and heterogeneous media. It has been suggested that the long depth-of-field and self-reconstructing property of a Bessel beam enables an increased penetration depth of the focused beam in tissues compared to a conventional Gaussian beam. However, a study is needed to better quantify the magnitude of the beam steering as well as the distortion of focused Gaussian and Bessel beams in tissues with microscopic heterogeneities. Here, we have developed an imaging method and quantitative metrics to evaluate the motion and distortion of low-numerical-aperture (NA) Gaussian and Bessel beams focused in water, heterogeneous phantoms, and fresh mouse esophagus tissues. Our results indicate that low-NA Bessel beams exhibit reduced beam-steering artifacts and distortions compared to Gaussian beams, and are therefore potentially useful for microscopy applications in which pointing accuracy and beam quality are critical, such as dual-axis confocal (DAC) microscopy.
Eulerian Gaussian beams for Schroedinger equations in the semi-classical regime
Leung, Shingyu Qian Jianliang
2009-05-01
We propose Gaussian-beam based Eulerian methods to compute semi-classical solutions of the Schroedinger equation. Traditional Gaussian beam type methods for the Schroedinger equation are based on the Lagrangian ray tracing. Based on the first Eulerian Gaussian beam framework proposed in Leung et al. [S. Leung, J. Qian, R. Burridge, Eulerian Gaussian beams for high frequency wave propagation, Geophysics 72 (2007) SM61-SM76], we develop a new Eulerian Gaussian beam method which uses global Cartesian coordinates, level-set based implicit representation and Liouville equations. The resulting method gives uniformly distributed phases and amplitudes in phase space simultaneously. To obtain semi-classical solutions to the Schroedinger equation with different initial wave functions, we only need to slightly modify the summation formula. This yields a very efficient method for computing semi-classical solutions to the Schroedinger equation. For instance, in the one-dimensional case the proposed algorithm requires only O(sNm{sup 2}) operations to compute s different solutions with s different initial wave functions under the influence of the same potential, where N=O(1/h),h is the Planck constant, and m<
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
Waveform synthesis of surface waves in a laterally heterogeneous earth by the Gaussian beam method
NASA Technical Reports Server (NTRS)
Yomogida, K.; Aki, K.
1985-01-01
The present investigation is concerned with an application of the Gaussian beam method to surface waves in the laterally heterogeneous earth. The employed method has been developed for ray tracing and synthesizing seismograms of surface waves in cases involving the laterally heterogeneous earth. The procedure is based on formulations derived by Yomogida (1985). Vertical structure of the wave field is represented by the eigenfunctions of normal mode theory, while lateral variation is expressed by the parabolic equation as in two-dimensional acoustic waves or elastic body waves. It is demonstrated that a large-amplitude change can result from a slight perturbation in the phase velocity model.
Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere.
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.
Xiao, Xifeng; Voelz, David G; Toselli, Italo; Korotkova, Olga
2016-05-20
Experimental and theoretical work has shown that atmospheric turbulence can exhibit "non-Kolmogorov" behavior including anisotropy and modifications of the classically accepted spatial power spectral slope, -11/3. In typical horizontal scenarios, atmospheric anisotropy implies that the variations in the refractive index are more spatially correlated in both horizontal directions than in the vertical. In this work, we extend Gaussian beam theory for propagation through Kolmogorov turbulence to the case of anisotropic turbulence along the horizontal direction. We also study the effects of different spatial power spectral slopes on the beam propagation. A description is developed for the average beam intensity profile, and the results for a range of scenarios are demonstrated for the first time with a wave optics simulation and a spatial light modulator-based laboratory benchtop counterpart. The theoretical, simulation, and benchtop intensity profiles show good agreement and illustrate that an elliptically shaped beam profile can develop upon propagation. For stronger turbulent fluctuation regimes and larger anisotropies, the theory predicts a slightly more elliptical form of the beam than is generated by the simulation or benchtop setup. The theory also predicts that without an outer scale limit, the beam width becomes unbounded as the power spectral slope index α approaches a maximum value of 4. This behavior is not seen in the simulation or benchtop results because the numerical phase screens used for these studies do not model the unbounded wavefront tilt component implied in the analytic theory.
Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.
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.
NASA Astrophysics Data System (ADS)
Li, Yucui
1996-04-01
The field and imaging formulas of two orthogonally polarized Gaussian light beams through a nonlinear parabolic graded-index rod lens are derived by use of a variational approach and the ABCD law of Gaussian beam propagation. The effects of power and position of one optical beam on the field and propagation and imaging properties of the other optical beam are analyzed.
3-D Gaussian beam scattering from a gyromagnetic perforated layer: Quasi-static approach
NASA Astrophysics Data System (ADS)
Yachin, Vladimir V.; Zinenko, Tatiana L.
2016-12-01
This paper is devoted to the study of the scattering of a three-dimensional (3-D) Gaussian beam with the circular cross section from a double periodic perforated gyromagnetic layer with polarization independent unit-cell, in the quasi-static approximation. We used the plane-wave spectrum representation for Gaussian beam field representation and reduced it to a single integral representation. The phenomena of the lateral beam shift influenced by Faraday rotation and the nearly total beam transmission when passing through gyromagnetic slab biased with an external static magnetic field in the Faraday configuration were considered.
Generalised Hermite-Gaussian beams and mode transformations
NASA Astrophysics Data System (ADS)
Wang, Yi; Chen, Yujie; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-05-01
Generalised Hermite-Gaussian modes (gHG modes), an extended notion of Hermite-Gaussian modes (HG modes), are formed by the summation of normal HG modes with a characteristic function α, which can be used to unite conventional HG modes and Laguerre-Gaussian modes (LG modes). An infinite number of normalised orthogonal modes can thus be obtained by modulation of the function α. The gHG mode notion provides a useful tool in analysis of the deformation and transformation phenomena occurring in propagation of HG and LG modes with astigmatic perturbation.
NASA Astrophysics Data System (ADS)
Zhi, Dong; Chen, Yizhu; Tao, Rumao; Ma, Yanxing; Zhou, Pu; Si, Lei
2015-11-01
The propagation properties of a radial Gaussian beam array through oceanic turbulence are studied analytically. The analytical expressions for the average intensity and the beam quality (power-in-the-bucket (PIB) and M 2-factor) of a radial beam array in a turbulent ocean are derived based on an account of statistical optics methods, the extended Huygens-Fresnel principle, and the second order moments of the Wigner distribution function. The influences of w, ε, and χ T on the average intensity are investigated. The array divergence increases and the laser beam spreads as the salinity-induced dominant, ε decreased, and χ T increased. Further, the analytical expression of PIB and the M 2-factor in the target plane is obtained. The changes of PIB and the M 2-factor with three oceanic turbulence parameters indicate that the stronger turbulence with a larger w, smaller ε, and larger χ T results in the value of PIB decreasing, the value of the M 2-factor increasing, and the beam quality degrading.
A Fast Incremental Gaussian Mixture Model
Pinto, Rafael Coimbra; Engel, Paulo Martins
2015-01-01
This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD3) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD2) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets. PMID:26444880
Propagation and self-healing ability of a Bessel-Gaussian beam modulated by Bessel gratings
NASA Astrophysics Data System (ADS)
Qiao, Chunhong; Feng, Xiaoxing; Chu, Xiuxiang
2016-04-01
A new type of Bessel-like beam which can be generated by using Bessel gratings to modulate the amplitude and phase of a Bessel beam is proposed. In analogy to study a Bessel beam in free space, the intensity evolution and self-healing property of the Bessel-like beam have been studied. Meanwhile, based on the Fresnel diffraction integral, the propagation of the Bessel-like beam in free space has also been investigated. Results show that the Bessel-like beam and the Bessel-Gaussian-like beams have some special and interesting properties.
2DPUF: A sequential gaussian puff model
Addis, R.P.; O'Steen, B.L.
1990-01-01
This report documents the Environmental Transport Section's (ETS) two-dimensional, sequential gaussian puff transport and dispersion model for emergency response. The sequential puff scheme is described, and the dispersion equations are presented. The advantages of this model over the ETS's PUFF/PLUME model are discussed. Options are calculating a two-dimensional wind field, interpolation procedures, and the wind field grid are described. The various grid systems for puff transport calculations and dose estimates are also described. A flow diagram for the modules comprising the 2DPUF code and a description of each module is presented.
2DPUF: A sequential gaussian puff model
Addis, R.P.; O`Steen, B.L.
1990-12-31
This report documents the Environmental Transport Section`s (ETS) two-dimensional, sequential gaussian puff transport and dispersion model for emergency response. The sequential puff scheme is described, and the dispersion equations are presented. The advantages of this model over the ETS`s PUFF/PLUME model are discussed. Options are calculating a two-dimensional wind field, interpolation procedures, and the wind field grid are described. The various grid systems for puff transport calculations and dose estimates are also described. A flow diagram for the modules comprising the 2DPUF code and a description of each module is presented.
NASA Astrophysics Data System (ADS)
Wang, Li; Hong, Xue-Ren; Sun, Jian-An; Tang, Rong-An; Yang, Yang; Zhou, Wei-Jun; Tian, Jian-Min; Duan, Wen-Shan
2017-07-01
The propagation of q-Gaussian laser beam in a preformed plasma channel is investigated by means of the variational method. A differential equation for the spot size has been obtained by including the effects of relativistic self-focusing, ponderomotive self-channeling and preformed channel focusing. The propagation behaviors and their corresponding physical conditions are identified. The comparison of the propagation between q-Gaussian and Gaussian laser beams is done by theoretical and numerical analysis. It is shown that, in the same channel, the focusing power of q-Gaussian laser beam is lower than that of Gaussian laser beam, i.e., the q-Gaussian laser beam is easier to focus than Gaussian laser beam.
Exact image method for Gaussian beam problems involving a planar interface
NASA Technical Reports Server (NTRS)
Lindell, I. V.
1987-01-01
Exact image method, recently introduced for the solution of electromagnetic field problems involving sources above a planar interface or two homogeneous media, is shown to be valid also for sources located in complex space, which makes its application possible for Gaussian beam analysis. It is demonstrated that the Goos-Hanchen shift and the angular shift of a TE polarized beam are correctly given as asymptotic results by the exact reflection image theory. Also, the apparent image location giving the correct Gaussian beam transmitted through the interface is obtained as another asymptotic check. The present theory makes it possible to calculate the exact coupling from the Gaussian beam to the reflected and refracted beams, as well as to the surface wave.
Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes
NASA Astrophysics Data System (ADS)
Kwak, Sehyun; Svensson, J.; Brix, M.; Ghim, Y.-C.; Contributors, JET
2017-03-01
A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy (Li-BES) system, measuring Li I (2p-2s) line radiation using 26 channels with ∼1 cm spatial resolution and 10∼ 20 ms temporal resolution. The density profile is modelled using a Gaussian process prior, and the uncertainty of the density profile is calculated by a Markov Chain Monte Carlo (MCMC) scheme. From the spectra measured by the transmission grating spectrometer, the Li I line intensities are extracted, and modelled as a function of the plasma density by a multi-state model which describes the relevant processes between neutral lithium beam atoms and plasma particles. The spectral model fully takes into account interference filter and instrument effects, that are separately estimated, again using Gaussian processes. The line intensities are inferred based on a spectral model consistent with the measured spectra within their uncertainties, which includes photon statistics and electronic noise. Our newly developed method to infer JET edge electron density profiles has the following advantages in comparison to the conventional method: (i) providing full posterior distributions of edge density profiles, including their associated uncertainties, (ii) the available radial range for density profiles is increased to the full observation range (∼26 cm), (iii) an assumption of monotonic electron density profile is not necessary, (iv) the absolute calibration factor of the diagnostic system is automatically estimated overcoming the limitation of the conventional technique and allowing us to infer the electron density profiles for all pulses without preprocessing the data or an additional boundary condition, and (v) since the full spectrum is modelled, the procedure of modulating the beam to measure the background signal is only necessary for the case of overlapping of the Li I line with impurity lines.
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.
Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium
NASA Astrophysics Data System (ADS)
Chen, Bo; Chen, Chidao; Peng, Xi; Peng, Yulian; Zhou, Meiling; Deng, Dongmei; Guo, Hong
2016-05-01
Nonlinear optical phenomena are of great practical interest in optics. The evolution of ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium is investigated using the nonlinear Schrödinger equation. Numerical simulations indicate that the distribution factor b can influence the formation of the ring Airy Gaussian beams. Results show that the beams can be oscillating, and the light filament can be achieved under appropriate laser input power. On the other hand, the evolution of the ring Airy Gaussian beams with a spiral phase in the nonlinear Kerr medium can be implemented, and the numerical simulations of the holographic generation of the ring Airy Gaussian vortex beams propagated in the medium demonstrate that the vortex can be preserved along the propagation. The Poynting vector shows that the energy flow of the ring Airy Gaussian beams flows in the opposite direction on both sides of the focus plane; however, for beams with a spiral phase, the flow direction remains the same; the energy flow can rotate in opposite directions on both sides of the focal plane.
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.
Cylindrical light pipes for collecting light scattered from a Gaussian beam
NASA Astrophysics Data System (ADS)
Hopkins, George W.; Simons, Tad D.
1999-10-01
An investigation to enhance the efficiency of Raman- scattered light showed that cylindrical light pipes can significantly increase light collection from a Gaussian beam. Further, the enhanced signal from the light pipe retains the image of the laser beam, permitting the use of smaller detectors and resulting in a favorable signal-to- noise ratios. This investigation focussed on real-time measurements of gaseous media in a laser buildup cavity; however, the imaging properties of the light pipe apply to all measurements of molecular scattering. The light pipe matched the constraints of our measurement system: spectral separation and detection with an optical spectrograph, the need to reduce background light, the need to minimize cost, and stimulation by a laser beam in an optical cavity. After initial experiments collecting light from the ends of light pipes, we developed light pipes with a window on the cylindrical surface. Light emitted from these windows is much more intense than the direct image of the laser beam (typically 10X for light pipes 50 - 100 mm long), and the signal retains the image of the beam. Computer ray tracing modeled this side collection using Monte Carlo techniques, which are discussed in detail. We fabricated and tested light pipes using several different coatings.
Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams.
Naik, Dinesh N; Pradeep Chakravarthy, T; Viswanathan, Nirmal K
2016-04-20
We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section.
Deep transmission of Laguerre-Gaussian vortex beams through turbid scattering media.
Wang, W B; Gozali, Richard; Shi, Lingyan; Lindwasser, Lukas; Alfano, R R
2016-05-01
Light scattering and transmission of Gaussian (G) and Laguerre-Gaussian (LG) vortex beams with different orbital angular momentum (L) in various turbid media were investigated. Transmittance was measured with varied ratios of sample thickness (z) to scattering mean free path (l_{s}) of turbid media, z/l_{s}. In the ballistic region, the LG and G beams were found to have no significant difference on transmittance, while in the diffusive region, the LG beams showed a higher received signal than the G beams, and the LG beams with higher L values showed a higher received signal than those with lower L values. The transition points from ballistic to diffusive regions for different scattering media were determined. This newly observed transmittance difference of LG and G beams may be used for deep target detection in turbid media through LG beam imaging.
Intensity-based modal analysis of partially coherent beams with Hermite-Gaussian modes.
Gori, F; Santarsiero, M; Borghi, R; Guattari, G
1998-07-01
Many partially coherent beams are made up of a superposition of mutually uncorrelated Hermite-Gaussian modes. We prove that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way. Simulations indicate that the proposed method resists noise well.
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]°.
Device and method for creating Gaussian aberration-corrected electron beams
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.
Second-harmonic generation excited by a rotating Laguerre-Gaussian beam
Petrov, Dmitri
2010-09-15
Experimental data demonstrate that unlike linear optical processes, an optical Laguerre-Gaussian beam of frequency {omega}, with topological charge m, rotating with angular frequency {Omega}<<{omega}, may not be considered as a monochromatic beam with the shifted frequency {omega}+m{Omega} (Doppler angular shift) for the second-harmonic generation nonlinear process.
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.
Zavalin, Andre; Yang, Junhai; Haase, Andreas; Holle, Armin; Caprioli, Richard
2014-01-01
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. PMID:24692046
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.
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.
Tight Focusing Properties of Phase Modulated Radially Polarized Laguerre Bessel Gaussian Beam
NASA Astrophysics Data System (ADS)
Prabakaran, K.; Sangeetha, P.; Karthik, V.; Rajesh, K. B.; Musthafa, A. M.
2017-05-01
We propose a new approach for generating a multiple focal spot segment of subwavelength size, by tight focusing of a phase modulated radially polarized Laguerre Bessel Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observe that the focal segment with multiple focal structures is separated with different axial distances and a super long dark channel can be generated by properly tuning the phase of the incident radially polarized Laguerre Bessel Gaussian beam. We presume that such multiple focal patterns and high intense beam may find applications in atom optics, optical manipulations and multiple optical trapping.
NASA Astrophysics Data System (ADS)
El Halba, E. M.; Boustimi, M.; Ez-zariy, L.; Belafhal, A.
2017-02-01
In this paper, the focusing properties of radially polarized modified Bessel-modulated Gaussian (RPMQBG) beam with quadratic radial dependence through a high numerical aperture (NA) lens are investigated, theoretically and numerically, using the vector diffraction theory model. The tight focusing properties are studied in great detail. The numerical simulation results show that the intensity distribution of the RPMQBG beam at the focal region of the numerical aperture can be changed considerably by the variation of the optical vortex beam topological charge l and by the high numerical aperture angle (NA).
Fraunhofer diffraction of Laguerre-Gaussian laser beam by helical axicon
NASA Astrophysics Data System (ADS)
Topuzoski, S.
2014-11-01
In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with “0” radial mode number and “l” azimuthal mode number (LG0l) by helical axicon. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the back focal plane of a convergent lens are derived in a form of product of a Gauss-doughnut function and a sum of hypergeometric Kummer functions. Also, the diffracted LG beam by axicon only, as well as by spiral phase plate only, and the diffracted Gaussian beam by helical axicon, are described mathematically in the back focal plane of a convergent lens. Different possibilities for obtaining output vortex beam with reduced or increased topological charge compared to that of the incident beam, or for obtaining chargeless beam are analyzed.
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.
Direct evidence for three-dimensional off-axis trapping with single Laguerre-Gaussian beam
Otsu, T.; Ando, T.; Takiguchi, Y.; Ohtake, Y.; Toyoda, H.; Itoh, H.
2014-01-01
Optical tweezers are often applied to control the dynamics of objects by scanning light. However, there is a limitation that objects fail to track the scan when the drag exceeds the trapping force. In contrast, Laguerre-Gaussian (LG) beams can directly control the torque on objects and provide a typical model for nonequilibrium systems such as Brownian motion under external fields. Although stable “mid-water” trapping is essential for removing extrinsic hydrodynamic effects in such studies, three-dimensional trapping by LG beams has not yet been clearly established. Here we report the three-dimensional off-axis trapping of dielectric spheres using high-quality LG beams generated by a special holographic method. The trapping position was estimated as ~ half the wavelength behind the beam waist. These results establish the scientific groundwork of LG trapping and the technical basis of calibrating optical torque to provide powerful tools for studying energy-conversion mechanisms and the nonequilibrium nature of biological molecules under torque. PMID:24694781
Direct evidence for three-dimensional off-axis trapping with single Laguerre-Gaussian beam
NASA Astrophysics Data System (ADS)
Otsu, T.; Ando, T.; Takiguchi, Y.; Ohtake, Y.; Toyoda, H.; Itoh, H.
2014-04-01
Optical tweezers are often applied to control the dynamics of objects by scanning light. However, there is a limitation that objects fail to track the scan when the drag exceeds the trapping force. In contrast, Laguerre-Gaussian (LG) beams can directly control the torque on objects and provide a typical model for nonequilibrium systems such as Brownian motion under external fields. Although stable ``mid-water'' trapping is essential for removing extrinsic hydrodynamic effects in such studies, three-dimensional trapping by LG beams has not yet been clearly established. Here we report the three-dimensional off-axis trapping of dielectric spheres using high-quality LG beams generated by a special holographic method. The trapping position was estimated as ~ half the wavelength behind the beam waist. These results establish the scientific groundwork of LG trapping and the technical basis of calibrating optical torque to provide powerful tools for studying energy-conversion mechanisms and the nonequilibrium nature of biological molecules under torque.
Li, Jinhong; Yang, Ailin; Lü, Baida
2008-11-01
Taking the partially coherent Hermite-sinh-Gaussian (H-ShG) beam as a more general type of partially coherent beams, a comparative study of the beam-width spreading of partially coherent H-ShG beams in atmospheric turbulence is performed by using the relative width, normalized beam width, and turbulence length. It is shown that the relative width versus the beam parameters, such as the spatial correlation length sigma(0), beam orders m, n, Sh-part parameter Omega(0), and waist width w(0), provides a simple and intuitive insight into the beam-width spreading of partially coherent H-ShG beams in turbulence, and the results are consistent with those using the turbulence length. The validity of our results is interpreted physically.
Intensity-based modal decomposition of optical beams in terms of Hermite-Gaussian functions
Xue; Wei; Kirk
2000-06-01
We show that when an arbitrary optical beam is decomposed into a superposition of Hermite-Gaussian functions, it is sufficient to record a number of intensity profiles sampled at various transverse planes to uniquely determine the relative modal weights. This result follows from the parity relation and the nature of the Gouy phase, in addition to the orthogonality of the Fourier-transformed intensity profiles associated with the Hermite-Gaussian modes.
Propagation properties of partially coherent four-petal Gaussian vortex beams in oceanic turbulence
NASA Astrophysics Data System (ADS)
Liu, Dajun; Wang, Yaochuan; Wang, Guiqiu; Luo, Xixian; Yin, Hongming
2017-01-01
Based on the extended Huygens-Fresnel principle, the analytical expressions for partially coherent four-petal Gaussian vortex beams propagating in oceanic turbulence are obtained, and the influence of the coherence length, beam order N, topological charge M and oceanic turbulence parameters on the evolution properties of beams are discussed in detail using numerical examples. The results show that the beam will evolve into a Gauss-like beam rapidly with decreasing coherence length σ and oceanic parameters \\varsigma and \\varepsilon , or increasing oceanic parameter {χ\\text{T}} in the far field due to the influence of the coherence length and oceanic turbulence.
Intrinsically shaping the focal behavior with multi-ring Bessel-Gaussian beam
NASA Astrophysics Data System (ADS)
Ye, H.; Huang, K.; Liu, H.; Wen, F.; Jin, Z.; Teng, J.; Qiu, C.-W.
2017-07-01
Traditional manipulation of light generally employs diffractive optical elements such as binary phase or amplitude masks. However, we have found that vector Bessel-Gaussian (BG) beams have the intrinsic capacity of forming a special intensity pattern without additional optical elements. Using the vector diffraction theory, we theoretically show that several optical patterns (e.g., hollow beam, bottle beam, optical needle, and spot) can be created only by dynamically tailoring vector BG beams through their beam parameters (viz., polarization order n, transverse wave number β, and beam waist w0). These results yield a useful guideline for the adjustable beam parameter to generate a certain optical pattern in the focal region. The proposed roadmap of manipulating the structured beams by their intrinsic properties might open an alternative avenue for beam shaping.
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.
NASA Astrophysics Data System (ADS)
Zhi, Dong; Tao, Rumao; Zhou, Pu; Ma, Yanxing; Wu, Wuming; Wang, Xiaolin; Si, Lei
2017-03-01
A new ring Airy Gaussian (RAiG) vortex beam generation method by coherent combination of Gaussian beam array has been proposed. To validate the feasibility of this method, the propagation properties of the RAiG vortex beam and the coherent combining beam in vacuum have been studied and analyzed. From the comparisons of the intensity distributions and phase patterns along the propagation path, we can conclude that the coherent combining beam has the same properties as those of the ideal RAiG vortex beam. So this method can be used to obtain RAiG vortex beam in practice. Then the general analytical expression of the root-mean-square (RMS) beam width of the RAiG vortex beam, which is appropriately generated by coherent combining method, through anisotropic non-Kolmogorov turbulence has been derived. The influence of anisotropic turbulence on RMS beam width of the generated RAiG vortex beam has been numerically calculated. This generation method has good appropriation to the ideal RAiG vortex beam and is very useful for deriving the analytical expression of propagation properties through a random media. The conclusions are useful in practical applications, such as laser communication and remote sensing systems.
NASA Astrophysics Data System (ADS)
Gardner, Judd Steven
1999-10-01
Optical proximity sensing is often used in industry and the commercial realm to provide a system with information it may use in some decision making process. The applications for optical proximity sensing have changed and expanded over the years, and has presented a continually increased demand for higher accuracy. In order to satisfy this demand, new optical techniques have been established which have provided more precise proximity data than ever before, e.g. Atomic Force Microscopy and Photothermal Detection. To accommodate the increase in sensing precision, the precision of the mathematical models used to predict the behavior of the optical scheme must also increase. The particular interest pursued in this dissertation involves the detection of the change in the position of a beam due to some phenomena, e.g. Photothermal Deflection or Atomic Force Microscopy. The deflection of the beam in these cases may be on the order of microradians, and too small to detect with ordinary means. To remedy this, a reflecting cylinder is strategically positioned to reflect the incident deflected beam and, by the cylinder geometry, the reflected beam from the cylinder shows an increased deflection angle compared to the incident beam. If the optical scheme has been designed successfully, the resulting deflection of the reflected beam will be large enough to be detected by a sensor. In order to predict the optical behavior of an incident deflected beam reflected from a cylinder, three mathematical methods, Geometrical Optics, Physical Optics, and an Exact Formulation rigorously based on Maxwell's equations are employed. From these methods, a Geometrical Optics solution, two Physical Optics solutions, and an Exact solution are obtained and compared to demonstrate the accuracy of these mathematical models to predict the electric field behavior of a beam reflected from a cylinder. In all cases a Gaussian, well focused beam is used. The near, transitional, and far zones are considered
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…
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…
Propagation and interaction of cos-Gaussian beams in photorefractive crystals
NASA Astrophysics Data System (ADS)
Jiang, Qichang; Su, Yanli; Nie, Hexian; Ma, Ziwei; Li, Yonghong
2017-07-01
Investigate numerically the propagation and interaction of cos-Gaussian beams in a biased photorefractive crystal by the finite difference method. The results show that the single cos-Gaussian beam can evolve into Y-type breathing solitons when the self-focusing nonlinearity is small, and the soliton properties can be controlled by adjusting the nonlinear parameter or cos modulation parameter. The distance between two components of Y-type breathing solitons will decrease with increasing the nonlinear parameter or decreasing the cos modulation parameter. The breathing soliton with two weak sidebands can form when the self-focusing nonlinearity is big. Moreover, two internal components of two cos-Gaussian beams have obvious interaction but two outside components have tiny interaction.
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
NASA Astrophysics Data System (ADS)
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-09-01
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.
Spot size characterization of focused non-Gaussian X-ray laser beams.
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.
Chaitanya, N Apurv; Jabir, M V; Banerji, J; Samanta, G K
2016-09-01
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.
Chirped Airy-Gaussian beam in a medium with a parabolic potential
NASA Astrophysics Data System (ADS)
Zhang, Liping; Deng, Fu; Peng, Yulian; Chen, Bo; Peng, Xi; Li, Dongdong; Deng, Dongmei
2017-01-01
By solving the normalized dimensionless linear parabolic (Schrödinger-like) equations in the paraxial approximation, we can obtain the analytic solutions of the chirped Airy-Gaussian (CAiG) beam in a medium with a parabolic potential. We study the propagation properties of the finite energy CAiG beam in a parabolic potential and the influence of the distribution factor and the chirped factor on the CAiG beam. The propagation of the CAiG beam changes drastically with the distribution factor increasing: the CAiG beam tends to the chirped Airy beam when the distribution factor is very small; while as the distribution factor increases further, the CAiG beam tends to the chirped Gaussian beam. At the same time, the CAiG beam with a chirp has big changes when the chirped factor is increasing: the multi-peak structure is not obvious, the accelerated velocity and the peak intensity are larger, but the period does not change; when the CAiG beam has a quadratic chirp, the maximum intensity of the CAiG beam becomes smaller and the envelope is gradually smoother with the increasing of the chirped factor.
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.
Kuo, Hung-Fei; Frederick
2014-04-01
Optical scatterometry has attracted extensive interest in extracting the geometric shape information of nanolithography patterns because of the trend of shrinking device size and complicated stack structure. RCWA is the numerical algorithm implemented in the current scatterometry tool to calculate the diffraction efficiency. However, the known weakness for the RCWA method is the analysis of metallic gratings illuminated by the TM wave. This research applies the FDTD method using the Gaussian beam excitation source to analyze the diffraction efficiency of HKMG gratings for the use in the optical scatterometry and verifies the numerical diffraction efficiency discrepancy between the Gaussian beam and plane wave excitation methods. The numerical study is carried out with the line/space nanolithography patterns on the HKMG process stacks at 45 nm node technology. The nanolithography patterns are modeled as 1-D surface relief gratings. The 0th order diffraction efficiency is analyzed as a function of CDs, SWAs, incident angles and pitches of the gratings. The study presents the impact of the polarizations of the incident waves on the diffraction efficiency. In addition, this research investigates the phase of the 0th diffraction order as a function of the SWAs and illustrates the corresponding SWA parameter effect on the phase distribution. This research suggests the minimum beam radius to converge the numerical diffraction efficiency using Gaussian beam excitation to it using the plan wave.
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.
S., Juan Manuel Franco; Cywiak, Moises; Cywiak, David; Mourad, Idir
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 field through an optical system.
Acoustic radiation force on a double-layer microsphere by a Gaussian focused beam
Wu, Rongrong; Cheng, Kaixuan; Liu, Jiehui; Mao, Yiwei; Gong, Xiufen; Liu, Xiaozhou
2014-10-14
A new model for calculating the radiation force on double-layer microsphere is proposed based on the ray acoustics approach. The axial acoustic radiation force resulting from a focused Gaussian beam incident on spherical shells immersed in water is examined theoretically in relation to its thickness and the contents of its double-layer. The attenuation both in the water and inside the sphere is considered in this method, which cannot be ignored while the high frequency ultrasonic is used. Results of numerical calculations are presented for fat and low density polyethylene materials, with the hollow region filled with animal oil, water, or air. These results show how the acoustic impedance and the sound velocity of both layers, together with the thickness of the shell, affect the acoustic radiation force.
Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams
Lloyd, David T.; O’Keeffe, Kevin; Anderson, Patrick N.; Hooker, Simon M.
2016-01-01
High harmonic generation (HHG) is an established means of producing coherent, short wavelength, ultrafast pulses from a compact set-up. Table-top high-harmonic sources are increasingly being used to image physical and biological systems using emerging techniques such as coherent diffraction imaging and ptychography. These novel imaging methods require coherent illumination, and it is therefore important to both characterize the spatial coherence of high-harmonic beams and understand the processes which limit this property. Here we investigate the near- and far-field spatial properties of high-harmonic radiation generated in a gas cell. The variation with harmonic order of the intensity profile, wavefront curvature, and complex coherence factor is measured in the far-field by the SCIMITAR technique. Using the Gaussian-Schell model, the properties of the harmonic beam in the plane of generation are deduced. Our results show that the order-dependence of the harmonic spatial coherence is consistent with partial coherence induced by both variation of the intensity-dependent dipole phase as well as finite spatial coherence of the driving radiation. These findings are used to suggest ways in which the coherence of harmonic beams could be increased further, which would have direct benefits to imaging with high-harmonic radiation. PMID:27465654
Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams.
Lloyd, David T; O'Keeffe, Kevin; Anderson, Patrick N; Hooker, Simon M
2016-07-28
High harmonic generation (HHG) is an established means of producing coherent, short wavelength, ultrafast pulses from a compact set-up. Table-top high-harmonic sources are increasingly being used to image physical and biological systems using emerging techniques such as coherent diffraction imaging and ptychography. These novel imaging methods require coherent illumination, and it is therefore important to both characterize the spatial coherence of high-harmonic beams and understand the processes which limit this property. Here we investigate the near- and far-field spatial properties of high-harmonic radiation generated in a gas cell. The variation with harmonic order of the intensity profile, wavefront curvature, and complex coherence factor is measured in the far-field by the SCIMITAR technique. Using the Gaussian-Schell model, the properties of the harmonic beam in the plane of generation are deduced. Our results show that the order-dependence of the harmonic spatial coherence is consistent with partial coherence induced by both variation of the intensity-dependent dipole phase as well as finite spatial coherence of the driving radiation. These findings are used to suggest ways in which the coherence of harmonic beams could be increased further, which would have direct benefits to imaging with high-harmonic radiation.
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.
Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.
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.
Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity
Sharma, Prerana
2015-07-31
This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel–Kramers–Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.
Accelerating the annihilation of an optical vortex dipole in a Gaussian beam.
Chen, Mingzhou; Roux, Filippus S
2008-06-01
When a Gaussian beam with two oppositely charged vortices propagates in free space, these two vortices will move around on the transverse beam plane. They may either move toward each other and annihilate each other spontaneously or survive all the way depending on the conditions. Here, we investigate how to force vortex dipoles to annihilate. We find that the background phase function created by two oppositely charged vortices during beam propagation can cause the vortices to move together and annihilate each other. The background phase function on a transverse plane just beyond the point where a dipole annihilated is continuous and retains the potential that forces a dipole to annihilate. We use this background phase function to accelerate the annihilation of vortex dipoles. Numerical results are provided to show the acceleration of dipole annihilation in a Gaussian beam, using such a background phase function.
Rayleigh scattering of a Gaussian laser beam from expanding clusters
Kumar, Manoj; Tripathi, V. K.
2009-12-15
Rayleigh scattering of an intense laser with Gaussian temporal and radial profiles from clustered gases is examined. The laser quickly converts the clusters into plasma balls with electron cloud of each ball executing large excursions about the ion sphere. The laser also heats the electrons. As the clusters expand under hydrodynamic pressure, plasma frequency of the cluster electrons omega{sub pe} decreases. The temporal rate of decrease in omega{sub pe} is maximum on laser axis and falls off with r. As the electron density of a cluster approaches plasma resonance, omega{sub pe}=omegasq root(3) (where omega is the frequency of the laser) the oscillatory electron cloud of the cluster produces resonantly enhanced Rayleigh scattering. This resonant enhancement first occurs in clusters on laser axis and afterward in farther clusters. The diffraction divergence of the laser limits the length of the cluster plasma, hence the Rayleigh scattering.
Peng Xiaoyu; Toncian, Toma; Jung, Ralph; Willi, Oswald; Li Chun; Li Yutong; Wang Weimin; Wang Shoujun; Liu Feng; Chen Min; Pukhov, Alexander; Sheng Zhengming; Zhang Jie
2009-03-09
Terahertz radiation generated by focusing the fundamental laser pulse and its second harmonic into ambient air strongly saturates with increasing pump laser energy. We demonstrate a simple method to control the Gaussian pump laser beam to improve the output of terahertz radiation with an adjustable aperture. With the optimal aperture-limited pump laser beams, the terahertz wave amplitudes can be enhanced by more than eight times depending on the pump laser parameters than those of aperture-free cases.
Terahertz generation by mixing of two super-Gaussian laser beams in collisional plasma
Singh, Divya; Malik, Hitendra K. E-mail: hkmalik@physics.iitd.ac.in
2014-08-15
Considering a realistic situation, where electron-neutral collisions persist in plasma, analytical calculations are carried out for the Terahertz (THz) radiation generation by beating of two Super-Gaussian (SG) lasers of index p. The competency of these lasers over Gaussian lasers is discussed in detail with respect to the effects of collision and beam width on the THz field amplitude and efficiency of the mechanism. A critical transverse distance of the peak of the THz field is defined that shows a dependence on the index of SG lasers. Although electron-neutral collisions and larger beam width lead to the drastic reduction in the THz field when the SG lasers are used in the plasma, the efficiency of the mechanism remains much larger than the case of Gaussian lasers. Moreover, the higher index SG lasers produce stronger and focused THz radiation.
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.
On the reconstruction of parameters of quasi-Gaussian pump beams during transient SBS
Dementjev, Aleksandr S; Kosenko, E K; Murauskas, E; Girdauskas, V
2006-08-31
The radii and radii of curvature of Stokes stimulated Brillouin scattering (SBS) beams are measured by the method of moments for smooth nearly Gaussian focused pump beams with the propagation ratio M{sup 2}{sub {sigma}p{<=}}1.2. It is shown that in the case of sufficiently deeply focused pump radiation, the propagation ratio M{sup 2}{sub {sigma}S} of Stokes beams near the threshold of the transient SBS is smaller than M{sup 2}{sub {sigma}p} and approaches it with increasing the pump pulse energy. It is also found that the radii of Stokes beams at the output from a nonlinear medium are smaller than the radii of pump beams, while the radii of wave-front curvature are close (in modulus) to the radii of wave-front curvature for pump beams. (laser beams)
Optical apparatus for conversion of whispering-gallery modes into a free space gaussian like beam
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
The design of Gaussian beam zoom system in intermediate and long distance measurement
NASA Astrophysics Data System (ADS)
Wang, Mengcheng; Zhou, Jian
2016-10-01
It is well known that laser possesses high brightness, high coherence, good directivity and other unique properties. In many practical applications, it is necessary to get small light spot in intermediate and long distance. Intermediate and long distance laser measurement demands to minimize the spot radius in order to improve the spatial resolution of the system and signal quality. Therefore, the study of Gaussian beam focusing property has high value for practical applications. In order to achieve intermediate and long distance laser measurement, this paper studies the method to adjust Gaussian beam spot diameter within a certain range after a near-field optical system transformation to improve the signal quality. Based on the fundamental characteristics of the Gaussian beam, this paper deduces the theoretical formula for the position and radius of the Gaussian beam waist and measures them by means of the CCD method. Then Matlab is used to simulate the spot diameter in the far field, and by combining numerical simulation results as well as optimizing the structure of the actual optical system, we make the light spot diameter in the target area fit the requirements of the laser velocimeter in intermediate and long distance measurement.
NASA Astrophysics Data System (ADS)
Zhang, Shuang; Zhang, Xiaohui; Sun, Chunsheng
2014-12-01
Laser reflection characteristics from the two-dimensional randomly rough sea surface are affected by the sea state, weather conditions, the incident laser parameters and other factors. All of the factors could not be artificially changed except the incident laser parameters. Therefore, the research of the relationship between laser reflection characteristics from 2-D randomly rough sea surface and incident laser parameters will give support to laser detection on the sea surface. This paper deals with the simulated calculation of the Gaussian beam reflection characteristics from the 2-D randomly rough sea surface with different incident laser parameters. In this paper, the 2-D rough sea surface is simulated with fractal method, after which the sea surface is divided into a lot of small planes, the width or length of which is much greater than the wavelength of the incident laser. Then the geometrical optics method is used to calculate the Gaussian beam reflection from 2-D randomly and rough sea surface. After that, the Gaussian beam reflection characteristics varies different incident laser parameters are numerical calculated. Finally, the detailed discussion of some factors including the divergence angle and the incident angle of the Gaussian beam which have influences on reflection properties is given.
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.
Levy, Uri; Silberberg, Yaron
2017-03-01
The always diverging-converging laser beams, more rigorously referred to as Gaussian beams, are part of many physical and electro-optical systems. Obviously, a single set of analytic expressions describing these beams in a large span of divergence-convergence angles at the focal plane, and at any distance away from the focal plane, will prove very handy. We have recently published three such analytic sets, one set for linearly polarized beams and two sets for radially polarized beams. However, our published analytic set for linearly polarized beams describes nonsymmetric electric-magnetic field components. Specifically, the strong transverse magnetic field component does not become elliptic at very large divergence angles as it should be, and the other transverse magnetic component, indeed very weak, is missing altogether. Here we present an analytic set of expressions symmetrically describing linearly polarized Gaussian beams. The symmetry applies to the x-electric y-magnetic components and vice versa and to the two electric-magnetic z-components. An important property of the presented set of expressions is power conservation. That is, the electromagnetic power crossing a plane transverse to the propagation direction in a unit time is conserved. Power conservation assures beam description accuracy at any axial distance. The presented analytic expressions, although not strictly satisfying Maxwell's equations, describe Gaussian beams with very reasonable accuracy from low divergence angles up to divergence angles as large as 0.8 rad in a medium with refractive index of 1.5, i.e., up to a NA of 1.1. These expressions should then readily assist in the design of practically all laser-related systems and in the research of diverse physics and electro-optic fields.
Diffraction of a gaussian beam around a strip mask.
Glass, M
1998-05-01
A theoretical treatment is given for the diffraction of a Gaussianbeam around an opaque strip mask. Such situations arise frequentlyin the diffraction of laser beams around wires and fibers. Scalarderivations are given for the Fraunhofer and Fresnel regions with bothdevelopments, leading to similar forms of rapidly convergent series forthe field at an observation plane. Predictions show good agreementwith measurements on the diffraction patterns from wires.
Generating a Bessel-Gaussian beam for the application in optical engineering
NASA Astrophysics Data System (ADS)
Chu, Xiuxiang; Sun, Quan; Wang, Jing; Lü, Pin; Xie, Wenke; Xu, Xiaojun
2015-12-01
Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology.
NASA Astrophysics Data System (ADS)
Singh, Navpreet; Gupta, Naveen; Singh, Arvinder
2016-12-01
This paper investigates second harmonic generation (SHG) of an intense Cosh-Gaussian (ChG) laser beam propagating through a preformed underdense collisional plasma with nonlinear absorption. Nonuniform heating of plasma electrons takes place due to the nonuniform irradiance of intensity along the wavefront of laser beam. This nonuniform heating of plasma leads to the self-focusing of the laser beam and thus produces strong density gradients in the transverse direction. The density gradients so generated excite an electron plasma wave (EPW) at pump frequency that interacts with the pump beam to produce its second harmonics. To envision the propagation dynamics of the ChG laser beam, moment theory in Wentzel-Kramers-Brillouin (W.K.B) approximation has been invoked. The effects of nonlinear absorption on self-focusing of the laser beam as well as on the conversion efficiency of its second harmonics have been theoretically investigated.
Generating a Bessel-Gaussian beam for the application in optical engineering.
Chu, Xiuxiang; Sun, Quan; Wang, Jing; Lü, Pin; Xie, Wenke; Xu, Xiaojun
2015-12-22
Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bessel beam. Even more, we give an innovative idea to form vortex phase by using discontinuous piston phase. To confirm the validity of this method, the intensity evolution of the combined beam and the Bessel-Gaussian beam at different propagation distance have been studied and compared. Meanwhile, the experimental realization has been discussed from the existing experimental result related to the coherent combining technology.
Gaussian beams for a linearized cold plasma confined in a torus
NASA Astrophysics Data System (ADS)
Cardinali, A.; Dobrokhotov, S. Yu.; Klevin, A.; Tirozzi, B.
2016-04-01
We consider a system of linear pde describing a cold plasma in a toroidal region in three-dimensional space. This system simulates the passage of a laser beam through the TOKAMAK, it consists of 9 equations for the electric field and the velocities of electrons and ions in a given magnetic field. Asymptotic solutions describing high-frequency Gaussian beams are constructed using the theory of Maslov complex germ in a fairly effective form. The solutions of the system are localized in the neighborhood of the beam passing through the toroidal domain (the camera). The equations for a ray take into account the density of particles in the camera and don't ``feel'' the presence of the magnetic field because of the high frequency of the Gaussian beam; the dependence on the magnetic field is contained in the amplitude of the electric field. Before the TOKAMAK camera the amplitude of the Gaussian beam is the same as in free space, but after the camera the amplitude vector rotates under the influence of the magnetic field. The formula for the angle of rotation is given explicitly. An analytical-numerical algorithm based on the asymptotic solutions is used to analyze the parameters of the magnetic field in the TOKAMAK.
Spot size, depth-of-focus, and diffraction ring intensity formulas for truncated Gaussian beams.
Urey, Hakan
2004-01-20
Simple polynomial formulas to calculate the FWHM and full width at 1/e2 intensity diffraction spot size and the depth of focus at a Strehl ratio of 0.8 and 0.5 as a function of a Gaussian beam truncation ratio and a system f-number are presented. Formulas are obtained by use of the numerical integration of a Huygens-Fresnel diffraction integral and can be used to calculate the number of resolvable spots, the modulation transfer function, and the defocus tolerance of optical systems that employ laser beams. I also derived analytical formulas for the diffraction ring intensity as a function of the Gaussian beam truncation ratio and the system f-number. Such formulas can be used to estimate the diffraction-limited contrast of display and imaging systems.
Multi-Gaussian Schell-model beams.
Korotkova, Olga; Sahin, Serkan; Shchepakina, Elena
2012-10-01
In a recent publication [Opt. Lett.37, 2970 (2012)10.1364/OL.37.002970], a novel class of planar stochastic sources, generating far fields with flat intensity profiles, was introduced. In this paper we examine the behavior of the spectral density and the state of coherence of beamlike fields generated by such sources on propagation in free space and linear isotropic random media. In particular, we find that at sufficiently large distances from the source, the medium destroys the flat intensity profile, even if it remains such for intermediate distances from the source.
Optical apparatus for conversion of whispering-gallery modes into a free space gaussian like beam
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.
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.
Design of a 1-MW, CW coaxial gyrotron with two gaussian beam outputs
NASA Astrophysics Data System (ADS)
Hirata, Y.; Hayashi, K.; Mitsunaka, Y.; Itoh, Y.; Sugawara, T.
1995-04-01
The design of a 170 GHz, 1 MW-CW gyrotron for electron cyclotron heating of nuclear fusion plasmas is presented. The designed gyrotron incorporates a coaxial cavity to reduce mode competition, and a coaxial electron gun to support the cavity inner conductor. A new mode converter splits the generated wave into two beams and radiates them in different directions. The radiated beams are transmitted to two output windows through two mirror systems, being transformed into Gaussian-like beams. A single-stage depressed collector improves the overall efficiency of the gyrotron and reduces the heat flux to the collector surface.
Miniaturized photogenerated electro-optic axicon lens Gaussian-to-Bessel beam conversion.
Di Domenico, G; Parravicini, J; Antonacci, G; Silvestri, S; Agranat, A J; DelRe, E
2017-04-01
We experimentally demonstrate an electro-optic Gaussian-to-Bessel beam-converter miniaturized down to a 30×30 μm pixel in a potassium-lithium-tantalate-niobate (KLTN) paraelectric crystal. The converter is based on the electro-optic activation of a photoinduced and reconfigurable volume axicon lens achieved using a prewritten photorefractive funnel space-charge distribution. The transmitted light beam has a tunable depth of field that can be more than twice that of a conventional beam with the added feature of being self-healing.
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
Gaussian beam displacement sensor for monitoring interstory drift in smart buildings
NASA Astrophysics Data System (ADS)
Bennett, Kim D.; Hoover, C. W., III; Chen, Ru Z.; Plone, M. D.
1994-05-01
A method for measuring lateral displacements in structures is proposed based on the motion of a Gaussian optical beam. A sensor is designed and constructed using the free space output of a single mode optical fiber, which well approximates the Gaussian intensity distribution, and is tested in both quasi-static and dynamic displacement modes. Good agreement between the experimental data and the predicted output is obtained for small displacements of the size expected in real buildings. It is envisioned that this sensor could serve as the input to an active control system used to stabilize smart buildings experiencing earthquake and wind loads.
Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.
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.
Propagation of an Airy-Gaussian-Vortex beam in a chiral medium
NASA Astrophysics Data System (ADS)
Hua, Sen; Liu, Youwen; Zhang, Huijie; Tang, Liangzun; Feng, Yunxcai
2017-04-01
Based on the Huygens diffraction integral, the analytical expressions of electric field distribution of the Airy-Gaussian-Vortex (AiGV) beam in a chiral medium are derived, and its propagation properties are investigated. With increasing the value of chiral parameter γ, the parabolic deflection of the LCP light increases and the RCP light decreases respectively. For the first-order AiGV beam with only one positive or negative optical vortex (OV), a half-moon-shaped intensity profile can be observed because of overlap of the OV and the Airy main lobe, and then the main lobe will be reconstructed and the vortex could be recovered after the overlap position. The intensity distribution of AiGV beam, the deflection trajectories of central positions of Airy beam and OV under different competing parameters between Gaussian and Airy terms have been studied. Furthermore, for the second-order counterrotating AiGV beam with positive and negative vortexes, it could be considered the superposition of two first-order AiGV beams with respective positive and negative vortexes. Two vortexes can regenerate during propagation and the intensity distribution the AiGV beam in the far zone can be controlled by adjusting the coordinates of two vortexes.
NASA Astrophysics Data System (ADS)
Deng, Jinping; Ji, Xiaoling
2014-05-01
By using the four-dimensional (4D) computer code of the time-dependent propagation of laser beams through atmospheric turbulence, the influence of atmospheric turbulence on the energy focusability of Gaussian beams with spherical aberration is studied in detail, where the mean-squared beam width, the power in the bucket (PIB), the β parameter and the energy Strehl ratio are taken as the characteristic parameters. It is shown that turbulence results in beam spreading, and the effect of spherical aberration on the beam spreading decreases due to turbulence. Gaussian beams with negative spherical aberration are more affected by turbulence than those with positive spherical aberration. For the negative spherical aberration case, the focus position moves to the source plane due to turbulence. It is mentioned that the influence of turbulence on the energy focusability defined by a certain energy (i.e. PIB = 63%) is very heavy when the negative spherical aberration is very heavy. On the other hand, the influence of turbulence on the energy focusability defined by the energy within a given bucket radius (i.e. mean-squared beam width) is heaviest when a certain negative spherical aberration coefficient is adopted.
Huang, Chaohong; Zheng, Yishu; Li, Hanqing
2016-11-01
The orbital angular momentum (OAM) and paraxial propagation characteristics of non-coaxial Laguerre-Gaussian (LG) beams are discussed. In the initial plane, the amplitudes of non-coaxial LG modes are the product of a Laguerre polynomial, a vortex phase factor, and a non-coaxial Gaussian window function. Because of displacement between the centroid and vortex center of the beams, the non-coaxial LG beams demonstrate a non-zero extrinsic OAM, which causes the propagation of beam centroid to have a small tilt angle relative to the z axis. Through separating the extrinsic OAM from the total OAM carried by the non-coaxial LG beams, the tilt angle and trajectory of the beam centroid are derived. Furthermore, the paraxial propagating characteristics of these beams are also discussed analytically. The results show the vortex center initially at origin demonstrates a linear lateral shift with propagation and the peak of transverse intensity has a trajectory of a straight line, although the intensity profile rotates itself with propagation.
Liu, Dajun; Wang, Yaochuan; Yin, Hongming
2015-09-01
The analytical propagation equations for partially coherent four-petal Gaussian vortex beams propagating through uniaxial crystals orthogonal to the optical axis are derived, and the propagation properties are analyzed by numerical examples. The influence of beam order n, topological charge M, the coherence length, and the ratio of refractive index n(e)/n(o) on the normalized intensity distribution of partially coherent four-petal Gaussian vortex beams is discussed.
NASA Astrophysics Data System (ADS)
Li, Ye; Zhang, Yixin; Wang, Donglin; Shan, Lei; Xia, Mingchao; Zhao, Yuanhang
2016-05-01
The effects of strong turbulence on the orbital angular momentum (OAM) states of infrared and non-diffraction beam propagation in a terrestrial atmosphere are investigated. A new probability density model for OAM states of Bessel-Gaussian-Schell beam in the paraxial and strong turbulent channel is modeled based on the modified Rytov approximation. We find that the normalization energy weight of signal OAM modes at each OAM level is approximate equivalence in strong turbulence regime, one can constitute multiple mode channels by choosing OAM modes with large energy level difference between modes to reduce mode interference, and one can utilize BGS beam with OAM modes increasing the channel capacity of optical communications.
Fresnel zone plate with apodized aperture for hard X-ray Gaussian beam optics.
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.
Ponderomotive self-focusing of Gaussian laser beam in warm collisional plasma
Jafari Milani, M. R.; Niknam, A. R.; Farahbod, A. H.
2014-06-15
The propagation characteristics of a Gaussian laser beam through warm collisional plasma are investigated by considering the ponderomotive force nonlinearity and the complex eikonal function. By introducing the dielectric permittivity of warm unmagnetized plasma and using the WKB and paraxial ray approximations, the coupled differential equations defining the variations of laser beam parameters are obtained and solved numerically. Effects of laser and plasma parameters such as the collision frequency, the initial laser intensity and its spot size on the beam width parameter and the axis laser intensity distribution are analyzed. It is shown that, self-focusing of the laser beam takes place faster by increasing the collision frequency and initial laser spot size and then after some distance propagation the laser beam abruptly loses its initial diameter and vastly diverges. Furthermore, the modified electron density distribution is obtained and the collision frequency effect on this distribution is studied.
Experimental generation of Laguerre-Gaussian beam using digital micromirror device.
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.
Reflection and transmission of Gaussian beam from a uniaxial crystal slab
NASA Astrophysics Data System (ADS)
Wang, Yan; Yu, Ke; Zha, Xuejun; Xu, Jiwei; Yan, Jinkui
2006-08-01
We investigate the characteristics of Gaussian beams reflected and transmitted from a uniaxial crystal slab with an arbitrary orientation of its optical axis. The formulas of the total electric and magnetic fields inside and outside the slab are derived by use of Maxwell's equations and by matching the boundary conditions at the interfaces. Numerical simulations are presented and the field values as well as the power densities are computed. Negative refractions are demonstrated when the beam is transmitted through a uniaxial crystal slab. Beam splitting of the reflected beam is observed and is explained by the resonant transmission for plane waves. Dependences of the lateral shift on the incident angle and beam width are discussed. Negative and positive lateral shifts are observed due to the spatial anisotropic properties.
Stochastic modeling of seafloor morphology: A parameterized Gaussian model
Goff, J.A.; Jordan, T.H. )
1989-01-01
Stochastic methods of analysis are useful for quantifying ensemble properties of small-scale bathymetric features such as abyssal hills. In this paper the authors model the seafloor as a stationary, zero-mean, Gaussian random field completely specified by its autocovariance function. They formulate an anisotropic autocovariance function that has five free parameters describing the amplitude, anisotropic orientation and aspect ratio, characteristic length, and Hausdorff (fractal) dimension of seafloor topography. Parameters estimated from various seafloor exhibits a wide range of stochastic characteristics within the constraints of the model. Synthetic topography can be generated at arbitrary scale and resolution from the Gaussian model using a Fourier method. Color images of these synthetics are useful for illustrating the stochastic behavior of the model.
Negative refraction and backward wave in chiral mediums: Illustrations of Gaussian beams
NASA Astrophysics Data System (ADS)
Chern, Ruey-Lin; Chang, Po-Han
2013-04-01
We investigate the phenomena of negative refraction and backward wave in chiral mediums, with illustrations of Gaussian beams. Due to symmetry breaking intrinsic in chiral mediums, there exist two circularly polarized eigenwaves with different wave vectors. The two waves begin to split from each other as the chirality parameter increases from zero. The right (left)-handed circularly polarized wave tends to move toward (away from) the normal to the interface. As the chirality exceeds a critical value, the left-handed wave is flipped to the other side of the interface normal, that is, negatively refracted, and becomes a backward wave. These features are illustrated with Gaussian beams based on Fourier integral formulations. The special condition of perfectly negative refraction in chiral mediums is also discussed.
Negative refraction and backward wave in pseudochiral mediums: illustrations of Gaussian beams.
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.
Type I parametric down conversion of highly focused Gaussian beams in finite length crystals
NASA Astrophysics Data System (ADS)
Jeronimo-Moreno, Yasser; Jáuregui, R.
2014-06-01
This paper presents a study of the correlations in wave vector space of photon pairs generated by type I spontaneous parametric down conversion using a Gaussian pump beam. The analysis covers both moderate focused and highly focused regimes, paying special attention to the angular spectrum and the conditional angular spectrum. Simple analytic expressions are derived that allow a detailed study of the dependence of these spectra on the waist of the source and the length of the nonlinear crystal. These expressions are in good agreement with numerical expectations and reported experimental results. They are used to make a systematic search of optimization parameters that improve the feasibility of using highly focused Gaussian beams to generate idler and signal photons with predetermined mean values and spread of their transverse wave vectors.
Phase-only shaping algorithm for Gaussian-apodized Bessel beams.
Durfee, Charles G; Gemmer, John; Moloney, Jerome V
2013-07-01
Gaussian-apodized Bessel beams can be used to create a Bessel-like axial line focus at a distance from the focusing lens. For many applications it is desirable to create an axial intensity profile that is uniform along the Bessel zone. In this article, we show that this can be accomplished through phase-only shaping of the wavefront in the far field where the beam has an annular ring structure with a Gaussian cross section. We use a one-dimensional transform to map the radial input field to the axial Bessel field and then optimized the axial intensity with a Gerchberg-Saxton algorithm. By separating out the quadratic portion of the shaping phase the algorithm converges more rapidly.
Chen, Chunyi; Yang, Huamin; Tong, Shoufeng; Lou, Yan
2016-04-04
The radial average-power distribution and normalized average power of orbital-angular-momentum (OAM) modes in a vortex Gaussian beam after passing through weak-to-strong atmospheric turbulence are theoretically formulated. Based on numerical calculations, the role of the intrinsic mode index, initial beam radius and turbulence strength in OAM-mode variations of a propagated vortex Gaussian beam is explored, and the validity of the pure-phase-perturbation approximation employed in existing theoretical studies is examined. Comparison between turbulence-induced OAM-mode scrambling of vortex Gaussian beams and that of either Laguerre-Gaussian (LG) beams or pure vortex beams has been made. Analysis shows that the normalized average power of OAM modes changes with increasing receiver-aperture size until it approaches a nearly stable value. For a receiver-aperture size of practical interest, OAM-mode scrambling is severer with a larger mode index or smaller initial beam radius besides stronger turbulence. Under moderate-to-strong turbulence condition, for two symmetrically-neighboring extrinsic OAM modes, the normalized average power of the one with an index closer to zero may be greater than that of the other one. The validity of the pure-phase-perturbation approximation is determined by the intrinsic mode index, initial beam radius and turbulence strength. It makes sense to jointly control the amplitude and phase of a fundamental Gaussian beam for producing an OAM-carrying beam.
NASA Astrophysics Data System (ADS)
Kang, Xiaoping; He, Zhong; Lü, Baida
2007-07-01
The far-field properties and beam quality of vectorial nonparaxial Hermite-Laguerre-Gaussian (HLG) beams are studied in detail, where, instead of the second-order-moments-based M2 factor, the extended power in the bucket (PIB) and βparameter are used to characterize the beam quality in the far field and the intensity in the formulae is replaced by the z component of the time-averaged Poynting vector
Energy Extraction from the Electron Beam in a Free Electron Laser Resonator Gaussian Mode.
1983-01-01
Elias, Juan Gallardo and Peter Goldstein N00014-80-C-0308 S. PF OR -ING ORGANIZATION NAME AND ADDRESS I . PROGRAM ELEMt.T PROJECT, TASK * ,’ niwxrsity...Elias, Juan Gallardo , Peter Goldstein Quantum Institue, University of California Santa Barbara, California 93106 ABSTRACT We present preliminary...QUANTUM INSTITUTE FREE ELECTRON LASER PROJECT Energy Extraction fran the Electron Beam in a Free Electron Laser Resonator Gaussian Mode Luis Elias, Juan
Gaussian beams for surface waves in laterally slowly-varying media
NASA Technical Reports Server (NTRS)
Yomogida, K.
1985-01-01
Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. The elastodynamic equations of motion in ray-centered coordinates are derived, and a laterally slowly-varying approximation for elastodynamic equations is obtained. Parabolic equations for Love and Rayleigh waves are studied and solved, and the properties of Gaussian beams of seismic surface waves are examined.
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
Gaussian beams for surface waves in laterally slowly-varying media
NASA Technical Reports Server (NTRS)
Yomogida, K.
1985-01-01
Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. The elastodynamic equations of motion in ray-centered coordinates are derived, and a laterally slowly-varying approximation for elastodynamic equations is obtained. Parabolic equations for Love and Rayleigh waves are studied and solved, and the properties of Gaussian beams of seismic surface waves are examined.
Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing
NASA Astrophysics Data System (ADS)
Bárdossy, András.; Hörning, Sebastian
2016-06-01
This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.
Propagation properties of Airy-Gaussian vortex beams through the gradient-index medium.
Zhao, Ruihuang; Deng, Fu; Yu, Weihao; Huang, Jiayao; Deng, Dongmei
2016-06-01
Propagation of Airy-Gaussian vortex (AiGV) beams through the gradient-index medium is investigated analytically and numerically with the transfer matrix method. Deriving the analytic expression of the AiGV beams based on the Huygens diffraction integral formula, we obtain the propagate path, intensity and phase distributions, and the Poynting vector of the first- and second-order AiGV beams, which propagate through the paraxial ABCD system. The ballistic trajectory is no longer conventional parabolic but trigonometric shapes in the gradient-index medium. Especially, the AiGV beams represent the singular behavior at the propagation path and the light intensity distribution. The phase distribution and the Poynting vector exhibit in reverse when the AiGV beams through the singularity. As the order increases, the main lobe of the AiGV beams is gradually overlapped by the vortex core. Further, the sidelobe weakens when the AiGV beams propagate nearly to the singularity. Additionally, the figure of the Poynting vector of the AiGV beams proves the direction of energy flow corresponding to the intensity distribution. The vortex of the second-order AiGV beams is larger, and the propagation velocity is faster than that of the first order.
Use of Gaussian Beam Tracing in the Design of Millimeter-Wave Diagnostics on ITER
NASA Astrophysics Data System (ADS)
Joo, Heeseok; Bitter, Manfred; Tobias, Ben; Park, Hyeon; Zolfaghari, Ali
2016-10-01
When the wavelength of the radiation being studied is comparable to the size optical components, the diffraction effect cannot be ignored. Gaussian beam tracing (GBT) can be used by treating the propagation of the light as a beam with certain size rather than a ray used in geometrical optics when analyzing the optics of millimeter-wave diagnostics. Gaussian optics is an effective way to represent diffraction effect because of its ability to show the beam size and the intensity that could be altered from diffraction. GBT has been used in two millimeter-wave diagnostics suited to ITER geometry. The first is in a design of a Gaussian telescope for correction of transmission line misalignment in the ITER LFS reflectometer due to motion of the vessel during heating to operating temperature from room temperature. The second is a new concept of using spherical mirrors for electron cyclotron emission imaging (ECEI) and assessing its promise of a more realistic method of ECEI in ITER than previous idea of using a cylindrical mirror that requires large access ports that can be exposed to intense neutron radiation. The spherical mirror promises a smaller aperture on the first wall of ITER. The simulation of GBT of the two applications are analyzed and discussed. This work is supported by US DOE Contract No. DE-AC02-09CH11466.
Flat-topped Gaussian laser beam scintillation in weakly turbulent marine atmospheric medium
NASA Astrophysics Data System (ADS)
Gerçekcioğlu, Hamza; Abbas, Ahmed A.; Göktaş, H. Haldun
2017-09-01
In a weakly marine turbulent medium, formulation of the on-axis scintillation index of a flat topped Gaussian beam is derived by using the Rytov method and the intensity has log-normal distribution expressed. The scintillation index and average bit error rate
NASA Astrophysics Data System (ADS)
Li, Xinzhong; Tai, Yuping; Nie, Zhaogang; Wang, Hui; Li, Hehe; Wang, Jingge; Tang, Jie; Wang, Yishan
2015-12-01
We investigate the Fraunhofer diffraction of a Laguerre-Gaussian (LG) beam incident on a dynamic superposed dual-triangular aperture. The evolution of the diffraction pattern from this aperture is analyzed experimentally and theoretically. A special aperture, called the hex-star triangular aperture, demonstrates interesting diffraction patterns. Further, the diffraction properties of integer, half-integer, and fractional orders of topological charges at the Fraunhofer zone are studied by using the hex-star triangular aperture. This study can provide additional information to enhance the understanding of the diffraction properties of the LG beam transmitted through a complex aperture.
Properties of a strongly focused Gaussian beam with an off-axis vortex
NASA Astrophysics Data System (ADS)
Zhao, Xinying; Zhang, Jingcheng; Pang, Xiaoyan; Wan, Guobin
2017-04-01
The intensity distribution and the phase properties, especially the Gouy phase and the phase singularities are studied in a strongly focused Gaussian beam with an off-axis vortex. The symmetry relation of the focused field is also derived. It is found that the off-axis vortex induces a rotation of the field pattern, the transverse focal shift, and the asymmetric distribution of the phase singularities. Our results also show that the initial position of the off-axis vortex in the incident beam strongly influences the distance of the transverse focal shift, but does not have an effect on the Gouy phase along the central axis.
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.
Scintillation reduction for combined Gaussian-vortex beam propagating through turbulent atmosphere
Berman, Gennady P; Gorshkov, V. N.; Torous, S. V.
2010-12-14
We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams (PCBs), including the optical vortices, propagating in turbulent atmospheres, The influence of beam fragmentation and wandering relative to the axis of propagation (z-axis) on the value of the scintillation index (SI) of the signal at the detector is analyzed. A method for significantly reducing the SI, by averaging the signal at the detector over a set of PCBs, is described, This novel method is to generate the PCBs by combining two laser beams - Gaussian and vortex beams, with different frequencies (the difference between these two frequencies being significantly smaller than the frequencies themselves). In this case, the SI is effectively suppressed without any high-frequency modulators.
Determining the waist radius of a focused Gaussian laser beam using a millimeter-scale ruler
NASA Astrophysics Data System (ADS)
Yang, Pao-Keng; Liu, Jian-You
2017-03-01
We present a simple and inexpensive method for determining the waist radius of a focused Gaussian laser beam. This method is motivated by the fact that if you focus the laser beam using a lens, the distance from the lens to the waist will vary slightly as the lens is moved along the beam-propagating direction. We show how the waist radius can be calculated from four large longitudinal lengths, measurable using a conventional millimeter-scale ruler. Analyzing the dependence of the calculated waist radius on these four measured lengths numerically shows that the accuracy of the calculated waist radius is mainly affected by the error in the relative shift in the distance from the lens to the waist position. The calculated waist radius for a real HeNe laser is close to the one measured directly using a commercial beam profiler with an error within 7%.
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.
Theory and Modeling of Stimulated Raman Scattering
1993-06-01
nondiffraction- limited pump beam, Gaussian -Hermite (G-H) beams, Gaussian -Laguerre (G-L) beams, and Gaussian - Schell - model (GSM) beams are used. The AM2 factor...Laguerre (G-L) beams, and Gaussian - Schell - model (GSM) beams are used. The M 2 factor of these beams can be calculated analytically. A random...defined for elliptical beams and AM2 is not changed by astigmatic lenses. The Gaussian - Schell - model (GSM) beam has a Gaussian intensity profile given
NASA Astrophysics Data System (ADS)
Zhou, Nanrun; Zeng, Guihua
2004-03-01
Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-cosine-Gaussian (HcoG) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for HcoG beams of any order. Furthermore, the closed-form propagation expressions for the Gaussian, Hermite-Gaussian, cosine (sine)-Gaussian, cosh (sinh) and cosine (sine) beams passing through a paraxial optical ABCD system with hard-edge aperture can be obtained by treating them as special cases of the analytical propagation expression for HcoG beams. The advantages of our analytical results are analyzed, and the applications are illustrated with numerical examples.
NASA Astrophysics Data System (ADS)
Ghotra, Harjit Singh; Kant, Niti
2017-01-01
Electron acceleration due to a circularly polarized (CP) Gaussian laser field has been investigated theoretically in magnetized plasma. A Gaussian laser beam possesses trapping forces on electrons during its propagation through plasma. A single particle simulation indicates a resonant enhancement of electron acceleration with a Gaussian laser beam. The plasma is magnetized with an axial magnetic field in same direction as that of laser beam propagation. The dependence of laser beam width parameter on electron energy gain with propagation distance has been presented graphically for different values of laser intensity. Electron energy gain is relatively high where the laser beam parameter is at its minimum value. Enhanced energy gain of the order of GeV is reported with magnetic field under 20 MG in plasma. It is also seen that the axial magnetic field maintains the electron acceleration for large propagation distance even with an increasing beam width parameter.
A fast algorithm for depth migration by the Gaussian beam summation method
NASA Astrophysics Data System (ADS)
Gao, Zhenghui; Sun, Jianguo; Sun, Xu; Wang, Xueqiu; Sun, Zhangqing; Liu, Zhiqiang
2017-02-01
Depth migration by the Gaussian beam summation method has no limitation on the seismic acquisition configuration. In the past, this migration method applied the steepest descent approximation to reduce the dimension of the integrals over the ray parameters at the cost of a precision loss. However, the simplified formula was still in the frequency domain, thereby impairing the computational efficiency. We present a new fast algorithm which can increase the computational efficiency without losing precision. To develop the fast algorithm, we change the order of the integrals and treat the two innermost integrals as a couple of two-dimensional continuous functions with respect to the real and imaginary parts of the total traveltime. A couple of lookup tables corresponding to the values of the two innermost integrals are constructed at the sampling points. The results of the two innermost integrals at a certain imaging point can be obtained through interpolation in the two constructed lookup tables. Both the numerical analysis and examples validate the precision and efficiency of the fast algorithm. With the advantage of handling rugged topography, we apply the fast algorithm to the 2D Canadian Foothills velocity model.
NASA Astrophysics Data System (ADS)
Ferrando, A.; García-March, M. A.
2016-06-01
We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre-Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.
Femtosecond laser surface structuring of silicon with Gaussian and optical vortex beams
NASA Astrophysics Data System (ADS)
JJ Nivas, Jijil; He, Shutong; Song, Zhenming; Rubano, Andrea; Vecchione, Antonio; Paparo, Domenico; Marrucci, Lorenzo; Bruzzese, Riccardo; Amoruso, Salvatore
2017-10-01
We report an experimental analysis of femtosecond laser induced surface structuring of silicon by exploiting both Gaussian and Optical Vortex beams. In particular, we show how different surface patterns, consisting of quasi-periodic ripples and grooves, can be obtained by using different states of polarization offered by optical vortex beams. Both for Gaussian and optical vortex beams, an increase of the number of laser pulses, N, or beam energy, E0, leads to a progressive predominance of the grooves coverage, with ripples confined in specific regions of the irradiated area at lower fluence. The average period of ripples and grooves shows a different dependence as a function of both E0 and N, underlying important differences in mechanisms leading to the formation of ripples and grooves. In particular, our experimental characterization allows identifying a preliminary stage of grooves generation with rudimental surface structures, preferentially directed parallel to the laser polarization. This supports the idea that one possible mechanism of grooves formation lies in the progressive aggregation of clusters of nanoparticles densely decorating the ripples. Our experimental findings provide important indications on the basic understanding of the processes involved in laser surface structuring with ultrashort pulses that can guide the design of the surface patterns.
Yang, Ting; Xu, Yonggen; Tian, Huanhuan; Die, Dong; Du, Quan; Zhang, Biling; Dan, Youquan
2017-05-01
Analytical formulas for the root-mean-square (rms) spatial width, the rms angular width, and the M(2)-factor of partially coherent standard Laguerre Gaussian beams (PC-SLGBs) and partially coherent elegant Laguerre Gaussian beams (PC-ELGBs) in inhomogeneous turbulent atmosphere have been derived. The propagation properties of PC-SLGBs and PC-ELGBs in inhomogeneous atmospheric turbulence are studied numerically and comparatively. It can be found that the propagation of laser beams in inhomogeneous turbulence is different from that in homogeneous turbulence. It is also shown that relative rms spatial widths and M(2)-factors of PC-ELGBs are more affected by inhomogeneous turbulence than those of PC-SLGBs. Moreover, the relative rms spatial widths and M(2)-factors of PC-SLGBs and PC-ELGBs in inhomogeneous turbulent atmosphere are closely related with waist widths, coherence widths, zenith angles, inner scales, and beam orders. Furthermore, the saturation propagation distance of the relative M(2)-factor and rms angular width with zenith angles of π/6 are 20 km and 0.5 km, respectively.
Probing the interaction between two microspheres in a single Gaussian beam optical trap
NASA Astrophysics Data System (ADS)
Parthasarathi, Praveen; Iyengar, Shruthi Subhash; Lakkegowda, Yogesha; Bhattacharya, Sarbari; Ananthamurthy, Sharath
2016-09-01
Interactions between trapped microspheres have been studied in two geometries so far: (i) using line optical tweezers and (ii) in traps using two counter propagating laser beams. In both trap geometries, the stable inter bead separations have been attributed to optical binding. One could also trap two such beads in a single beam Gaussian laser trap. While there are reports that address this configuration through theoretical or simulation based treatments, there has so far been no detailed experimental work that measures the interactions. In this work, we have recorded simultaneously the fluctuation spectra of two beads trapped along the laser propagation direction in a single Gaussian beam trap by measuring the back scattered signal from the trapping and a tracking laser beam that are counter propagating . The backscattering from the trapping laser monitors the bead encountered earlier in the propagation path. The counter propagating tracking laser, on the other hand, is used to monitor the fluctuations of the second bead. Detection is by using quadrant photo detectors placed at either end. The autocorrelation functions of both beads reveal marked departures from that obtained when there is only one bead in the trap. Moreover, the fall-off profiles of the autocorrelation indicates the presence of more than one relaxation time. This indicates a method of detecting the presence of a second bead in a trap without directly carrying out measurements on it. Further, a careful analysis of the relaxation times could also reveal the nature of interactions between the beads.
Wu, Yuqian; Zhang, Yixin; Zhu, Yun
2016-08-01
We studied Gaussian beams with three different partially coherent models, including the Gaussian-Schell model (GSM), Laguerre-Gaussian Schell model (LGSM), and Bessel-Gaussian Schell model (BGSM), propagating through oceanic turbulence. The expressions of average intensity, beam spreading, and beam wander for GSM, LGSM, and BGSM beams in the paraxial channel are derived. We make a contrast for the three models in numerical simulations and find that the GSM beam has smaller spreading than the others, and the LGSM beam needs longer propagation distance to transform into a well-like profile of average intensity than the BGSM beam in the same conditions. The salinity fluctuation has a greater contribution to the wander of LGSM and BGSM beams than that of the temperature fluctuation. Our results can be helpful in the design of an optical wireless communication link operating in oceanic environment.
Conservation relation of nonclassicality and entanglement for Gaussian states in a beam splitter
NASA Astrophysics Data System (ADS)
Ge, Wenchao; Tasgin, Mehmet Emre; Zubairy, M. Suhail
2015-11-01
We study the relation between single-mode nonclassicality and two-mode entanglement in a beam splitter. We show that single-mode nonclassicality (the entanglement potential) of incident light cannot be transformed into two-mode entanglement completely after a single beam splitter. Some of the entanglement potential remains as single-mode nonclassicality in the two entangled output modes. Two-mode entanglement generated in the process can be equivalently quantified as an increase in the minimum uncertainty widths (or decrease in the squeezing) of the output states compared to the input states. We use the nonclassical depth and logarithmic negativity as single-mode nonclassicality and entanglement measures, respectively. We realize that a conservation relation between the two quantities can be adopted for Gaussian states, if one works in terms of uncertainty width. This conservation relation is extended to many sets of beam splitters.
A linear-time algorithm for Gaussian and non-Gaussian trait evolution models.
Ho, Lam si Tung; Ané, Cécile
2014-05-01
We developed a linear-time algorithm applicable to a large class of trait evolution models, for efficient likelihood calculations and parameter inference on very large trees. Our algorithm solves the traditional computational burden associated with two key terms, namely the determinant of the phylogenetic covariance matrix V and quadratic products involving the inverse of V. Applications include Gaussian models such as Brownian motion-derived models like Pagel's lambda, kappa, delta, and the early-burst model; Ornstein-Uhlenbeck models to account for natural selection with possibly varying selection parameters along the tree; as well as non-Gaussian models such as phylogenetic logistic regression, phylogenetic Poisson regression, and phylogenetic generalized linear mixed models. Outside of phylogenetic regression, our algorithm also applies to phylogenetic principal component analysis, phylogenetic discriminant analysis or phylogenetic prediction. The computational gain opens up new avenues for complex models or extensive resampling procedures on very large trees. We identify the class of models that our algorithm can handle as all models whose covariance matrix has a 3-point structure. We further show that this structure uniquely identifies a rooted tree whose branch lengths parametrize the trait covariance matrix, which acts as a similarity matrix. The new algorithm is implemented in the R package phylolm, including functions for phylogenetic linear regression and phylogenetic logistic regression.
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.
NASA Astrophysics Data System (ADS)
Volkov, S. N.; Makarov, Vladimir A.; Perezhogin, I. A.
2006-09-01
The distribution of polarisation of a light field in the cross section of a beam at the sum frequency is investigated upon the collinear interaction of two elliptically polarised Gaussian beams in a nonlinear isotropic gyrotropic medium. It is shown that the ellipticity, the angle of rotation of the principal axis of the polarisation ellipse, and the rotation direction of the electric field vector of radiation at the sum frequency in the beam cross section strongly depend on the angle in the polar coordinate system. The ranges of parameters of elliptically polarised fundamental Gaussian beams are found where the cross section of the sum-frequency beam is divided into sectors with different rotation directions of the electric field vector. The equations of the straight lines determining the boundaries of these sectors contain parameters specifying the shape and orientation of polarisation ellipses of the fundamental waves and the ratio of their wave vectors. In the case of opposite circular polarisations of these waves, the ellipticity of the sum-frequency beam does not change in the beam cross section and the principal axes of polarisation ellipses of the light field are oriented perpendicular to the radius in polar coordinates.
Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams
NASA Astrophysics Data System (ADS)
Chen, Musheng; Huang, Sujuan; Shao, Wei; Liu, Xianpeng
2017-08-01
The auto-focusing and auto-healing profiles of linearly polarized ring Airy Gaussian vortex (RAiGV) beams in linear media are investigated experimentally based on spatial light modulators and computer-generated holograms. It is found that the parameters of incident beams greatly affect the auto-focusing profiles of RAiGV. The focal length increases as the radius of the primary ring, scaling factor and waist radius increases, and the focal length decreases slightly as topological charges increase. The peak intensity at focal point increases with the increasing topological charges and waist radius, or with the decreasing scaling factor and the radius of the primary ring. The phase singularity of the RAiGV beams remains unchanged during propagation. The RAiGV beams also exhibit remarkable resilience against perturbations and tend to reconstruct its intensity sharp. Meanwhile, the abruptly auto-focusing property can be controlled by blocking few inner or outer rings of the RAiGV beams. These studies provide useful insight in the study of Airy vortex beam and its further applications.
Reflection and transmission of Laguerre-Gaussian beams in a dielectric slab
NASA Astrophysics Data System (ADS)
Li, Haiying; Honary, Farideh; Wu, Zhensen; Bai, Lu
2017-07-01
This paper considers the reflection and transmission characteristics of a Laguerre-Gaussian (LG) beam in a dielectric slab. The fields of the reflected and transmitted beams are described based on plane-wave angular spectrum representation. Using the generalized Fresnel amplitude reflectance and transmittance, the reflected and transmitted fields in each region are expressed. With the Taylor series approximation of reflectance and transmittance, the analytical expressions of the total reflected and transmitted fields in the input and output regions are derived. The effects of the beam-waist radius and topological charge on the reflected and transmitted field intensities are simulated and discussed in detail. The centroid shifts of the reflected beam are also presented. It is concluded that the distortion of the intensity distribution including the size of the intensity contour, is influenced by the beam-waist radius and the topological charge of the incident beam. The total intensity of the slab, in particular for the case of the transmitted field, is found to be distinguishable from the case of the single interface.
Yan, Weichao; Nie, Zhongquan; Zhang, Xueru; Wang, Yuxiao; Song, Yinglin
2017-03-01
Combining the vector diffraction theory with the inverse Faraday effect, we have theoretically studied magnetization shaping generated by tight focusing of an azimuthally polarized multi-Gaussian beam superimposed with a helical phase. By selecting optimized parameters of a multi-Gaussian beam and topological charge of a spiral phase plate, not only a super-long and sub-wavelength longitudinal magnetization needle with single/dual channels for a single-lens high numerical aperture focusing system, but also an extra-long and three-dimensional super-resolution longitudinal magnetization chain with single/dual channels for a 4π high numerical aperture focusing system is achieved in the focal region. Furthermore, by continuously changing the phase difference between two counter-propagating beams, these super-long longitudinal magnetization chains with three-dimensional super-resolution can dynamically move along the z-axis. It is expected that these results pave the path for fabricating magnetic lattices for spin wave operation, multiple atoms or magnetic particle trapping and transportation, confocal and magnetic resonance microscopy, as well as multilayer ultrahigh density magnetic storage.
Flores, J. Mauricio; Cywiak, Moises; Servin, Manuel; Juarez P, Lorenzo
2008-09-20
Recently, an interferometric profilometer based on the heterodyning of three Gaussian beams has been reported. This microscope interferometer, called a three Gaussian beam interferometer, has been used to profile high quality optical surfaces that exhibit constant reflectivity with high vertical resolution and lateral resolution near {lambda}. We report the use of this interferometer to measure the profiles of two commercially available optical surfaces for data storage, namely, the compact disk (CD-R) and the digital versatile disk (DVD-R). We include experimental results from a one-dimensional radial scan of these devices without data marks. The measurements are taken by placing the devices with the polycarbonate surface facing the probe beam of the interferometer. This microscope interferometer is unique when compared with other optical measuring instruments because it uses narrowband detection, filters out undesirable noisy signals, and because the amplitude of the output voltage signal is basically proportional to the local vertical height of the surface under test, thus detecting with high sensitivity. We show that the resulting profiles, measured with this interferometer across the polycarbonate layer, provide valuable information about the track profiles, making this interferometer a suitable tool for quality control of surface storage devices.
Flores, J Mauricio; Cywiak, Moisés; Servín, Manuel; Juárez, Lorenzo
2008-09-20
Recently, an interferometric profilometer based on the heterodyning of three Gaussian beams has been reported. This microscope interferometer, called a three Gaussian beam interferometer, has been used to profile high quality optical surfaces that exhibit constant reflectivity with high vertical resolution and lateral resolution near lambda. We report the use of this interferometer to measure the profiles of two commercially available optical surfaces for data storage, namely, the compact disk (CD-R) and the digital versatile disk (DVD-R). We include experimental results from a one-dimensional radial scan of these devices without data marks. The measurements are taken by placing the devices with the polycarbonate surface facing the probe beam of the interferometer. This microscope interferometer is unique when compared with other optical measuring instruments because it uses narrowband detection, filters out undesirable noisy signals, and because the amplitude of the output voltage signal is basically proportional to the local vertical height of the surface under test, thus detecting with high sensitivity. We show that the resulting profiles, measured with this interferometer across the polycarbonate layer, provide valuable information about the track profiles, making this interferometer a suitable tool for quality control of surface storage devices.
Araujo, Marcos A. de; Silva, Rubens; Lima, Emerson de; Pereira, Daniel P.; Oliveira, Paulo C. de
2009-01-10
We revisited the well known Khosrofian and Garetz inversion algorithm [Appl. Opt.22, 3406-3410 (1983)APOPAI0003-6935] that was developed to analyze data obtained by the application of the traveling knife-edge technique. We have analyzed the approximated fitting function that was used for adjusting their experimental data and have found that it is not optimized to work with a full range of the experimentally-measured data. We have numerically calculated a new set of coefficients, which makes the approximated function suitable for a full experimental range, considerably improving the accuracy of the measurement of a radius of a focused Gaussian laser beam.
Greco, Vincenzo; Giusfredi, Giovanni
2007-02-01
The formulas for the reflection and refraction of a narrow Gaussian beam with general astigmatism at a tilted optical surface are derived by ray-tracing techniques. The propagation direction of the reflected and refracted beams is computed by tracing the central ray of the incident beam, and the characteristic parameters of the respective wavefronts are worked out by applying the formulas developed for the generalized ray tracing. Moreover, the Gaussian form of the reflected and refracted amplitude distributions along the transverse coordinates is determined by requiring the matching of the incident, reflected, and refracted light spots on the optical surface. No limiting assumptions are made regarding the form of the optical interface or the orientation of the incident astigmatic wavefront. In the end, to illustrate a simple application of these formulas, the reflection of a Gaussian beam at a conicoid is considered, and a simple property of the conicoidal mirrors is reported.
Pang, Zihao; Deng, Dongmei
2017-06-12
We investigate the propagation properties and the radiation forces of Airy Gaussian vortex (AiGV) beams in a harmonic potential analytically and numerically in this paper. Obtaining the propagation expression of AiGV beams by solving the dimensionless linear (2+1) D Schrödinger equation in a harmonic potential, we perform the track, the intensity and phase distributions, the propagation shapes, the energy flow and the angular momentum of AiGV beams in a harmonic potential with the method of numerical simulations. The trajectory acting like a cosine curve is shown. Periodic inversion and phase oscillation are demonstrated during propagation. The influence of the distribution factor and the vortex factor on the propagation of AiGV beams in a harmonic potential are discussed. Likewise, the motion of the Poynting vector and the angular momentum is elucidated respectively. As for the radiation forces, we explore the gradient and scattering forces on Rayleigh dielectric particles induced by AiGV beams. In particular, it's found that the value of the scattering force is approximately seven orders of magnitude larger than that of the gradient force during the propagation in a harmonic potential.
Velocity fields in non-Gaussian cold dark matter models
NASA Astrophysics Data System (ADS)
Lucchin, F.; Matarrese, S.; Messina, A.; Moscardini, L.; Tormen, G.
1995-02-01
We analyse the large-scale velocity field obtained by N-body simulations of cold dark matter (CDM) models with non-Gaussian primordial density fluctuations, considering models with both positive and negative primordial skewness in the density fluctuation distribution. We study the velocity probability distribution and calculate the dependence of the bulk flow, one-point velocity dispersion and cosmic Mach number on the filtering size. We find that the sign of the primordial skewness of the density field provides poor discriminatory power on the evolved velocity field. All non-Gaussian models considered here tend to have lower velocity dispersion and bulk flow than the standard Gaussian CDM model, while the cosmic Mach number turns out to be a poor statistic in characterizing the models. We also compare the large-scale velocity field of a composite sample of optically selected galaxies as described by the Local Group properties, bulk flow, velocity correlation function and cosmic Mach number with the velocity field of mock catalogues extracted from the N-body simulations. The comparison does not clearly single out the best model: the standard Gaussian model is, however, marginally preferred by the maximum likelihood analysis.
Effect of relativistic self-focusing on plasma wave excitation by a hollow Gaussian beam
NASA Astrophysics Data System (ADS)
Gupta, Ruchika; Rafat, M.; Sharma, R. P.
2011-12-01
A paraxial-like approach has been invoked to understand the nature of propagation of a hollow Gaussian beam (HGB) propagating in plasma under the influence of relativistic non-linearity. In this approach, the parameters are expanded in terms of the radial distance from the maximum of irradiance rather than that from the axis. This paper investigates the excitation of plasma wave in a hot collision less plasma by HGB. On account of the × force, a plasma wave at 2ω0 (here, ω0 is the pump laser frequency) is generated. The solution of the HGB has been obtained within the paraxial ray approximation. Filamentary structures of the laser beam are observed due to relativistic non-linearity.
NASA Astrophysics Data System (ADS)
Nakajima, Nobuharu; Yoshino, Masayuki
2017-01-01
We present a proof-of-principle experiment of an analytic (noniterative) phase-retrieval method for coherent imaging systems under scanning illumination of a probe beam. This method allows to reconstruct the amplitude and phase distribution of a semi-transparent object over a wide area from intensities measured at three points in the Fourier plane of the object under scanning illumination of a known Gaussian-amplitude beam in the object plane. The present measurement system is very simple in contrast to ones of interferometric techniques, and also the speed of the calculation of phase retrieval in this method is faster than that in iterative algorithms since this method is based on an analytic solution to the phase retrieval. The effectiveness of this method is shown in experimental examples of the object reconstructions of a converging lens and a plastic plate for scratch standards.
Purohit, Gunjan 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 to 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.
A study of Gaussian approximations of fluorescence microscopy PSF models
NASA Astrophysics Data System (ADS)
Zhang, Bo; Zerubia, Josiane; Olivo-Marin, Jean-Christophe
2006-02-01
Despite the availability of rigorous physical models of microscopy point spread functions (PSFs), approximative PSFs, particularly separable Gaussian approximations are widely used in practical microscopic data processing. In fact, compared with a physical PSF model, which usually involves non-trivial terms such as integrals and infinite series, a Gaussian function has the advantage that it is much simpler and can be computed much faster. Moreover, due to its special analytical form, a Gaussian PSF is often preferred to facilitate the analysis of theoretical models such as Fluorescence Recovery After Photobleaching (FRAP) process and of processing algorithms such as EM deconvolution. However, in these works, the selection of Gaussian parameters and the approximation accuracy were rarely investigated. In this paper, we present a comprehensive study of Gaussian approximations for diffraction-limited 2D/3D paraxial/non-paraxial PSFs of Wide Field Fluorescence Microscopy (WFFM), Laser Scanning Confocal Microscopy (LSCM) and Disk Scanning Confocal Microscopy (DSCM) described using the Debye integral. Besides providing an optimal Gaussian parameter for the 2D paraxial WFFM PSF case, we further derive nearly optimal parameters in explicit forms for each of the other cases, based on Maclaurin series matching. Numerical results show that the accuracy of the 2D approximations is very high (Relative Squared Error (RSE) < 2% in WFFM, < 0.3% in LSCM and < 4% in DSCM). For the 3D PSFs, the approximations are average in WFFM (RSE ~= 16-20%), accurate in DSCM (RSE~= 3-6%) and nearly perfect in LSCM (RSE ~= 0.3-0.5%).
Spatial solitons in a three-level atomic medium supported by a Laguerre-Gaussian control beam
Hang Chao; Konotop, V. V.
2011-05-15
We investigate the existence and stability of various types of spatial solitons in a three-level atomic medium with Laguerre-Gaussian control beam. Radial and azimuthal modulations of the medium properties, introduced by the control beam, provide possibilities for existence of diverse soliton patterns and dynamics. Beam diffraction provides additional soliton controllability. All types of solitons can be generated at very low input energy at a few-photon level.
Jiang, Tao; Shan, Guogen
2016-01-01
Residue fluctuations in protein structures have been shown to be highly associated with various protein functions. Gaussian network model (GNM), a simple representative coarse-grained model, was widely adopted to reveal function-related protein dynamics. We directly utilized the high frequency modes generated by GNM and further performed Gaussian Naive Bayes (GNB) to identify hot spot residues. Two coding schemes about the feature vectors were implemented with varying distance cutoffs for GNM and sliding window sizes for GNB based on tenfold cross validations: one by using only a single high mode and the other by combining multiple modes with the highest frequency. Our proposed methods outperformed the previous work that did not directly utilize the high frequency modes generated by GNM, with regard to overall performance evaluated using F1 measure. Moreover, we found that inclusion of more high frequency modes for a GNB classifier can significantly improve the sensitivity. The present study provided additional valuable insights into the relation between the hot spots and the residue fluctuations. PMID:27882325
Gaussian Markov Random Field Model without Boundary Conditions
NASA Astrophysics Data System (ADS)
Katakami, Shun; Sakamoto, Hirotaka; Murata, Shin; Okada, Masato
2017-06-01
In this study, we analyzed a Gaussian Markov random field model without periodic boundary conditions. On the basis of a Bayesian inference framework, we showed that image restoration, hyperparameter estimation, and an expectation value of free energy can be conducted analytically. Through numerical simulations, we showed the difference between methods with and without periodic boundary conditions and verified the effectiveness of the proposed method.
Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings.
Janicijevic, Ljiljana; Topuzoski, Suzana
2008-11-01
Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.
A symplectic coherent beam-beam model
Furman, M.A.
1989-05-01
We consider a simple one-dimensional model to study the effects of the beam-beam force on the coherent dynamics of colliding beams. The key ingredient is a linearized beam-beam kick. We study only the quadrupole modes, with the dynamical variables being the 2nd-order moments of the canonical variables q, p. Our model is self-consistent in the sense that no higher order moments are generated by the linearized beam-beam kicks, and that the only source of violation of symplecticity is the radiation. We discuss the round beam case only, in which vertical and horizontal quantities are assumed to be equal (though they may be different in the two beams). Depending on the values of the tune and beam intensity, we observe steady states in which otherwise identical bunches have sizes that are equal, or unequal, or periodic, or behave chaotically from turn to turn. Possible implications of luminosity saturation with increasing beam intensity are discussed. Finally, we present some preliminary applications to an asymmetric collider. 8 refs., 8 figs.
Fresnel diffraction by circular aperture of Gaussian beams in gradient index media
NASA Astrophysics Data System (ADS)
Acosta, E.; Gomez-Reino, Carlos C.; Gonzalez, R. M.
1990-07-01
The intensity distribution of a gaussian beam propagating through GRIN media that has been truncated by a centered circular aperture is calculated by Fresnel-Kirchoff theory. On axis intensity is evaluated. 1 MATHEMATICAL TREATMENT AND DISCUSSION. The circular aperture in an opaque screen is located at z r is the radial coordinate. In the z half-space the medium has a refractive index profile given by 2 2 2 2 n (r (z)r ). For the z half-space the medium is considered to be homogeneous with n''l. The diffracted field in the z region when a gaussian beam source at z0 in the z region is evaluated in terms of Bessel functions. The beam at z can be represented in terms of its waist size and its half-width w(z0) and curvature radius R(z0) at the aperture plane. The Huygens-Fresnel diffraction formula with the Fresnel approximation can be evaluated as an infinite sum yielding: S 2 Akwn iknHr 2 J(aa) 00 01 1 1 2 n u(r w(z )JexP[ 2H JJ : exp(a C) (1) 1 0 1 n 2n! (aa) where H(z) and H2(z) are respectively the axial and the field rays1 a and C intensity distribution in the diffraction pattern is given by I(r This treatment predicts for the on axis intensity: I 2 2 nH 1 I I a 1 ia ki 1 0 2 I (z)cx . coshi
NASA Astrophysics Data System (ADS)
Chen, Zhixiao; Yu, Song; Wang, Tianyi; Wu, Guohua; Guo, Hong; Gu, Wanyi
2013-01-01
The spatial correlation between signals arising from a pair of constituent transmitters in a spatial multiple-input-multiple-output (MIMO) system is investigated. General formulations for the spatial correlation functions considering Gaussian-beam waves and receiver aperture effects are given under weak turbulence condition. Based on the analytical expressions, we find that spatial correlation decreases with separation distance, but increases with receiver aperture sizes, turbulence strength and wavelengths. In particular, receiver aperture averaging effects can evidently increase the correlation. It is also shown that decreasing the beam widths can generally reduce the spatial correlation, and convergent beams have lower spatial correlation than their collimated counterparts. It is found that Gaussian beams with the Fresnel ratios larger than 1 have advantages in reducing both the spatial correlation and the beam scintillations.
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.
Patil, S. D.; 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.
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
Nanda, Vikas; Kant, Niti
2014-07-15
The effect of plasma density ramp on self-focusing of cosh-Gaussian laser beam considering ponderomotive nonlinearity is analyzed using WKB and paraxial approximation. It is noticed that cosh-Gaussian laser beam focused earlier than Gaussian beam. The focusing and de-focusing nature of the cosh-Gaussian laser beam with decentered parameter, intensity parameter, magnetic field, and relative density parameter has been studied and strong self-focusing is reported. It is investigated that decentered parameter “b” plays a significant role for the self-focusing of the laser beam as for b=2.12, strong self-focusing is seen. Further, it is observed that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For b=2.12, with the increase in the value of magnetic field self-focusing effect, in case of extraordinary mode, becomes very strong under plasma density ramp. Present study may be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers. Moreover, plasma density ramp plays a vital role to enhance the self-focusing effect.
BEAMS3D Neutral Beam Injection Model
Lazerson, Samuel
2014-04-14
With the advent of applied 3D fi elds in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous velocity reduction, and pitch angle scattering are modeled with the ADAS atomic physics database [1]. Benchmark calculations are presented to validate the collisionless particle orbits, neutral beam injection model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields.
Thermal field emission sources and optics for Gaussian electron-beam lithography
NASA Astrophysics Data System (ADS)
Chisholm, Tom; Wallman, Bernard A.; Romijn, Johannes C.
1995-09-01
The use of Schottky emitters has enabled the designers of Gaussian vector-scan e-beam lithography equipment to meet the ever more stringent demands of the semiconductor industry. Although these emitters are expensive, their long life means that they are economical in total cost. Measurements of the influence of noise on the drives to each element of the Leica EBPG- 5FE column show that the only critical parts are the beam alignment units. Stable, low-noise drivers allow the beam positional noise to be within acceptable limits. A numerical technique has been developed to compute the total spot-size in the presence of spherical and chromatic aberrations and this allows the efficiency of the automatic spot optimization routines of the EBPG-5FE to be examined. The present emitter in the EBPG-5FE in DIMES has been in operation since August 1993 and stable and reproducible performance is obtained. The machine is in constant use for a wide range of tasks.
Comparing flat top and Gaussian focal beam shapes when micromachining steel
NASA Astrophysics Data System (ADS)
Lizotte, Todd E.; Ohar, Orest
2011-10-01
Laser micromachining, drilling and marking is extensively used within the aerospace, automotive and firearms industries. The unique properties of lasers make them ideal tools for micromachining a wide diversity of materials, including steel alloys [1]. We describe the results of micromachining of low carbon steel and stainless steel alloys, using a high powered diode pumped solid state (DPSS) laser operating at a wavelength of 355nm. The laser was configured with beam conditioning optics to produce either a flat top beam or a Gaussian output which was then sent through a galvanometer scanner and telecentric lens beam delivery system. This paper outlines the interrelationship of process variables when micromachining fine features in steel and stainless steel alloys. Process variables measured included the optimum laser focus plane, energy density, galvanometer scan rate, and pulse overlap and focal spot diameter. Optimum process performance was evaluated based on a dimensional comparison of the micromachined features from each test coupon, including uniformity and surface roughness of the micromachined surface and the minimization of surface irregularities (stalagmite type slag / debris / corn row patterns) and taper angle of the micromachined feature side walls.
Tan, Liying; Zhai, Chao; Yu, Siyuan; Ma, Jing; Lu, Gaoyuan
2015-05-04
In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.
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.
Diffraction of a Gaussian beam by a four-sector binary grating with a shift between adjacent sectors
NASA Astrophysics Data System (ADS)
Janicijevic, Lj.; Topuzoski, S.; Stoyanov, L.; Dreischuh, A.
2017-04-01
In this article as a diffractive optical element we consider a composed four-sector binary grating under Gaussian laser beam illumination. The angular sectors are bounded by the directions y = x and y = - x , and consist of parts of a binary rectilinear grating; thereby, two neighboring parts are shifted by a half spatial rectilinear grating period. The diffracted wave field amplitude is calculated, showing that the straight-through, zeroth-diffraction-order beam is an amplitude-reduced Gaussian beam, and the higher-diffraction-order beams, deviated with respect to the propagation axis, are non-vortex beams described by modified Bessel functions. The transverse intensity profiles of the higher-diffraction-order beams, numerically and experimentally obtained, have form of a four-leaf clover; they are similar to the Laguerre-Gaussian LG(0,2) beam (with radial mode number n = 0 and azimuthal mode number l = 2) described by circular cosine function, in a paraxial, far-field approximation.
Li, Feifei; Park, Ji-Yeon; Barraclough, Brendan; Lu, Bo; Li, Jonathan; Liu, Chihray; Yan, Guanghua
2017-03-01
The aim of this study is to perform a direct comparison of the source model for photon beams with and without flattening filter (FF) and to develop an efficient independent algorithm for planar dose calculation for FF-free (FFF) intensity-modulated radiotherapy (IMRT) quality assurance (QA). The source model consisted of a point source modeling the primary photons and extrafocal bivariate Gaussian functions modeling the head scatter, monitor chamber backscatter, and collimator exchange effect. The model parameters were obtained by minimizing the difference between the calculated and measured in-air output factors (Sc ). The fluence of IMRT beams was calculated from the source model using a backprojection and integration method. The off-axis ratio in FFF beams were modeled with a fourth degree polynomial. An analytical kernel consisting of the sum of three Gaussian functions was used to describe the dose deposition process. A convolution-based method was used to account for the ionization chamber volume averaging effect when commissioning the algorithm. The algorithm was validated by comparing the calculated planar dose distributions of FFF head-and-neck IMRT plans with measurements performed with a 2D diode array. Good agreement between the measured and calculated Sc was achieved for both FF beams (<0.25%) and FFF beams (<0.10%). The relative contribution of the head-scattered photons reduced by 34.7% for 6 MV and 49.3% for 10 MV due to the removal of the FF. Superior agreement between the calculated and measured dose distribution was also achieved for FFF IMRT. In the gamma comparison with a 2%/2 mm criterion, the average passing rate was 96.2 ± 1.9% for 6 MV FFF and 95.5 ± 2.6% for 10 MV FFF. The efficient independent planar dose calculation algorithm is easy to implement and can be valuable in FFF IMRT QA.
Wu, Xuecheng; Wu, Yingchun; Yang, Jing; Wang, Zhihua; Zhou, Binwu; Gréhan, Gérard; Cen, Kefa
2013-05-20
Application of the modified convolution method to reconstruct digital inline holography of particle illuminated by an elliptical Gaussian beam is investigated. Based on the analysis on the formation of particle hologram using the Collins formula, the convolution method is modified to compensate the astigmatism by adding two scaling factors. Both simulated and experimental holograms of transparent droplets and opaque particles are used to test the algorithm, and the reconstructed images are compared with that using FRFT reconstruction. Results show that the modified convolution method can accurately reconstruct the particle image. This method has an advantage that the reconstructed images in different depth positions have the same size and resolution with the hologram. This work shows that digital inline holography has great potential in particle diagnostics in curvature containers.
Global Low-Rank Image Restoration With Gaussian Mixture Model.
Zhang, Sibo; Jiao, Licheng; Liu, Fang; Wang, Shuang
2017-06-27
Low-rank restoration has recently attracted a lot of attention in the research of computer vision. Empirical studies show that exploring the low-rank property of the patch groups can lead to superior restoration performance, however, there is limited achievement on the global low-rank restoration because the rank minimization at image level is too strong for the natural images which seldom match the low-rank condition. In this paper, we describe a flexible global low-rank restoration model which introduces the local statistical properties into the rank minimization. The proposed model can effectively recover the latent global low-rank structure via nuclear norm, as well as the fine details via Gaussian mixture model. An alternating scheme is developed to estimate the Gaussian parameters and the restored image, and it shows excellent convergence and stability. Besides, experiments on image and video sequence datasets show the effectiveness of the proposed method in image inpainting problems.
Eckstein, Hans-Christoph; Zeitner, Uwe Detlef
2009-09-28
Unstable resonators show an intense discrimination of undesired higher order modes but a high beam quality cannot be obtained with conventional resonators composed of spherical mirrors. In the present paper we demonstrate the possibility to tailor the fundamental mode by inserting diffractive elements into the resonator to generate a desirable output beam profile even for unstable resonators. We show a concept to design such surface structured elements for customizing the amplitude shape of the outcoupled beam. Further we demonstrate the first experimental realization of an unstable diffractive resonator with a Gaussian shaped amplitude profile of the laser beam for a vertical external cavity surface emitting laser (VECSEL).
Shi, Li; Li, Jing; Tao, Tao; Wu, Xiaoping
2012-09-10
In this paper, the influence of radially higher index p of Laguerre-Gaussian (LG) beams on the rotation of nanowires is studied. Radially higher-order LG beams are produced by computer-generated holograms, which are displayed on a spatial light modulator. A series of experiments on manipulating ZnO nanowires was performed on our holographic optical tweezers platform. The experiments demonstrated that radially higher-order LG beams could effectively rotate nanowires along the innermost bright ring of themselves. Compared with radially low-order LG beams, they have larger torques exerted on nanowires and can make nanowires rotate more quickly.
Propagation of higher-order cosh-Gaussian beams in uniaxial crystals orthogonal to the optical axis
NASA Astrophysics Data System (ADS)
Li, J.; Chen, Y.; Xin, Y.; Xu, S.
2010-04-01
Propagation properties of higher-order cosh-Gaussian (HOCG) beams in uniaxial crystals orthogonal to the optical axis are studied. Analytical formulae for electric fields and kurtosis parameters are derived. Results show that a HOCG beam with larger acentric parameters or beam orders would better preserve its intensity profile when it propagates in uniaxial crystals. At arbitrary propagation distance flat-topped beams can be shaped by selecting appropriate acentric parameters. It is also indicated that kurtosis parameters τx and τy both increase when acentric parameters take larger values, however, they show different behaviors due to effects of anisotropic crystals.
NASA Astrophysics Data System (ADS)
Wang, Ying; Yuan, Chengxun; Jia, Jieshu; Gao, Ruilin; Hong, Yunhai; Yao, Jingfeng; Li, Hui; Zhou, Zhongxiang; Wu, Jian
2017-06-01
The multiple coherent identical Gaussian beams with symmetry distribution are abbreviated as multi-Gaussian beam, of which the propagation characters in collisionless plasma are studied with the WKB method and higher order paraxial theory. The initial beam profile presents the flat top like or hollow like distribution when the eccentric displacement is large enough. Based on the derived nonlinear propagation equations, the initial condition analyses are performed, and the impact of eccentric displacement on the free propagation effect and ponderomotive nonlinearity is thoroughly discussed. The propagation characters of dimensionless beam width parameter, spot intensity, and spatial distribution of plasma electron density are presented. Results show that the initial spot intensity is expanding outwards along the propagation and the ring structure of electron evacuation in plasmas is generated.
Singh, Arvinder E-mail: naveens222@rediffmail.com; Gupta, Naveen E-mail: naveens222@rediffmail.com
2015-01-15
This paper presents an investigation of relativistic self-focusing effect of a q-Gaussian laser beam on second harmonic generation in a preformed parabolic plasma channel. An expression has been derived for density perturbation associated with the plasma wave excited by the laser beam. This in turn acts as a source of second harmonic generation. The moment theory approach has been used to derive a differential equation that governs the evolution of spot size of the laser beam with the distance of propagation. The detailed effects of intensity distribution deviation from Gaussian distribution, intensity of laser beam, density, and depth of the channel have been studied on self-focusing as well as on second harmonic generation.
The time series modelling of non-Gaussian engineering processes
NASA Astrophysics Data System (ADS)
Watson, W.; Spedding, T. A.
1982-12-01
The basic methods of the time series modeling of surface profiles are extended to non-Gaussian processes which can involve complex correlation structures (e.g., periodic components obtained from turning and other similar processes). Particular attention is given to a class of models for time series formed by a combination of autoregressive (AR) and moving average (MA) processes. The results presented here show that these models are capable of accurately simulating a wide range of surface profile characteristics. The models can be programmed to run automatically and can be combined with standard procedures for fitting ARMA models and, if required, with one or several methods for separating random and periodic components.
Liu, Hongzhan; Liu, Liren; Xu, Rongwei; Luan, Zhu
2005-08-10
We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using theABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements.
Olarte, Omar E.; Licea-Rodriguez, Jacob; Palero, Jonathan A.; Gualda, Emilio J.; Artigas, David; Mayer, Jürgen; Swoger, Jim; Sharpe, James; Rocha-Mendoza, Israel; Rangel-Rojo, Raul; Loza-Alvarez, Pablo
2012-01-01
We present the implementation of a combined digital scanned light-sheet microscope (DSLM) able to work in the linear and nonlinear regimes under either Gaussian or Bessel beam excitation schemes. A complete characterization of the setup is performed and a comparison of the performance of each DSLM imaging modality is presented using in vivo Caenorhabditis elegans samples. We found that the use of Bessel beam nonlinear excitation results in better image contrast over a wider field of view. PMID:22808423
NASA Astrophysics Data System (ADS)
Zhong, Yu; Ran, Lixin; Cheng, Xiangxiang; Kong, Jin Au
2006-02-01
In this paper, the transmission of a Gaussian beam passing through a slab made of a one-dimensional left-handed meta-material (1D LHM) is studied. The analytical solution of the electric and the magnetic fields inside and outside the slab are given. The calculation of the power flow of the beam predicts that in the negative pass band of the 1D LHM, there exist different directions of lateral displacements. Such phenomenon is further verified by experiment.
Classifying gamma-ray bursts with Gaussian Mixture Model
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Bin; Yang, En-Bo; Choi, Chul-Sung; Chang, Heon-Young
2016-11-01
Using Gaussian Mixture Model (GMM) and expectation-maximization algorithm, we perform an analysis of time duration (T90) for Compton Gamma Ray Observatory (CGRO)/BATSE, Swift/BAT and Fermi/GBM gamma-ray bursts (GRBs). The T90 distributions of 298 redshift-known Swift/BAT GRBs have also been studied in both observer and rest frames. Bayesian information criterion has been used to compare between different GMM models. We find that two Gaussian components are better to describe the CGRO/BATSE and Fermi/GBM GRBs in the observer frame. Also, we caution that two groups are expected for the Swift/BAT bursts in the rest frame, which is consistent with some previous results. However, Swift GRBs in the observer frame seem to show a trimodal distribution, of which the superficial intermediate class may result from the selection effect of Swift/BAT.
Detecting Clusters in Atom Probe Data with Gaussian Mixture Models.
Zelenty, Jennifer; Dahl, Andrew; Hyde, Jonathan; Smith, George D W; Moody, Michael P
2017-04-01
Accurately identifying and extracting clusters from atom probe tomography (APT) reconstructions is extremely challenging, yet critical to many applications. Currently, the most prevalent approach to detect clusters is the maximum separation method, a heuristic that relies heavily upon parameters manually chosen by the user. In this work, a new clustering algorithm, Gaussian mixture model Expectation Maximization Algorithm (GEMA), was developed. GEMA utilizes a Gaussian mixture model to probabilistically distinguish clusters from random fluctuations in the matrix. This machine learning approach maximizes the data likelihood via expectation maximization: given atomic positions, the algorithm learns the position, size, and width of each cluster. A key advantage of GEMA is that atoms are probabilistically assigned to clusters, thus reflecting scientifically meaningful uncertainty regarding atoms located near precipitate/matrix interfaces. GEMA outperforms the maximum separation method in cluster detection accuracy when applied to several realistically simulated data sets. Lastly, GEMA was successfully applied to real APT data.
Mean-field fluid behavior of the gaussian core model
Louis; Bolhuis; Hansen
2000-12-01
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated "mean-field fluid" over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
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.
Robust image reconstruction enhancement based on Gaussian mixture model estimation
NASA Astrophysics Data System (ADS)
Zhao, Fan; Zhao, Jian; Han, Xizhen; Wang, He; Liu, Bochao
2016-03-01
The low quality of an image is often characterized by low contrast and blurred edge details. Gradients have a direct relationship with image edge details. More specifically, the larger the gradients, the clearer the image details become. Robust image reconstruction enhancement based on Gaussian mixture model estimation is proposed here. First, image is transformed to its gradient domain, obtaining the gradient histogram. Second, the gradient histogram is estimated and extended using a Gaussian mixture model, and the predetermined function is constructed. Then, using histogram specification technology, the gradient field is enhanced with the constraint of the predetermined function. Finally, a matrix sine transform-based method is applied to reconstruct the enhanced image from the enhanced gradient field. Experimental results show that the proposed algorithm can effectively enhance different types of images such as medical image, aerial image, and visible image, providing high-quality image information for high-level processing.
A Gaussian Copula Model for Multivariate Survival Data
Othus, Megan; Li, Yi
2011-01-01
We consider a Gaussian copula model for multivariate survival times. Estimation of the copula association parameter is easily implemented with existing software using a two-stage estimation procedure. Using the Gaussian copula, we are able to test whether the association parameter is equal to zero. When the association term is positive, the model can be extended to incorporate cluster-level frailty terms. Asymptotic properties are derived under the two-stage estimation scheme. Simulation studies verify finite sample utility. We apply the method to a Children’s Oncology Group multi-center study of acute lymphoblastic leukemia. The analysis estimates marginal treatment effects and examines potential clustering within treatment institution. PMID:22162742
Mean-field fluid behavior of the Gaussian core model
NASA Astrophysics Data System (ADS)
Louis, A. A.; Bolhuis, P. G.; Hansen, J. P.
2000-12-01
We show that the Gaussian core model of particles interacting via a penetrable repulsive Gaussian potential, first considered by Stillinger [J. Chem. Phys. 65, 3968 (1976)], behaves as a weakly correlated ``mean-field fluid'' over a surprisingly wide density and temperature range. In the bulk, the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function, and by the more sophisticated hypernetted chain integral equation. The resulting pressure deviates very little from a simple mean-field-like quadratic form in the density, while the low density virial expansion turns out to have an extremely small radius of convergence. Density profiles near a hard wall are also very accurately described by the corresponding mean-field free-energy functional. The binary version of the model exhibits a spinodal instability against demixing at high densities. Possible implications for semidilute polymer solutions are discussed.
Model for non-Gaussian intraday stock returns.
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.
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.
Zhang, Guo-Bo; Chen, Min E-mail: yanyunma@126.com; Luo, Ji; Zeng, Ming; Yu, Lu-Le; Weng, Su-Ming; Schroeder, C. B.; Esarey, E.; Li, Fei-Yu; Ma, Yan-Yun E-mail: yanyunma@126.com; Yu, Tong-Pu; Sheng, Zheng-Ming
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 radius 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.
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.
Stochastic model updating utilizing Bayesian approach and Gaussian process model
NASA Astrophysics Data System (ADS)
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces
NASA Astrophysics Data System (ADS)
Grosche, Simon; Ornigotti, Marco; Szameit, Alexander
2015-11-01
We present a theoretical study of the Goos-H\\"anchen and Imbert-Fedorov shifts for a fundamental Gaussian beam impinging on a surface coated with a single layer of graphene. We show that the graphene surface conductibility $\\sigma(\\omega)$ is responsible for the appearance of a giant and negative spatial Goos-H\\"anchen shift.
Goos-Hänchen and Imbert-Fedorov shifts for Gaussian beams impinging on graphene-coated surfaces.
Grosche, Simon; Ornigotti, Marco; Szameit, Alexander
2015-11-16
We present a theoretical study of the Goos-Hänchen and Imbert-Fedorov shifts for a fundamental Gaussian beam impinging on a surface coated with a single layer of graphene. We show that the graphene surface conductivity σ(ω) is responsible for the appearance of a giant and negative spatial Goos-Hänchen shift.
Image estimation using doubly stochastic gaussian random field models.
Woods, J W; Dravida, S; Mediavilla, R
1987-02-01
The two-dimensional (2-D) doubly stochastic Gaussian (DSG) model was introduced by one of the authors to provide a complete model for spatial filters which adapt to the local structure in an image signal. Here we present the optimal estimator and 2-D fixed-lag smoother for this DSG model extending earlier work of Ackerson and Fu. As the optimal estimator has an exponentially growing state space, we investigate suboptimal estimators using both a tree and a decision-directed method. Experimental results are presented.
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.
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.
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
Serdyuk, Vladimir; Rudnitsky, Anton
2015-05-01
We present an approximate 2D asymptotic analytic theory of light field excitation in a plane thin dielectric layer under conditions of frustrated total internal reflection, when an inclined Gaussian beam, falling from a triangular prism, excites a decaying field in air spacing between a prism and a plane dielectric. Ignoring the radiation scattering on the sharp edges of a prism, we have obtained the formulas that allow us to compute spatial structures of an electromagnetic field in every point of space and to estimate the integral efficiency of waveguide mode excitation in a plane dielectric layer and the total energy of a reflected beam. It is shown that the width of an initial Gaussian beam has an effect on waveguide mode intensity.
Evolution of coherence singularities of Schell-model beams.
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.
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.
Patil, S. D.; Takale, M. V.
2013-08-15
We have studied the steady state self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive regime for upward increasing plasma ramp density profile. We have obtained the differential equation for beam width parameter by using parabolic equation approach under the usual Wentzel–Kramers–Brillouin and paraxial approximations. The variation of beam width parameter with respect to dimensionless distance of propagation is presented graphically by varying the parameters of density profile, intensity parameter, and electronic temperature. It shows that the above stated parameters play an important role in propagation characteristics and give reasonably interesting results.
Iketaki, Yoshinori; Watanabe, Takeshi; Bokor, Nándor; Fujii, Masaaki
2007-08-15
The vectorial Debye integral shows that tightly focused Laguerre-Gaussian (LG) beams have a residual intensity at the focal point for linear polarization, for a topological charge of m=1 and 2. We measured the shapes of linearly and circularly polarized LG beams and found that a central intensity appeared at m=1 and 2 for linear and right-handed circular polarization, however, it is completely canceled for left-handed circular polarization. In general, when the orbital angular momentum of the LG beam is parallel to the spin angular momentum of the photons, zero intensity is always achieved at the focus.
NASA Astrophysics Data System (ADS)
Malyutin, A. A.
2004-10-01
Several optical schemes performing the complex-order fractional Fourier transform are considered. It is shown that these schemes, containing only Gaussian apertures or their combination with lenses, have eigenbeams represented by Hermite—Gaussian modes with transverse indices m, n<=1 and Laguerre—Gaussian modes with p=0 and l=1. The wave front of the eigenbeams is, as a rule, spherical.
GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.
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.
Parameter Optimization for the Gaussian Model of Folded Proteins
NASA Astrophysics Data System (ADS)
Erman, Burak; Erkip, Albert
2000-03-01
Recently, we proposed an analytical model of protein folding (B. Erman, K. A. Dill, J. Chem. Phys, 112, 000, 2000) and showed that this model successfully approximates the known minimum energy configurations of two dimensional HP chains. All attractions (covalent and non-covalent) as well as repulsions were treated as if the monomer units interacted with each other through linear spring forces. Since the governing potential of the linear springs are derived from a Gaussian potential, the model is called the ''Gaussian Model''. The predicted conformations from the model for the hexamer and various 9mer sequences all lie on the square lattice, although the model does not contain information about the lattice structure. Results of predictions for chains with 20 or more monomers also agreed well with corresponding known minimum energy lattice structures. However, these predicted conformations did not lie exactly on the square lattice. In the present work, we treat the specific problem of optimizing the potentials (the strengths of the spring constants) so that the predictions are in better agreement with the known minimum energy structures.
Molecular Code Division Multiple Access: Gaussian Mixture Modeling
NASA Astrophysics Data System (ADS)
Zamiri-Jafarian, Yeganeh
Communications between nano-devices is an emerging research field in nanotechnology. Molecular Communication (MC), which is a bio-inspired paradigm, is a promising technique for communication in nano-network. In MC, molecules are administered to exchange information among nano-devices. Due to the nature of molecular signals, traditional communication methods can't be directly applied to the MC framework. The objective of this thesis is to present novel diffusion-based MC methods when multi nano-devices communicate with each other in the same environment. A new channel model and detection technique, along with a molecular-based access method, are proposed in here for communication between asynchronous users. In this work, the received molecular signal is modeled as a Gaussian mixture distribution when the MC system undergoes Brownian noise and inter-symbol interference (ISI). This novel approach demonstrates a suitable modeling for diffusion-based MC system. Using the proposed Gaussian mixture model, a simple receiver is designed by minimizing the error probability. To determine an optimum detection threshold, an iterative algorithm is derived which minimizes a linear approximation of the error probability function. Also, a memory-based receiver is proposed to improve the performance of the MC system by considering previously detected symbols in obtaining the threshold value. Numerical evaluations reveal that theoretical analysis of the bit error rate (BER) performance based on the Gaussian mixture model match simulation results very closely. Furthermore, in this thesis, molecular code division multiple access (MCDMA) is proposed to overcome the inter-user interference (IUI) caused by asynchronous users communicating in a shared propagation environment. Based on the selected molecular codes, a chip detection scheme with an adaptable threshold value is developed for the MCDMA system when the proposed Gaussian mixture model is considered. Results indicate that the
Beam spreading of vortex beams propagating in turbulent atmosphere.
Lukin, Vladimir P; Konyaev, Peter A; Sennikov, Victor A
2012-04-01
We present some results obtained by numerical modeling of the propagation of vortex beams LG(0l) through a randomly inhomogeneous medium. The vortex beams are the lower order Laguerre-Gaussian modes. Such beams, if propagated under conditions of weak turbulence, also experience distortions, like a Gaussian beam. However, the statistically averaged vortex beams (LG(0l)) conserve the central intensity dip with a nonzero intensity on the beam axis. The beam broadening of vortex beams is analyzed. The average vortex beams are found to be broadened less than the Gaussian beam while propagated through a randomly inhomogeneous medium. The higher the topological charge l is, the smaller the beam broadening is.
Designing Multi-target Compound Libraries with Gaussian Process Models.
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.
Generic inference of inflation models by local non-Gaussianity
NASA Astrophysics Data System (ADS)
Dorn, Sebastian; Ramirez, Erandy; Kunze, Kerstin E.; Hofmann, Stefan; Enßlin, Torsten A.
2014-05-01
The presence of multiple fields during inflation might seed a detectable amount of non-Gaussianity in the curvature perturbations, which in turn becomes observable in present data sets like the cosmic microwave background (CMB) or the large scale structure (LSS). Within this proceeding we present a fully analytic method to infer inflationary parameters from observations by exploiting higher-order statistics of the curvature perturbations. To keep this analyticity, and thereby to dispense with numerically expensive sampling techniques, a saddle-point approximation is introduced whose precision has been validated for a numerical toy example. Applied to real data, this approach might enable to discriminate among the still viable models of inflation.
Gaussian-Schell model sources in one-dimensional first-order systems with loss or gain.
Kauderer, M
1993-02-20
A detailed examination of the propagation of Gaussian-Schell model sources in one-dimensional, possibly nonlossless, first-order systems is constructed. The laws of focusing are derived. The conditions for periodicity of the Gaussian-Schell model source are derived. This result generalizes the well-known result -2 Gaussian beam to the partially coherent nonlossless case. When loss or gain is present several conditions must be satisfied simultaneously for periodicity. The self-consistent solutions are derived and the perturbation stability of the solutions is studied. A physical realization of an arbitrary nonlossless one-dimensional ABCD system is derived, which yields a convenient formula for deciding whether the ABCD system has loss or gain. Special attention is devoted to real and ripple systems.
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.
Marshall, Jeffrey S.; Wu, Junru
2015-10-15
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.
Direct simulation of multiple scattering by discrete random media illuminated by Gaussian beams
Mackowski, Daniel W.; Mishchenko, Michael I.
2011-01-15
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.
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.
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.
Beyond Gaussians: a study of single-spot modeling for scanning proton dose calculation.
Li, Yupeng; Zhu, Ronald X; Sahoo, Narayan; Anand, Aman; Zhang, Xiaodong
2012-02-21
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 this 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.
Beyond Gaussians: a study of single spot modeling for scanning proton dose calculation
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
Phase diagram of the Gaussian-core model.
Prestipino, Santi; Saija, Franz; Giaquinta, Paolo V
2005-05-01
We trace with high numerical accuracy the phase diagram of the Gaussian-core model, a classical system of point particles interacting via a Gaussian-shaped, purely repulsive potential. This model, which provides a reliable qualitative description of the thermal behavior of interpenetrable globular polymers, is known to exhibit a polymorphic fcc-bcc transition at low densities and reentrant melting at high densities. Extensive Monte Carlo simulations, carried out in conjunction with accurate calculations of the solid free energies, lead to a thermodynamic scenario that is partially modified with respect to previous knowledge. In particular, we find that: (i) the fluid-bcc-fcc triple-point temperature is about one third of the maximum freezing temperature; (ii) upon isothermal compression, the model exhibits a fluid-bcc-fcc-bcc-fluid sequence of phases in a narrow range of temperatures just above the triple point. We discuss these results in relation to the behavior of star-polymer solutions and of other softly repulsive systems.
Learning Gaussian mixture models with entropy-based criteria.
Penalver Benavent, Antonio; Escolano Ruiz, Francisco; Saez, Juan Manuel
2009-11-01
In this paper, we address the problem of estimating the parameters of Gaussian mixture models. Although the expectation-maximization (EM) algorithm yields the maximum-likelihood (ML) solution, its sensitivity to the selection of the starting parameters is well-known and it may converge to the boundary of the parameter space. Furthermore, the resulting mixture depends on the number of selected components, but the optimal number of kernels may be unknown beforehand. We introduce the use of the entropy of the probability density function (pdf) associated to each kernel to measure the quality of a given mixture model with a fixed number of kernels. We propose two methods to approximate the entropy of each kernel and a modification of the classical EM algorithm in order to find the optimum number of components of the mixture. Moreover, we use two stopping criteria: a novel global mixture entropy-based criterion called Gaussianity deficiency (GD) and a minimum description length (MDL) principle-based one. Our algorithm, called entropy-based EM (EBEM), starts with a unique kernel and performs only splitting by selecting the worst kernel attending to GD. We have successfully tested it in probability density estimation, pattern classification, and color image segmentation. Experimental results improve the ones of other state-of-the-art model order selection methods.
Elliptic flow in the Gaussian model of eccentricity fluctuations
NASA Astrophysics Data System (ADS)
Voloshin, Sergei A.; Poskanzer, Arthur M.; Tang, Aihong; Wang, Gang
2008-01-01
We discuss a specific model of elliptic flow fluctuations due to Gaussian fluctuations in the initial spatial x and y eccentricity components { < (σy2 -σx2) / (σx2 +σy2) > , < 2σxy / (σx2 +σy2) > }. We find that in this model v2 { 4 }, elliptic flow determined from 4-particle cumulants, exactly equals the average flow value in the reaction plane coordinate system,
Damping modeling in Timoshenko beams
NASA Technical Reports Server (NTRS)
Banks, H. T.; Wang, Y.
1992-01-01
Theoretical and numerical results of damping model studies for composite material beams using the Timoshenko theory is presented. Based on the damping models developed for Euler-Bernoulli beams, the authors develop damping methods for both bending and shear in investigation of Timoshenko beams. A computational method for the estimation of the damping parameters is given. Experimental data with high-frequency excitation were used to test Timoshenko beam equations with different types of damping models for bending and shear in various combinations.
Mourka, A; Mazilu, M; Wright, E M; Dholakia, K
2013-01-01
The modal characterization of various families of beams is a topic of current interest. We recently reported a new method for the simultaneous determination of both the azimuthal and radial mode indices for light fields possessing orbital angular momentum. The method is based upon probing the far-field diffraction pattern from a random aperture and using the recorded data as a 'training set'. We then transform the observed data into uncorrelated variables using the principal component analysis (PCA) algorithm. Here, we show the generic nature of this approach for the simultaneous determination of the modal parameters of Hermite-Gaussian and Bessel beams. This reinforces the widespread applicability of this method for applications including information processing, spectroscopy and manipulation. Additionally, preliminary results demonstrate reliable decomposition of superpositions of Laguerre-Gaussians, yielding the intensities and relative phases of each constituent mode. Thus, this approach represents a powerful method for characterizing the optical multi-dimensional Hilbert space.
Mourka, A.; Mazilu, M.; Wright, E. M.; Dholakia, K.
2013-01-01
The modal characterization of various families of beams is a topic of current interest. We recently reported a new method for the simultaneous determination of both the azimuthal and radial mode indices for light fields possessing orbital angular momentum. The method is based upon probing the far-field diffraction pattern from a random aperture and using the recorded data as a ‘training set'. We then transform the observed data into uncorrelated variables using the principal component analysis (PCA) algorithm. Here, we show the generic nature of this approach for the simultaneous determination of the modal parameters of Hermite-Gaussian and Bessel beams. This reinforces the widespread applicability of this method for applications including information processing, spectroscopy and manipulation. Additionally, preliminary results demonstrate reliable decomposition of superpositions of Laguerre-Gaussians, yielding the intensities and relative phases of each constituent mode. Thus, this approach represents a powerful method for characterizing the optical multi-dimensional Hilbert space. PMID:23478330
Transform Coding for Point Clouds Using a Gaussian Process Model.
De Queiroz, Ricardo; Chou, Philip A
2017-04-28
We propose using stationary Gaussian Processes (GPs) to model the statistics of the signal on points in a point cloud, which can be considered samples of a GP at the positions of the points. Further, we propose using Gaussian Process Transforms (GPTs), which are Karhunen-Lo`eve transforms of the GP, as the basis of transform coding of the signal. Focusing on colored 3D point clouds, we propose a transform coder that breaks the point cloud into blocks, transforms the blocks using GPTs, and entropy codes the quantized coefficients. The GPT for each block is derived from both the covariance function of the GP and the locations of the points in the block, which are separately encoded. The covariance function of the GP is parameterized, and its parameters are sent as side information. The quantized coefficients are sorted by eigenvalues of the GPTs, binned, and encoded using an arithmetic coder with bin-dependent Laplacian models whose parameters are also sent as side information. Results indicate that transform coding of 3D point cloud colors using the proposed GPT and entropy coding achieves superior compression performance on most of our data sets.
BEAMS3D Neutral Beam Injection Model
NASA Astrophysics Data System (ADS)
McMillan, Matthew; Lazerson, Samuel A.
2014-09-01
With the advent of applied 3D fields in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous slowing down, and pitch angle scattering are modeled with the ADAS atomic physics database. Elementary benchmark calculations are presented to verify the collisionless particle orbits, NBI model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields. Notice: this manuscript has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the US Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
Gaussian Mixture Model and Rjmcmc Based RS Image Segmentation
NASA Astrophysics Data System (ADS)
Shi, X.; Zhao, Q. H.
2017-09-01
For the image segmentation method based on Gaussian Mixture Model (GMM), there are some problems: 1) The number of component was usually a fixed number, i.e., fixed class and 2) GMM is sensitive to image noise. This paper proposed a RS image segmentation method that combining GMM with reversible jump Markov Chain Monte Carlo (RJMCMC). In proposed algorithm, GMM was designed to model the distribution of pixel intensity in RS image. Assume that the number of component was a random variable. Respectively build the prior distribution of each parameter. In order to improve noise resistance, used Gibbs function to model the prior distribution of GMM weight coefficient. According to Bayes' theorem, build posterior distribution. RJMCMC was used to simulate the posterior distribution and estimate its parameters. Finally, an optimal segmentation is obtained on RS image. Experimental results show that the proposed algorithm can converge to the optimal number of class and get an ideal segmentation results.
NASA Astrophysics Data System (ADS)
Bellinzona, V. E.
2017-05-01
Challenging issues in treatment planning system for hadrontherapy are the accurate and fast calculation of dose distribution, the reduction in memory space required to store the dose kernel of individual pencil beams and the shortening of computation time for dose optimization and calculation. In this framework, the prediction of lateral dose distributions is a topic of great interest because currently the double gaussian parametrization is typically used as approximation although other parameterizations are also available. The best accuracy for this kind of calculations can be obtained by Monte Carlo methods, at the expense of a long computing time. This work aims to present a flexible computational model for the calculation of the lateral profile of a pencil proton beam and the results of its implementation in a treatment planning system. The model calculation are compared with the currently used double gaussian approximation and the Monte Carlo calculations, and the tests are performed in water and in presence of inhomogeneities.
González-Cardel, Mario; Arguijo, Pedro; Díaz-Uribe, Rufino
2013-06-01
A method for approximating the inverse error function involved in the determination of the radius of a Gaussian beam is proposed. It is based on a polynomial inversion that can be developed to any desired degree, according to an a priori defined error budget. Analytic expressions are obtained and used to determine the radius of a TEM(oo) He-Ne laser beam from intensity measurements experimentally obtained by using the knife edge method. The error and the interval of validity of the approximation are determined for polynomials of different degrees. The analysis of the theoretical and experimental errors is also presented.
Huang, Yongping; Wang, Fanhou; Gao, Zenghui; Zhang, Bin
2015-01-26
Propagation properties of partially coherent electromagnetic hyperbolic-sine-Gaussian (PCESHG) vortex beams through non-Kolmogorov atmospheric turbulence, including the spectral degree of polarization and evolution behavior of coherent vortices and average intensity are investigated in detail by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of non-Kolmogorov turbulence. It is shown that the motion, creation and annihilation of the coherent vortices of PCESHG vortex beams in non-Kolmogorov turbulence may appear with the increasing propagation distance, and the distance for the conservation of the topological charge depends on the turbulence parameters and beam parameters. In additions, the evolution behavior of coherent vortices, average intensity and spectral degree of polarization vary significantly for different values of the generalized exponent parameter and the generalized refractive-index structure parameter of non-Kolmogorov turbulence, and the beam parameters as well as the propagation distance.
Covariant gaussian approximation in Ginzburg-Landau model
NASA Astrophysics Data System (ADS)
Wang, J. F.; Li, D. P.; Kao, H. C.; Rosenstein, B.
2017-05-01
Condensed matter systems undergoing second order transition away from the critical fluctuation region are usually described sufficiently well by the mean field approximation. The critical fluctuation region, determined by the Ginzburg criterion, | T /Tc - 1 | ≪ Gi, is narrow even in high Tc superconductors and has universal features well captured by the renormalization group method. However recent experiments on magnetization, conductivity and Nernst effect suggest that fluctuations effects are large in a wider region both above and below Tc. In particular some ;pseudogap; phenomena and strong renormalization of the mean field critical temperature Tmf can be interpreted as strong fluctuations effects that are nonperturbative (cannot be accounted for by ;gaussian fluctuations;). The physics in a broader region therefore requires more accurate approach. Self consistent methods are generally ;non-conserving; in the sense that the Ward identities are not obeyed. This is especially detrimental in the symmetry broken phase where, for example, Goldstone bosons become massive. Covariant gaussian approximation remedies these problems. The Green's functions obey all the Ward identities and describe the fluctuations much better. The results for the order parameter correlator and magnetic penetration depth of the Ginzburg-Landau model of superconductivity are compared with both Monte Carlo simulations and experiments in high Tc cuprates.
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-05
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less
The Gaussian streaming model and convolution Lagrangian effective field theory
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-05
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
A Gaussian graphical model approach to climate networks
Zerenner, Tanja; Friederichs, Petra; Hense, Andreas; Lehnertz, Klaus
2014-06-15
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
The Gaussian streaming model and convolution Lagrangian effective field theory
NASA Astrophysics Data System (ADS)
Vlah, Zvonimir; Castorina, Emanuele; White, Martin
2016-12-01
We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.
A Gaussian graphical model approach to climate networks.
Zerenner, Tanja; Friederichs, Petra; Lehnertz, Klaus; Hense, Andreas
2014-06-01
Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.
Inversion of hierarchical Bayesian models using Gaussian processes.
Lomakina, Ekaterina I; Paliwal, Saee; Diaconescu, Andreea O; Brodersen, Kay H; Aponte, Eduardo A; Buhmann, Joachim M; Stephan, Klaas E
2015-09-01
Over the past decade, computational approaches to neuroimaging have increasingly made use of hierarchical Bayesian models (HBMs), either for inferring on physiological mechanisms underlying fMRI data (e.g., dynamic causal modelling, DCM) or for deriving computational trajectories (from behavioural data) which serve as regressors in general linear models. However, an unresolved problem is that standard methods for inverting the hierarchical Bayesian model are either very slow, e.g. Markov Chain Monte Carlo Methods (MCMC), or are vulnerable to local minima in non-convex optimisation problems, such as variational Bayes (VB). This article considers Gaussian process optimisation (GPO) as an alternative approach for global optimisation of sufficiently smooth and efficiently evaluable objective functions. GPO avoids being trapped in local extrema and can be computationally much more efficient than MCMC. Here, we examine the benefits of GPO for inverting HBMs commonly used in neuroimaging, including DCM for fMRI and the Hierarchical Gaussian Filter (HGF). Importantly, to achieve computational efficiency despite high-dimensional optimisation problems, we introduce a novel combination of GPO and local gradient-based search methods. The utility of this GPO implementation for DCM and HGF is evaluated against MCMC and VB, using both synthetic data from simulations and empirical data. Our results demonstrate that GPO provides parameter estimates with equivalent or better accuracy than the other techniques, but at a fraction of the computational cost required for MCMC. We anticipate that GPO will prove useful for robust and efficient inversion of high-dimensional and nonlinear models of neuroimaging data. Copyright © 2015. Published by Elsevier Inc.
Automatic domain decomposition of proteins by a Gaussian Network Model.
Kundu, Sibsankar; Sorensen, Dan C; Phillips, George N
2004-12-01
Proteins are often comprised of domains of apparently independent folding units. These domains can be defined in various ways, but one useful definition divides the protein into substructures that seem to move more or less independently. The same methods that allow fairly accurate calculation of motion can be used to help classify these substructures. We show how the Gaussian Network Model (GNM), commonly used for determining motion, can also be adapted to automatically classify domains in proteins. Parallels between this physical network model and graph theory implementation are apparent. The method is applied to a nonredundant set of 55 proteins, and the results are compared to the visual assignments by crystallographers. Apart from decomposing proteins into structural domains, the algorithm can generally be applied to any large macromolecular system to decompose it into motionally decoupled sub-systems. Copyright 2004 Wiley-Liss, Inc.
NASA Astrophysics Data System (ADS)
Wu, Yuqian; Zhang, Yixin; Wang, Qiu; Hu, Zhengda
2016-11-01
For Gaussian beams with three different partially coherent models, including Gaussian-Schell model (GSM), Laguerre-Gaussian Schell-model (LGSM) and Bessel-Gaussian Schell-model (BGSM) beams propagating through a biological turbulent tissue, the expression of the spatial coherence radius of a spherical wave propagating in a turbulent biological tissue, and the average intensity and beam spreading for GSM, LGSM and BGSM beams are derived based on the fractal model of power spectrum of refractive-index variations in biological tissue. Effects of partially coherent model and parameters of biological turbulence on such beams are studied in numerical simulations. Our results reveal that the spreading of GSM beams is smaller than LGSM and BGSM beams on the same conditions, and the beam with larger source coherence width has smaller beam spreading than that with smaller coherence width. The results are useful for any applications involved light beam propagation through tissues, especially the cases where the average intensity and spreading properties of the light should be taken into account to evaluate the system performance and investigations in the structures of biological tissue.
NASA Astrophysics Data System (ADS)
McCallum, Matthew S.
An integral transform which reproduces a transformable input function after a finite number N of successive applications is known as a cyclic transform. Of course, such a transform will reproduce an arbitrary transformable input after N applications, but it also admits eigenfunction inputs which will be reproduced after a single application of the transform. These transforms and their eigenfunctions appear in various applications, and the systematic determination of eigenfunctions of cyclic integral transforms has been a problem of interest to mathematicians since at least the early twentieth century. In this work we review the various approaches to this problem, providing generalizations of published expressions from previous approaches. We then develop a new formalism, differential eigenoperators, that reduces the eigenfunction problem for a cyclic transform to an eigenfunction problem for a corresponding ordinary differential equation. In this way we are able to relate eigenfunctions of integral equations to boundary-value problems, which are typically easier to analyze. We give extensive examples and discussion via the specific case of the Fourier transform. We also relate this approach to two formalisms that have been of interest to the mathematical physics community---hyperdifferential operators and linear canonical transforms. We show how this new approach reproduces known results of Fourier optics regarding free-space diffractive propagation of Gaussian beams in both one and two dimensions. Finally we discuss the group-theoretical aspects of the formalism and describe an isomorphism between roots of the identity transform and complex roots of unity. In the appendix we derive several technical results related to integrability and transformability of solutions in the Fourier transform case, and we prove two theorems---one of them new---on polynomial roots. We conclude that the formalism offers a new and equally valuable perspective on an interesting
Gaussian predictive process models for large spatial data sets.
Banerjee, Sudipto; Gelfand, Alan E; Finley, Andrew O; Sang, Huiyan
2008-09-01
With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial modelling, given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations, rendering such models infeasible for large spatial data sets. This computational burden is exacerbated in multivariate settings with several spatially dependent response variables. It is also aggravated when data are collected at frequent time points and spatiotemporal process models are used. With regard to this challenge, our contribution is to work with what we call predictive process models for spatial and spatiotemporal data. Every spatial (or spatiotemporal) process induces a predictive process model (in fact, arbitrarily many of them). The latter models project process realizations of the former to a lower dimensional subspace, thereby reducing the computational burden. Hence, we achieve the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets. We discuss attractive theoretical properties of these predictive processes. We also provide a computational template encompassing these diverse settings. Finally, we illustrate the approach with simulated and real data sets.
Habibi, M.; 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)].
Efficient speaker verification using Gaussian mixture model component clustering.
De Leon, Phillip L.; McClanahan, Richard D.
2012-04-01
In speaker verification (SV) systems that employ a support vector machine (SVM) classifier to make decisions on a supervector derived from Gaussian mixture model (GMM) component mean vectors, a significant portion of the computational load is involved in the calculation of the a posteriori probability of the feature vectors of the speaker under test with respect to the individual component densities of the universal background model (UBM). Further, the calculation of the sufficient statistics for the weight, mean, and covariance parameters derived from these same feature vectors also contribute a substantial amount of processing load to the SV system. In this paper, we propose a method that utilizes clusters of GMM-UBM mixture component densities in order to reduce the computational load required. In the adaptation step we score the feature vectors against the clusters and calculate the a posteriori probabilities and update the statistics exclusively for mixture components belonging to appropriate clusters. Each cluster is a grouping of multivariate normal distributions and is modeled by a single multivariate distribution. As such, the set of multivariate normal distributions representing the different clusters also form a GMM. This GMM is referred to as a hash GMM which can be considered to a lower resolution representation of the GMM-UBM. The mapping that associates the components of the hash GMM with components of the original GMM-UBM is referred to as a shortlist. This research investigates various methods of clustering the components of the GMM-UBM and forming hash GMMs. Of five different methods that are presented one method, Gaussian mixture reduction as proposed by Runnall's, easily outperformed the other methods. This method of Gaussian reduction iteratively reduces the size of a GMM by successively merging pairs of component densities. Pairs are selected for merger by using a Kullback-Leibler based metric. Using Runnal's method of reduction, we were able
Statistical assessment of non-Gaussian diffusion models.
Kristoffersen, Anders
2011-12-01
In human brain diffusion measurements, there are deviations from monoexponential signal decay at high values of the diffusion-weighting factor b. This is known as non-Gaussian diffusion and can provide novel kinds of image contrast. We evaluated quantitatively the goodness-of-fit of five popular diffusion models. Because of the Rician signal distribution and physiological noise, the measurement errors are unknown. This precludes standard χ(2) testing. By repeating the measurement 25 times, the errors were estimated. Hypothesis testing based on the residual after least squares curve fitting was then carried out. Systematic errors originating from the Rician signal bias were eliminated in the fitting procedure. We performed diffusion measurements on four healthy volunteers with b-values ranging from 0 to 5000 s/mm(2) . The data were analyzed voxelwise. The null hypothesis of a given model being adequate was rejected, if the residual after fitting exceeded a limit that corresponds to a significance level of 1%. The fraction of rejected voxels depended strongly on the number of free model parameters. The rejected fraction was: monoexponential model with two parameters, 94%; statistical model with three parameters, 29%; stretched exponential model with three parameters, 35%; cumulant model with three parameters, 48%; cumulant model with four parameters, 11%; biexponential model with four parameters, 2.9%. Copyright © 2011 Wiley Periodicals, Inc.
Gaussian-Charge Polarizable and Nonpolarizable Models for CO2.
Jiang, Hao; Moultos, Othonas A; Economou, Ioannis G; Panagiotopoulos, Athanassios Z
2016-02-11
A polarizable intermolecular potential model using three classical Drude oscillators on the atomic sites has been developed for CO2. The model is rigid with bond lengths and molecular geometries set to their experimental values. Electrostatic interactions are represented by three Gaussian charges connected to the molecular frame by harmonic springs. Nonelectrostatic interactions are represented by the Buckingham exponential-6 potential, with potential parameters optimized to vapor-liquid equilibria (VLE) data. A nonpolarizable CO2 model that shares the other ingredients of the polarizable model was also developed and optimized to VLE data. Gibbs ensemble Monte Carlo and molecular dynamics simulations were used to evaluate the two models with respect to a variety of thermodynamic and transport properties, including the enthalpy of vaporization, second virial coefficient, density in the one-phase fluid region, isobaric and isochoric heat capacities, radial distribution functions, self-diffusion coefficient, and shear viscosity. Excellent agreement between model predictions and experimental data was found for all properties studied. The polarizable and nonpolarizable models provide a similar representation of CO2 properties, which indicates that the properties of pure CO2 fluid are not strongly affected by polarization. The polarizable model, which has an order of magnitude higher computational cost than the nonpolarizable model, will likely be useful for the study of a mixture of CO2 and polar components for which polarization is important.
Gaussian Process for Activity Modeling and Anomaly Detection
NASA Astrophysics Data System (ADS)
Liao, W.; Rosenhahn, B.; Yang, M. Ying
2015-08-01
Complex activity modeling and identification of anomaly is one of the most interesting and desired capabilities for automated video behavior analysis. A number of different approaches have been proposed in the past to tackle this problem. There are two main challenges for activity modeling and anomaly detection: 1) most existing approaches require sufficient data and supervision for learning; 2) the most interesting abnormal activities arise rarely and are ambiguous among typical activities, i.e. hard to be precisely defined. In this paper, we propose a novel approach to model complex activities and detect anomalies by using non-parametric Gaussian Process (GP) models in a crowded and complicated traffic scene. In comparison with parametric models such as HMM, GP models are nonparametric and have their advantages. Our GP models exploit implicit spatial-temporal dependence among local activity patterns. The learned GP regression models give a probabilistic prediction of regional activities at next time interval based on observations at present. An anomaly will be detected by comparing the actual observations with the prediction at real time. We verify the effectiveness and robustness of the proposed model on the QMUL Junction Dataset. Furthermore, we provide a publicly available manually labeled ground truth of this data set.
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.
Thermodynamical Limit for Correlated Gaussian Random Energy Models
NASA Astrophysics Data System (ADS)
Contucci, P.; Esposti, M. Degli; Giardinà, C.; Graffi, S.
Let {EΣ(N)}ΣΣN be a family of |ΣN|=2N centered unit Gaussian random variables defined by the covariance matrix CN of elements cN(Σ,τ):=Av(EΣ(N)Eτ(N)) and the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition N=N1+N2, and all pairs (Σ,τ)ΣN×ΣN:
NASA Astrophysics Data System (ADS)
Hertog, Maarten L. A. T. M.; Scheerlinck, Nico; Nicolaï, Bart M.
2009-01-01
When modelling the behaviour of horticultural products, demonstrating large sources of biological variation, we often run into the issue of non-Gaussian distributed model parameters. This work presents an algorithm to reproduce such correlated non-Gaussian model parameters for use with Monte Carlo simulations. The algorithm works around the problem of non-Gaussian distributions by transforming the observed non-Gaussian probability distributions using a proposed SKN-distribution function before applying the covariance decomposition algorithm to generate Gaussian random co-varying parameter sets. The proposed SKN-distribution function is based on the standard Gaussian distribution function and can exhibit different degrees of both skewness and kurtosis. This technique is demonstrated using a case study on modelling the ripening of tomato fruit evaluating the propagation of biological variation with time.
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing; Cheng, Qi; Zhang, Dan
2016-06-10
The analytical formulas for the orbital angular momentum (OAM) mode probability density, signal OAM mode detection probability, and spiral spectrum of partially coherent Laguerre-Gaussian (LG) beams with optical vortices propagation in weak horizontal oceanic turbulent channels were developed, based on the Rytov approximation theory. The effect of oceanic turbulence and beam source parameters on the propagation behavior of the optical vortices carried by partially coherent LG beams was investigated in detail. Our results indicated that optical turbulence in an ocean environment produced a much stronger effect on the optical vortex than that in an atmosphere environment; the effective range of the signal OAM mode of LG beams with a smaller ratio of the mode crosstalk was limited to only several tens of meters in turbulent ocean. The existence of oceanic turbulence evidently induced OAM mode crosstalk and spiral spectrum spread. The effects of oceanic turbulence on the OAM mode detection probability increased with the increase of radial and azimuthal mode orders, oceanic turbulent equivalent temperature structure parameter, and temperature-salinity balance parameter. The spatial partial coherence of the beam source would enhance the effect of turbulent aberrations on the signal OAM mode detection probability, and fully coherent vortex beams provided better performance than partially coherent ones. Increasing wavelength of the vortex beams would help improve the performance of this quantum optical communication system. These results might be of interest for the potential application of optical vortices in practical underwater quantum optical communication among divers, submarines, and sensors in the ocean environment.
Beam modeling and verification of a photon beam multisource model
Ahnesjoe, Anders; Weber, Lars; Murman, Anders; Saxner, Mikael; Thorslund, Ingvar; Traneus, Erik
2005-06-15
Dose calculations for treatment planning of photon beam radiotherapy require a model of the beam to drive the dose calculation models. The beam shaping process involves scattering and filtering that yield radiation components which vary with collimator settings. The necessity to model these components has motivated the development of multisource beam models. We describe and evaluate clinical photon beam modeling based on multisource models, including lateral beam quality variations. The evaluation is based on user data for a pencil kernel algorithm and a point kernel algorithm (collapsed cone) used in the clinical treatment planning systems Helax-TMS and Nucletron-Oncentra. The pencil kernel implementations treat the beam spectrum as lateral invariant while the collapsed cone involves off axis softening of the spectrum. Both algorithms include modeling of head scatter components. The parameters of the beam model are derived from measured beam data in a semiautomatic process called RDH (radiation data handling) that, in sequential steps, minimizes the deviations in calculated dose versus the measured data. The RDH procedure is reviewed and the results of processing data from a large number of treatment units are analyzed for the two dose calculation algorithms. The results for both algorithms are similar, with slightly better results for the collapsed cone implementations. For open beams, 87% of the machines have maximum errors less than 2.5%. For wedged beams the errors were found to increase with increasing wedge angle. Internal, motorized wedges did yield slightly larger errors than external wedges. These results reflect the increased complexity, both experimentally and computationally, when wedges are used compared to open beams.
Comparisons of Non-Gaussian Statistical Models in DNA Methylation Analysis
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
Model-Based Visual Self-localization Using Gaussian Spheres
NASA Astrophysics Data System (ADS)
Gonzalez-Aguirre, David; Asfour, Tamim; Bayro-Corrochano, Eduardo; Dillmann, Ruediger
A novel model-based approach for global self-localization using active stereo vision and density Gaussian spheres is presented. The proposed object recognition components deliver noisy percept subgraphs, which are filtered and fused into an ego-centered reference frame. In subsequent stages, the required vision-to-model associations are extracted by selecting ego-percept subsets in order to prune and match the corresponding world-model subgraph. Ideally, these coupled subgraphs hold necessary information to obtain the model-to-world transformation, i.e., the pose of the robot. However, the estimation of the pose is not robust due to the uncertainties introduced when recovering Euclidean metric from images and during the mapping from the camera to the ego-center. The approach models the uncertainty of the percepts with a radial normal distribution. This formulation allows a closed-form solution which not only derives the maximal density position depicting the optimal ego-center but also ensures the solution even in situations where pure geometric spheres might not intersect.
Bayesian Gaussian Mixture Models for High-Density Genotyping Arrays
Sabatti, Chiara; Lange, Kenneth
2011-01-01
Affymetrix's SNP (single-nucleotide polymorphism) genotyping chips have increased the scope and decreased the cost of gene-mapping studies. Because each SNP is queried by multiple DNA probes, the chips present interesting challenges in genotype calling. Traditional clustering methods distinguish the three genotypes of an SNP fairly well given a large enough sample of unrelated individuals or a training sample of known genotypes. This article describes our attempt to improve genotype calling by constructing Gaussian mixture models with empirically derived priors. The priors stabilize parameter estimation and borrow information collectively gathered on tens of thousands of SNPs. When data from related family members are available, our models capture the correlations in signals between relatives. With these advantages in mind, we apply the models to Affymetrix probe intensity data on 10,000 SNPs gathered on 63 genotyped individuals spread over eight pedigrees. We integrate the genotype-calling model with pedigree analysis and examine a sequence of symmetry hypotheses involving the correlated probe signals. The symmetry hypotheses raise novel mathematical issues of parameterization. Using the Bayesian information criterion, we select the best combination of symmetry assumptions. Compared to Affymetrix's software, our model leads to a reduction in no-calls with little sacrifice in overall calling accuracy. PMID:21572926
Gaussian process dynamical models for multimodal affect recognition.
Garcia, Hernan F; Alvarez, Mauricio A; Orozco, Alvaro A
2016-08-01
Affective computing systems has a great potential in applications for biofeedback systems and cognitive conductual therapies. Here, by analyzing the physiological behavior of a given subject, we can infer the affective state of an emotional process. Since, emotions can be modeled as dynamic manifestations of these signals, a continuous analysis in the valence/arousal space, brings more information of the affective state related to an emotional process. In this paper we propose a method for dynamic affect recognition from multimodal physiological signals. Our model is based on learning a latent space using Gaussian process latent variable models (GP-LVM), which maps high dimensional data (multimodal physiological signals) in a low dimensional latent space. We incorporate the dynamics to the model by learning the latent representation, with associated dynamics. Finally, a support vector classifier is implemented to evaluate the relevance of the latent space features in the affective recognition process. The results show that the proposed method can efficiently model a physiological time-series and recognize with high accuracy an affective process.
Gaussian and Lognormal Models of Hurricane Gust Factors
NASA Technical Reports Server (NTRS)
Merceret, Frank
2009-01-01
A document describes a tool that predicts the likelihood of land-falling tropical storms and hurricanes exceeding specified peak speeds, given the mean wind speed at various heights of up to 500 feet (150 meters) above ground level. Empirical models to calculate mean and standard deviation of the gust factor as a function of height and mean wind speed were developed in Excel based on data from previous hurricanes. Separate models were developed for Gaussian and offset lognormal distributions for the gust factor. Rather than forecasting a single, specific peak wind speed, this tool provides a probability of exceeding a specified value. This probability is provided as a function of height, allowing it to be applied at a height appropriate for tall structures. The user inputs the mean wind speed, height, and operational threshold. The tool produces the probability from each model that the given threshold will be exceeded. This application does have its limits. They were tested only in tropical storm conditions associated with the periphery of hurricanes. Winds of similar speed produced by non-tropical system may have different turbulence dynamics and stability, which may change those winds statistical characteristics. These models were developed along the Central Florida seacoast, and their results may not accurately extrapolate to inland areas, or even to coastal sites that are different from those used to build the models. Although this tool cannot be generalized for use in different environments, its methodology could be applied to those locations to develop a similar tool tuned to local conditions.
Diagnosing non-Gaussianity of forecast and analysis errors in a convective-scale model
NASA Astrophysics Data System (ADS)
Legrand, R.; Michel, Y.; Montmerle, T.
2016-01-01
In numerical weather prediction, the problem of estimating initial conditions with a variational approach is usually based on a Bayesian framework associated with a Gaussianity assumption of the probability density functions of both observations and background errors. In practice, Gaussianity of errors is tied to linearity, in the sense that a nonlinear model will yield non-Gaussian probability density functions. In this context, standard methods relying on Gaussian assumption may perform poorly. This study aims to describe some aspects of non-Gaussianity of forecast and analysis errors in a convective-scale model using a Monte Carlo approach based on an ensemble of data assimilations. For this purpose, an ensemble of 90 members of cycled perturbed assimilations has been run over a highly precipitating case of interest. Non-Gaussianity is measured using the K2 statistics from the D'Agostino test, which is related to the sum of the squares of univariate skewness and kurtosis. Results confirm that specific humidity is the least Gaussian variable according to that measure and also that non-Gaussianity is generally more pronounced in the boundary layer and in cloudy areas. The dynamical control variables used in our data assimilation, namely vorticity and divergence, also show distinct non-Gaussian behaviour. It is shown that while non-Gaussianity increases with forecast lead time, it is efficiently reduced by the data assimilation step especially in areas well covered by observations. Our findings may have implication for the choice of the control variables.
Vegetation Monitoring with Gaussian Processes and Latent Force Models
NASA Astrophysics Data System (ADS)
Camps-Valls, Gustau; Svendsen, Daniel; Martino, Luca; Campos, Manuel; Luengo, David
2017-04-01
Monitoring vegetation by biophysical parameter retrieval from Earth observation data is a challenging problem, where machine learning is currently a key player. Neural networks, kernel methods, and Gaussian Process (GP) regression have excelled in parameter retrieval tasks at both local and global scales. GP regression is based on solid Bayesian statistics, yield efficient and accurate parameter estimates, and provides interesting advantages over competing machine learning approaches such as confidence intervals. However, GP models are hampered by lack of interpretability, that prevented the widespread adoption by a larger community. In this presentation we will summarize some of our latest developments to address this issue. We will review the main characteristics of GPs and their advantages in vegetation monitoring standard applications. Then, three advanced GP models will be introduced. First, we will derive sensitivity maps for the GP predictive function that allows us to obtain feature ranking from the model and to assess the influence of examples in the solution. Second, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated radiative transfer data in a single GP model. The JGP regression provides more sensible confidence intervals for the predictions, respects the physics of the underlying processes, and allows for transferability across time and space. Finally, a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system is presented. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Empirical evidence of the performance of these models will be presented through illustrative examples.
Surrogacy Assessment Using Principal Stratification and a Gaussian Copula Model
Taylor, J.M.G.; Elliott, M.R.
2014-01-01
In clinical trials, a surrogate outcome (S) can be measured before the outcome of interest (T) and may provide early information regarding the treatment (Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin1 developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al..2 PMID:24947559
Surrogacy assessment using principal stratification and a Gaussian copula model.
Conlon, Asc; Taylor, Jmg; Elliott, M R
2017-02-01
In clinical trials, a surrogate outcome ( S) can be measured before the outcome of interest ( T) and may provide early information regarding the treatment ( Z) effect on T. Many methods of surrogacy validation rely on models for the conditional distribution of T given Z and S. However, S is a post-randomization variable, and unobserved, simultaneous predictors of S and T may exist, resulting in a non-causal interpretation. Frangakis and Rubin developed the concept of principal surrogacy, stratifying on the joint distribution of the surrogate marker under treatment and control to assess the association between the causal effects of treatment on the marker and the causal effects of treatment on the clinical outcome. Working within the principal surrogacy framework, we address the scenario of an ordinal categorical variable as a surrogate for a censored failure time true endpoint. A Gaussian copula model is used to model the joint distribution of the potential outcomes of T, given the potential outcomes of S. Because the proposed model cannot be fully identified from the data, we use a Bayesian estimation approach with prior distributions consistent with reasonable assumptions in the surrogacy assessment setting. The method is applied to data from a colorectal cancer clinical trial, previously analyzed by Burzykowski et al.
Segmentation of textured images using a multiresolution Gaussian autoregressive model.
Comer, M L; Delp, E J
1999-01-01
We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. The models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior marginals" (MMPM) estimate, and is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate. Previous multiresolution segmentation techniques have been based on the maximum a posterior (MAP) estimation criterion, which has been shown to be less appropriate for segmentation than the MPM criterion. It is assumed that the number of distinct textures in the observed image is known. The parameters of the MGAR model-the means, prediction coefficients, and prediction error variances of the different textures-are unknown. A modified version of the expectation-maximization (EM) algorithm is used to estimate these parameters. The parameters of the Gibbs distribution for the label pyramid are assumed to be known. Experimental results demonstrating the performance of the algorithm are presented.
Chow, James C L; Markel, Daniel; Jiang, Runqing
2010-09-01
The Gaussian error function was first used and verified in normal tissue complication probability (NTCP) calculation to reduce the dose-volume histogram (DVH) database by replacing the dose-volume bin set with the error function parameters for the differential DVH (dDVH). Seven-beam intensity modulated radiation therapy (IMRT) treatment planning was performed in three patients with small (40 cm3), medium (53 cm3), and large (87 cm3) prostate volume, selected from a group of 20 patients. Rectal dDVH varying with the interfraction prostate motion along the anterior-posterior direction was determined by the treatment planning system (TPS) and modeled by the Gaussian error function model for the three patients. Rectal NTCP was then calculated based on the routine dose-volume bin set of the rectum by the TPS and the error function model. The variations in the rectal NTCP with the prostate motion and volume were studied. For the ranges of prostate motion of 8-2, 4-8, and 4-3 mm along the anterior-posterior direction for the small, medium, and large prostate patient, the rectal NTCP was determined varying in the ranges of 4.6%-4.8%, 4.5%-4.7%, and 4.6%-4.7%, respectively. The deviation of the rectal NTCP calculated by the TPS and the Gaussian error function model was within +/- 0.1%. The Gaussian error function was successfully applied in the NTCP calculation by replacing the dose-volume bin set with the model parameters. This provides an option in the NTCP calculation using a reduced size of dose-volume database. Moreover, the rectal NTCP was found varying in about +/- 0.2% with the interfraction prostate motion along the anterior-posterior direction in the radiation treatment. The dependence of the variation in the rectal NTCP with the interfraction prostate motion on the prostate volume was found to be more significant in the patient with larger prostate.
Chow, James C L; Markel, Daniel; Jiang, Runqing
2010-09-01
The Gaussian error function was first used and verified in normal tissue complication probability (NTCP) calculation to reduce the dose-volume histogram (DVH) database by replacing the dose-volume bin set with the error function parameters for the differential DVH (dDVH). Seven-beam intensity modulated radiation therapy (IMRT) treatment planning was performed in three patients with small(40cm3), medium (53cm3), and large (87cm3) prostate volume, selected from a group of 20 patients. Rectal dDVH varying with the interfraction prostate motion along the anterior-posterior direction was determined by the treatment planning system (TPS) and modeled by the Gaussian error function model for the three patients. Rectal NTCP was then calculated based on the routine dose-volume bin set of the rectum by the TPS and the error function model. The variations in the rectal NTCP with the prostate motion and volume were studied. For the ranges of prostate motion of 8-2, 4-8, and 4-3 mm along the anterior-posterior direction for the small, medium, and large prostate patient, the rectal NTCP was determined varying in the ranges of 4.6%-4.8%, 4.5%-4.7%, and 4.6%-4.7%, respectively. The deviation of the rectal NTCP calculated by the TPS and the Gaussian error function model was within ±0.1%. The Gaussian error function was successfully applied in the NTCP calculation by replacing the dose-volume bin set with the model parameters. This provides an option in the NTCP calculation using a reduced size of dose-volume database. Moreover, the rectal NTCP was found varying in about ±0.2% with the interfraction prostate motion along the anterior-posterior direction in the radiation treatment. The dependence of the variation in the rectal NTCP with the interfraction prostate motion on the prostate volume was found to be more significant in the patient with larger prostate. © 2010 American Association of Physicists in Medicine.
Gupta, Naveen Singh, Arvinder; Singh, Navpreet
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 a 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.
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.
Zhang, Guo-Bo; Chen, Min E-mail: yanyunma@126.com; Luo, Ji; Zeng, Ming; Yuan, Tao; Yu, Ji-Ye; Yu, Lu-Le; Weng, Su-Ming; Ma, Yan-Yun E-mail: yanyunma@126.com; Yu, Tong-Pu; Sheng, Zheng-Ming
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 are 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.
Boyde, Lars; Chalut, Kevin J; Guck, Jochen
2011-03-01
The interaction of a Gaussian laser beam with a particle that is located off axis is a fundamental problem encountered across many scientific fields, including biological physics, chemistry, and medicine. For spherical geometries, generalized Lorenz-Mie theory affords a solution of Maxwell's equations for the scattering from such a particle. The solution can be obtained by expanding the laser fields in terms of vector spherical harmonics (VSHs). However, the computation of the VSH expansion coefficients for off-axis beams has proven challenging. In the present study, we provide a very viable, theoretical framework to efficiently compute the sought-after expansion coefficients with high numerical accuracy. We use the existing theory for the expansion of an on-axis laser beam and employ Cruzan's translation theorems [Q. Appl. Math.20, 33 (1962)] for the VSHs to obtain a description for more general off-axis beams. The expansion coefficients for the off-axis laser beam are presented in an analytical form in terms of an infinite series over the underlying translation coefficients. A direct comparison of the electromagnetic fields of such a beam expansion with the original laser fields and with results obtained using numerical quadratures shows excellent agreement (relative errors are on the order of ≲10(-3). In practice, the analytical approach presented in this study has numerous applications, reaching from multiparticle scattering problems in atmospheric physics and climatology to optical trapping, sorting, and sizing techniques.
Gaussian model-based partitioning using iterated local search.
Brusco, Michael J; Shireman, Emilie; Steinley, Douglas; Brudvig, Susan; Cradit, J Dennis
2017-02-01
The emergence of Gaussian model-based partitioning as a viable alternative to K-means clustering fosters a need for discrete optimization methods that can be efficiently implemented using model-based criteria. A variety of alternative partitioning criteria have been proposed for more general data conditions that permit elliptical clusters, different spatial orientations for the clusters, and unequal cluster sizes. Unfortunately, many of these partitioning criteria are computationally demanding, which makes the multiple-restart (multistart) approach commonly used for K-means partitioning less effective as a heuristic solution strategy. As an alternative, we propose an approach based on iterated local search (ILS), which has proved effective in previous combinatorial data analysis contexts. We compared multistart, ILS and hybrid multistart-ILS procedures for minimizing a very general model-based criterion that assumes no restrictions on cluster size or within-group covariance structure. This comparison, which used 23 data sets from the classification literature, revealed that the ILS and hybrid heuristics generally provided better criterion function values than the multistart approach when all three methods were constrained to the same 10-min time limit. In many instances, these differences in criterion function values reflected profound differences in the partitions obtained.
Bayesian modeling of JET Li-BES for edge electron density profiles using Gaussian processes
NASA Astrophysics Data System (ADS)
Kwak, Sehyun; Svensson, Jakob; Brix, Mathias; Ghim, Young-Chul; JET Contributors Collaboration
2015-11-01
A Bayesian model for the JET lithium beam emission spectroscopy (Li-BES) system has been developed to infer edge electron density profiles. The 26 spatial channels measure emission profiles with ~15 ms temporal resolution and ~1 cm spatial resolution. The lithium I (2p-2s) line radiation in an emission spectrum is calculated using a multi-state model, which expresses collisions between the neutral lithium beam atoms and the plasma particles as a set of differential equations. The emission spectrum is described in the model including photon and electronic noise, spectral line shapes, interference filter curves, and relative calibrations. This spectral modeling gets rid of the need of separate background measurements for calculating the intensity of the line radiation. Gaussian processes are applied to model both emission spectrum and edge electron density profile, and the electron temperature to calculate all the rate coefficients is obtained from the JET high resolution Thomson scattering (HRTS) system. The posterior distributions of the edge electron density profile are explored via the numerical technique and the Markov chain Monte Carlo (MCMC) samplings. See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia.
Nanda, Vikas; Kant, Niti
2014-04-15
Enhanced and early relativistic self-focusing of Hermite-cosh-Gaussian (HChG) beam in the plasmas under density transition has been investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices m=0, 1, and 2. The variation of beam width parameter with normalized propagation distance for m=0, 1, and 2 is reported, and it is observed that strong self-focusing occurs as the HChG beam propagates deeper inside the nonlinear medium as spot size shrinks due to highly dense plasmas and the results are presented graphically. A comparative study between self-focusing of HChG beam in the presence and absence of plasmas density transition is reported. The dependency of beam width parameter on the normalized propagation distance for different values of decentered parameter “b” has also been presented graphically. For m=0 and 1, strong self-focusing is reported for b=1.8, and for m=2 and b=1.8, beam gets diffracted. The results obtained indicate the dependency of the self-focusing of the HChG beam on the selected values of decentered parameter. Moreover, proper selection of decentered parameter results strong self-focusing of HChG beam. Stronger self-focusing of laser beam is observed due to the presence of plasma density transition which might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, etc.
NASA Astrophysics Data System (ADS)
Rodríguez-Marín, Francisco; Anera, Rosario G.; Alarcón, Aixa; Hita, E.; Jiménez, J. R.
2012-04-01
In this work, we propose an adjustment factor to be considered in ablation algorithms used in refractive surgery. This adjustment factor takes into account potential deviations of Lambert-Beer's law and the characteristics of a Gaussian-profile beam. To check whether the adjustment factor deduced is significant for visual function, we applied it to the paraxial Munnerlyn formula and found that it significantly influences the post-surgical corneal radius and p-factor. The use of the adjustment factor can help reduce the discrepancies in corneal shape between the real data and corneal shape expected when applying laser ablation algorithms.
Trapping of a micro-bubble by non-paraxial Gaussian beam: computation using the FDTD method.
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.
Lu,M.; Tennant, D.; Jacobsen, C.
2006-01-01
The width of tilted line patterns, such as are needed when drawing circular structures, is found to vary with the oblique angle when it falls into the sub-50-nm scale in Gaussian e-beam lithography. The authors analysis shows that this orientation dependence of linewidth variation originates from the nonuniformity of discrete primitive filling in Cartesian coordinates. Two correction schemes based on pattern segmentation are proposed. Test exposures of high resolution zone plate patterns show that both two schemes work well; a double-insert scheme is superior in terms of dose distribution uniformity.
NASA Astrophysics Data System (ADS)
Lanning, R. Nicholas; Xiao, Zhihao; Zhang, Mi; Novikova, Irina; Mikhailov, Eugeniy E.; Dowling, Jonathan P.
2017-07-01
We present a general, Gaussian spatial-mode propagation formalism for describing the generation of higher-order multi-spatial-mode beams generated during nonlinear interactions. Furthermore, to implement the theory, we simulate optical angular momentum transfer interactions and show how one can optimize the interaction to reduce the undesired modes. Past theoretical treatments of this problem have often been phenomenological, at best. Here we present an exact solution for the single-pass no-cavity regime, in which the nonlinear interaction is not overly strong. We apply our theory to two experiments, with very good agreement, and give examples of several more configurations, easily tested in the laboratory.
Doerner, Edgardo; Caprile, Paola
2016-09-01
The shape of the radiation source of a linac has a direct impact on the delivered dose distributions, especially in the case of small radiation fields. Traditionally, a single Gaussian source model is used to describe the electron beam hitting the target, although different studies have shown that the shape of the electron source can be better described by a mixed distribution consisting of two Gaussian components. Therefore, this study presents the implementation of a double Gaussian source model into the BEAMnrc Monte Carlo code. The impact of the double Gaussian source model for a 6 MV beam is assessed through the comparison of different dosimetric parameters calculated using a single Gaussian source, previously commissioned, the new double Gaussian source model and measurements, performed with a diode detector in a water phantom. It was found that the new source can be easily implemented into the BEAMnrc code and that it improves the agreement between measurements and simulations for small radiation fields. The impact of the change in source shape becomes less important as the field size increases and for increasing distance of the collimators to the source, as expected. In particular, for radiation fields delivered using stereotactic collimators located at a distance of 59 cm from the source, it was found that the effect of the double Gaussian source on the calculated dose distributions is negligible, even for radiation fields smaller than 5 mm in diameter. Accurate determination of the shape of the radiation source allows us to improve the Monte Carlo modeling of the linac, especially for treatment modalities such as IMRT, were the radiation beams used could be very narrow, becoming more sensitive to the shape of the source. PACS number(s): 87.53.Bn, 87.55.K, 87.56.B-, 87.56.jf.
Sokolov, V I; Marusin, N V; Molchanova, S I; Savelyev, A G; Khaydukov, E V; Panchenko, V Ya
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 depth 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)
Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data.
Ryoo, Ji Hoon; Long, Jeffrey D; Welch, Greg W; Reynolds, Arthur; Swearer, Susan M
2017-01-01
As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM) that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.
Gaussian model of explosive percolation in three and higher dimensions
NASA Astrophysics Data System (ADS)
Schrenk, K. J.; Araújo, N. A. M.; Herrmann, H. J.
2011-10-01
The Gaussian model of discontinuous percolation, recently introduced by Araújo and Herrmann [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.035701 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple cubic lattice, in the thermodynamic limit we report a finite jump of the order parameter J=0.415±0.005. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension dA=2.5±0.2. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with a finite number of clusters at the threshold.
Genetic-based EM algorithm for learning Gaussian mixture models.
Pernkopf, Franz; Bouchaffra, Djamel
2005-08-01
We propose a genetic-based expectation-maximization (GA-EM) algorithm for learning Gaussian mixture models from multivariate data. This algorithm is capable of selecting the number of components of the model using the minimum description length (MDL) criterion. Our approach benefits from the properties of Genetic algorithms (GA) and the EM algorithm by combination of both into a single procedure. The population-based stochastic search of the GA explores the search space more thoroughly than the EM method. Therefore, our algorithm enables escaping from local optimal solutions since the algorithm becomes less sensitive to its initialization. The GA-EM algorithm is elitist which maintains the monotonic convergence property of the EM algorithm. The experiments on simulated and real data show that the GA-EM outperforms the EM method since: 1) We have obtained a better MDL score while using exactly the same termination condition for both algorithms. 2) Our approach identifies the number of components which were used to generate the underlying data more often than the EM algorithm.
Gaussian Process Model for Collision Dynamics of Complex Molecules.
Cui, Jie; Krems, Roman V
2015-08-14
We show that a Gaussian process model can be combined with a small number (of order 100) of scattering calculations to provide a multidimensional dependence of scattering observables on the experimentally controllable parameters (such as the collision energy or temperature) as well as the potential energy surface (PES) parameters. For the case of Ar-C_{6}H_{6} collisions, we show that 200 classical trajectory calculations are sufficient to provide a ten-dimensional hypersurface, giving the dependence of the collision lifetimes on the collision energy, internal temperature, and eight PES parameters. This can be used for solving the inverse scattering problem, for the efficient calculation of thermally averaged observables, for reducing the error of the molecular dynamics calculations by averaging over the PES variations, and for the analysis of the sensitivity of the observables to individual parameters determining the PES. Trained by a combination of classical and quantum calculations, the model provides an accurate description of the quantum scattering cross sections, even near scattering resonances.
Plachenov, A B; Kudashov, V N; Radin, A M
2007-03-31
Explicit formulas are obtained for a resonator with the fundamental mode in the form of a Gaussian beam with complex astigmatism. The formulas describe the parameters of the beam directly in terms of the ray matrix without using the procedure of finding its eigenvectors. An example is considered. (resonators. modes)