Partially polarized Gaussian Schell-model beams
NASA Astrophysics Data System (ADS)
Gori, F.; Santarsiero, M.; Piquero, G.; Borghi, R.; Mondello, A.; Simon, R.
2001-01-01
We consider a class of beams that are both partially polarized and partially coherent from the spatial standpoint. They are characterized by a correlation matrix whose elements have the same form as the mutual intensity of a Gaussian Schell-model beam. We focus our attention on those beams that would appear identical to ordinary Gaussian Schell-model beams in a scalar treatment. After establishing some inequalities that limit the choice of the matrix parameters, we study the main effects of propagation. Starting from the source plane, in which the beam is assumed to be uniformly polarized, we find that in the course of propagation the degree of polarization generally becomes non-uniform across a typical section of the beam. Furthermore, we find that the intensity distribution at the output of an arbitrarily oriented linear polarizer is Gaussian shaped at the source plane whereas it can be quite different at other planes.
Gaussian beam ray-equivalent modeling and optical design.
Herloski, R; Marshall, S; Antos, R
1983-04-15
It is shown that the propagation and transformation of a simply astigmatic Gaussian beam by an optical system with a characteristic ABCD matrix can be modeled by relatively simple equations whose terms consist solely of the heights and slopes of two paraxial rays. These equations are derived from the ABCD law of Gaussian beam transformation. They can be used in conjunction with a conventional automatic optical design program to design and optimize Gaussian beam optical systems. Several design examples are given using the CODE-V optical design package. PMID:18195936
Ultrasonic field modeling for immersed components using Gaussian beam superposition.
Spies, Martin
2007-05-01
The Gaussian beam (GB) superposition approach can be applied to model ultrasound propagation in complex-structured materials and components. In this article, progress made in extending and applying the Gaussian beam superposition technique to model the beam fields generated by transducers with flat and focused rectangular apertures as well as with circular focused apertures is addressed. The refraction of transducer beam fields through curved surfaces is illustrated by calculation results for beam fields generated in curved components during immersion testing. In particular, the following developments are put forward: (i) the use of individually determined sets of GBs to model transducer beam fields with a number of less than ten beams; (ii) the application of the GB representation of rectangular transducers to focusing probes, as well as to the problem of transmission through interfaces; and (iii) computationally efficient transient modeling by superposition of 'temporally limited' GBs. PMID:17335863
a New Mathematical Model for a Propagating Gaussian Beam.
NASA Astrophysics Data System (ADS)
Landesman, Barbara Tehan
A new mathematical model for the fundamental mode of a propagating Gaussian beam is presented. The model is two-fold, consisting of a mathematical expression and a corresponding geometrical representation which interprets the expression in the light of geometrical optics. The mathematical description arises from the (0,0) order of a new family of exact, closed-form solutions to the scalar Helmholtz equation. The family consists of nonseparable functions in the oblate spheroidal coordinate system and can easily be transformed to a different set of solutions in the prolate spheroidal coordinate system, where the (0,0) order is a spherical wave. This transformation consists of two substitutions in the coordinate system parameters and represents a more general method of obtaining a Gaussian beam from a spherical wave than assuming a complex point source on axis. Further, each higher-order member of the family of solutions possesses an amplitude consisting of a finite number of higher-order terms with a zero-order term that is Gaussian. The geometrical interpretation employs the skew -line generator of a hyperboloid of one sheet as a ray-like element on a contour of constant amplitude in the Gaussian beam. The geometrical characteristics of the skew line and the consequences of treating it as a ray are explored in depth. The skew line is ultimately used to build a nonorthogonal coordinate system which allows straight-line propagation of a Gaussian beam in three-dimensional space. Highlights of the research into other methods used to model a propagating Gaussian beam--such as complex rays, complex point sources and complex argument functions --are reviewed and compared with this work.
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. PMID:11393633
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. PMID:27410801
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. PMID:18774152
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.
The subtraction of mutually displaced Gaussian Schell-model beams
NASA Astrophysics Data System (ADS)
de Sande, J. Carlos G.; Santarsiero, Massimo; Piquero, Gemma; Gori, Franco
2015-12-01
Using recently derived results about the difference of two cross-spectral densities, we consider a source whose correlation function is the difference of two mutually displaced Gaussian Schell-model cross-spectral densities. We examine the main features of this new cross-spectral density in terms of coherence and intensity distribution, both across the source plane and after free propagation.
Beam wander of Gaussian-Schell model beams propagating through oceanic turbulence
NASA Astrophysics Data System (ADS)
Wu, Yuqian; Zhang, Yixin; Li, Ye; Hu, Zhengda
2016-07-01
For Gaussian-Schell model beams propagating in the isotropic turbulent ocean, theoretical expression of beam wander is derived based on the extended Huygens-Fresnel principle. The spatial coherence radius of spherical waves propagating in the paraxial channel of turbulent ocean including inner scale is also developed. Our results show that the beam wander decreases with the increasing rate of dissipation of kinetic energy per unit mass of fluid ɛ, but it increases as the increasing of the dissipation rate of temperature variance χt and the relative strength of temperature and salinity fluctuations ϖ. The salinity fluctuation has greater influence on the beam wander than that of temperature fluctuations. The model can be evaluated submarine-to-submarine/ship optical wireless communication performance.
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.
On stochastic complex beam beam interaction models with Gaussian colored noise
NASA Astrophysics Data System (ADS)
Xu, Yong; Zhang, Huiqing; Xu, Wei
2007-10-01
This paper is to continue our study on complex beam-beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam-beam interaction model with random forcing [Physica A 336 (2004) 347-360]. The random noise is taken as the form of exponentially correlated Gaussian colored noise, and the transition probability density function is obtained in terms of a perturbation expansion of the parameter. Then the method of stochastic averaging based on perturbation technique is used to derive a Fokker-Planck equation for the transition probability density function. The solvability condition and the general transforms using the method of characteristics are proposed to obtain the approximate expressions of probability density function to order ε. Also the exact stationary probability density and the first and second moments of the amplitude are obtained, and one can find when the correlation time equals to zero, the result is identical to that derived from the Stratonovich-Khasminskii theorem for the same model under a broad-band excitation in our previous work.
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.
Propagation properties of partially polarized Gaussian Schell-model beams through an astigmatic lens
NASA Astrophysics Data System (ADS)
Pan, Liuzhan; Wang, Beizhan; Lu, Baida
2005-09-01
Based on the beam coherent-polarization (BCP) matrix approach and propagation law of partially coherent beams, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an astigmatic lens are derived, which enables us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through an astigmatic lens within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through an astigmatic lens are presented. A comparison with the aberration-free case is made, and shows that the astigmatism affects the propagation properties of PGSM beams.
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. PMID:26734567
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)
Chen, Xudong; Zhao, Daomu
2016-08-01
A model of electromagnetic rectangular multi-Gaussian Schell-model (ERMGSM) beams is introduced. Its analytic expression for the elements of the cross-spectral density matrix of such beams passing through oceanic turbulence is derived. It is shown that the rectangular shape of the ERMGSM beams holds a small distance on propagation in oceanic turbulence. The spectral density, the degree of coherence and the degree of polarization of ERMGSM beams are also studied in detail. The results will be helpful for underwater communication by using ERMGSM beams.
Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems.
Kochkina, Evgenia; Wanner, Gudrun; Schmelzer, Dennis; Tröbs, Michael; Heinzel, Gerhard
2013-08-20
The paper introduces the complete model of the general astigmatic Gaussian beam as the most general case of the Gaussian beam in the fundamental mode. This includes the laws of propagation, reflection, and refraction as well as the equations for extracting from the complex-valued beam description its real-valued parameters, such as the beam spot radii and the radii of curvature of the wavefront. The suggested model is applicable to the case of an oblique incidence of the beam at any 3D surface that can be approximated by the second-order equation at the point of incidence. Thus it can be used in simulations of a large variety of 3D optical systems. The provided experimental validation of the model shows good agreement with simulations. PMID:24085008
Scintillation reduction in pseudo Multi-Gaussian Schell Model beams in the maritime environment
NASA Astrophysics Data System (ADS)
Nelson, C.; Avramov-Zamurovic, S.; Korotkova, O.; Guth, S.; Malek-Madani, R.
2016-04-01
Irradiance fluctuations of a pseudo Multi-Gaussian Schell Model beam propagating in the maritime environment is explored as a function of spatial light modulator cycling rate and estimated atmospheric turnover rate. Analysis of the data demonstrates a strong negative correlation between the scintillation index of received optical intensity and cycling speed for the estimated atmospheric turnover rate.
Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model.
Jiang, Keli; Han, Xiang'e; Ren, Kuan Fang
2013-08-01
The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder. PMID:24323213
Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams
NASA Astrophysics Data System (ADS)
Cai, Y.; Korotkova, O.
2009-08-01
Electromagnetic Gaussian Schell-model (EGSM) beam with twist phase (i.e., twisted EGSM beam) is introduced as an extension of its scalar version based on the unified theory of coherence and polarization. We show how analytical paraxial propagation formulae of isotropic and anisotropic EGSM beams passing through a general astigmatic ABCD optical system can be modified in the presence of the twist phase. Numerical examples demonstrate that the twist phase affects the spectral density, the state of coherence, and the degree of polarization of EGSM beams on propagation.
NASA Astrophysics Data System (ADS)
Avramov-Zamurovic, S.; Nelson, C.; Guth, S.; Korotkova, O.; Malek-Madani, R.
2016-01-01
We report on experimental generation of Electromagnetic Bessel-Gaussian Schell-Model [EBGSM] beams via incoherent superposition of two mutually orthogonal electric field components, both originated from a laser source, whose phases are spatially modified by two nematic liquid crystal Spatial Light Modulators. The EBGSM beam is then passed through a weakly fluctuating turbulent channel and examined for contrast in its fluctuating intensity. It is demonstrated that after passing through turbulence the electromagnetic beam exhibits reduction in the scintillation index on the order of 50%, as compared with that for an equivalent scalar beam, in strong agreement with recent theoretical predictions.
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. PMID:26974789
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).
Improved Gaussian beam-scattering algorithm.
Lock, J A
1995-01-20
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. PMID:20963151
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.
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.
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.
Modelling Gaussian beam propagation through thick nonlinear refractive and absorptive media
NASA Astrophysics Data System (ADS)
Namarathne, D.; Walden, S.; Shortell, M.; Jaatinen, E.
2016-04-01
A novel numerical finite difference beam propagation method developed for quadratic refractive index media is presented and applied to TEM00 Gaussian beams propagating through nonlinear optical media. The beam's diffraction through the medium was calculated by using the nonlinear Schrodinger equation on small slices which proved to be effective for thick samples. The performance of the model was compared to experimental z-scan observations of colloidal ZnO particles at low cw and high pulsed peak powers at a wavelength of 532 nm. Different optical behaviours were observed in these two power regimes. Negligible nonlinear absorption and refraction were observed at low cw powers, with strong defocusing arising through thermal lensing in the colloidal solution. For the pulsed experiments with peak powers up to 43-kW and 7-ns pulses, values for the intensity-dependent absorption were determined to be β = 1.0 × 10^{ - 10} {text{m/W}} and n_{{2{text{R}}}} = 2.0 × 10^{ - 18} {text{m}}2 /{text{W}}. Despite the very different nonlinear and thermal-optical behaviours in two power regimes, there was good agreement between the model and observations. This demonstrates the effectiveness of the approach in extracting the nonlinear properties of a medium even if it is not optically thin and in the case when a sample displays both strong nonlinear refraction and absorption.
Focusing of truncated Gaussian beams
NASA Astrophysics Data System (ADS)
Horváth, Zoltán L.; Bor, Zsolt
2003-07-01
It is shown that the focusing of truncated Gaussian beams can be treated by the same manner as uniform spherical waves, i.e., the diffraction integral can be expressed by the Lommel functions, which offers a very efficient way for the calculation of the three-dimensional light distribution near focus. All the expressions for the uniform spherical waves hold good for Gaussian beams if the first variable in the Lommel functions is extended to the complex domain. The intensity distribution depending on the Fresnel number and the truncation coefficient is calculated. The location of the first few minima and maxima of the intensity in focal plane is given for different values of the truncation coefficient. The phase behavior depending on the truncation coefficient is studied.
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.
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.
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
2016-03-01
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.
NASA Astrophysics Data System (ADS)
Yuan, Xiao; Pan, Liuzhan; Ding, Chaoliang; Lü, Baida
2008-10-01
Starting from the propagation law of partially coherent light, the on-axis spectral shifts and spectral switches of Gaussian Schell-model (GSM) beams focused by an astigmatic aperture lens are studied. It is shown that, as compared with an aberration-free case whose spectral shifts and spectral switches are induced by spatial correlation and aperture diffraction, the spectral shifts and spectral switches of GSM beams also depend upon the astigmatism of the lens for an astigmatism case. Detailed numerical calculations are made to illustrate the behavior of spectral shifts and spectral switches of GSM beams focused by an astigmatic aperture lens.
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.
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.
Growth of Gaussian instabilities in Gaussian laser beams
Abbi, S.C.; Kothari, N.C.
1980-03-01
We present a theory for the growth of a Gaussian perturbation superimposed on a Gaussian profile laser beam. This theory gives an exponential growth of the perturbation for small distances z traveled inside the nonlinear medium. For larger values of z, the growth is not exponential. The growth parameter ..cap alpha.. is defined and an analytical expression for this parameter is obtained. Our theory gives a smooth matching between the exponential growth of perturbations in a linearized instability theory and the sharp self-focusing thresholds expected for smooth Gaussian profile laser beams propagating in nonlinear media.
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. PMID:19907577
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
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. PMID:27409215
Gaussian-Beam/Physical-Optics Design Of Beam Waveguide
NASA Technical Reports Server (NTRS)
Veruttipong, Watt; Chen, Jacqueline C.; Bathker, Dan A.
1993-01-01
In iterative method of designing wideband beam-waveguide feed for paraboloidal-reflector antenna, Gaussian-beam approximation alternated with more nearly exact physical-optics analysis of diffraction. Includes curved and straight reflectors guiding radiation from feed horn to subreflector. For iterative design calculations, curved mirrors mathematically modeled as thin lenses. Each distance Li is combined length of two straight-line segments intersecting at one of flat mirrors. Method useful for designing beam-waveguide reflectors or mirrors required to have diameters approximately less than 30 wavelengths at one or more intended operating frequencies.
Tilted Gaussian beam propagation in inhomogeneous media.
Hadad, Yakir; Melamed, Timor
2010-08-01
The present work is concerned with applying a ray-centered non-orthogonal coordinate system which is a priori matched to linearly-phased localized aperture field distributions. The resulting beam-waveobjects serve as the building blocks for beam-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave-velocity profile. By applying a rigorous paraxial-asymptotic analysis, a novel parabolic wave equation is obtained and termed "Non-orthogonal domain parabolic equation"--NoDope. Tilted Gaussian beams, which are exact solutions to this equation, match Gaussian aperture distributions over a plane that is tilted with respect to the beam-axes initial directions. A numerical example, which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones, is presented as well. PMID:20686589
Area scintillations of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order
NASA Astrophysics Data System (ADS)
Eyyuboğlu, H. T.
2010-01-01
As an extension of our previous study, the area scintillation aspects of Bessel Gaussian and modified Bessel Gaussian beams of zeroth order are investigated. The analysis is carried out on the basis of equal source sizes and equal source powers. It is found that, when compared on equal source size basis, modified Bessel Gaussian beams always have less area scintillations than a Gaussian beam, while Bessel Gaussian beams exhibit more area scintillations. Comparison on equal source power basis, however, removes the advantage of modified Bessel Gaussian beams, that is, their area scintillations become nearly the same as those of the Gaussian beam. On the other hand, for the case of equal source powers, Bessel Gaussian beams with larger width parameters continue to have higher area scintillations than the Gaussian beam. We provide graphical illustrations for profiles of equal source size beams, equal source power beams and the curves to aid the selection of equal source power beams.
Scintillation characterization for multiple incoherent uplink Gaussian beams
NASA Astrophysics Data System (ADS)
Wu, Wu-Ming; Ning, Yu; Ma, Yan-Xing; Xi, Fen-Jie; Xu, Xiao-Jun
2014-09-01
By means of numerical simulations, we analyze the scintillation characterization for multiple incoherent uplink Gaussian beams under weak fluctuations cases. Because truly independent beams are difficult to create, we present a more general but approximate model for the multiple of beams traveling through partially correlated paths. This model compares with wave-optics simulations and highlights the reduced correlation coefficient as the beam separation is increased. The scintillation index of three and six incoherent uplink Gaussian beams is also induced. The result shows that the scintillation index decreases with the increase of beams amount and beam separation. When the beams amount and strength of atmospheric turbulence are fixed, the reduction of scintillation index is affected by the ratio of beams separation and the Fried length. The corresponding physical mechanisms for the results are discussed.
Wang, Jing; Zhu, Shijun; Wang, Haiyan; Cai, Yangjian; Li, Zhenhua
2016-05-30
Recently, we introduced a new class of radially polarized cosine-Gaussian correlated Schell-model (CGCSM) beams of rectangular symmetry based on the partially coherent electromagnetic theory [Opt. Express23, 33099 (2015)]. In this paper, we extend the work to study the second-order statistics such as the average intensity, the spectral degree of coherence, the spectral degree of polarization and the state of polarization in anisotropic turbulence based on an extended von Karman power spectrum with a non-Kolmogorov power law α and an effective anisotropic parameter. Analytical formulas for the cross-spectral density matrix elements of a radially polarized CGCSM beam in anisotropic turbulence are derived. It is found that the second-order statistics are greatly affected by the source correlation function, and the change in the turbulent statistics induces relatively small effect. The significant effect of anisotropic turbulence on the beam parameters mainly appears nearα=3.1, and decreases with the increase of the anisotropic parameter. Furthermore, the polarization state exhibits self-splitting property and each beamlet evolves into a radially polarized structure in the far field. Our work enriches the classical coherence theory and may be important for free-space optical communications. PMID:27410089
Gaussian beam photothermal single particle microscopy.
Selmke, Markus; Braun, Marco; Cichos, Frank
2012-10-01
We explore the intuitive lensing picture of laser-heated nanoparticles occurring in single particle photothermal (PT) microscopy. The effective focal length of the thermal lens (TL) is derived from a ray-optics treatment and used to transform the probing focused Gaussian beam with ABCD Gaussian matrix optics. The relative PT signal is obtained from the relative beam-waist change far from the TL. The analytical expression is semiquantitative, capable of describing the entire phenomenology of single particle PT microscopy, and shows that the signal is the product of the point-spread functions of the involved lasers times a linear function of the axial coordinate. The presented particularly simple and intuitive Gaussian beam lensing picture compares favorably to the experimental results for 60 nm gold nanoparticles and provides the prescription for optimum setup calibration. PMID:23201674
Fresnel filtering of Gaussian beams in microcavities.
Shinohara, Susumu; Harayama, Takahisa; Fukushima, Takehiro
2011-03-15
We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory. PMID:21403763
Gaussian beam evolution in nonlinear inhomogeneous plasma
NASA Astrophysics Data System (ADS)
Berczynski, P.; Kravtsov, Yu. A.; Tikhonchuk, V.; Tikhonchuk
2014-04-01
The method of nonlinear complex geometrical optics (NCGO) is proposed in this paper for description of the evolution of a spatially narrow Gaussian beam (GB) in an inhomogeneous nonlinear plasma. NCGO method deals with first-order ordinary differential equations for the complex curvature of the wave front and for GB amplitude and for second-order ordinary differential equation for GB width. Thus, NCGO simplifies the description of GB diffraction and self-focusing effects as compared to the known methods of plasma physics and this way it can be assumed to be attractive and comprehensive approach in problems of plasma heating by electromagnetic waves. Moreover, we demonstrate in this paper some regularity for nonlinear inhomogeneous plasma in the framework of which central ray of a GB is not subjected to nonlinear refraction within NCGO method boundary applicability. On the contrary, the beam width, wave front curvature, and GB amplitude are modified by diffraction and self-focusing processes. General properties of the beam propagation are illustrated with results of numerical modeling for two particular cases: GB diffraction and self-focusing along curvilinear trajectory with torsion in axially symmetric plasma column and GB reflection from nonlinear inhomogeneous plasma layer. We prove in this paper that NCGO is new effective method of plasma physics, which can be applied for improvement of ray tracing techniques and plasma diagnostics.
Computational aspects of Gaussian beam migration
Hale, D.
1992-08-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
Computational aspects of Gaussian beam migration
Hale, D.
1992-01-01
The computational efficiency of Gaussian beam migration depends on the solution of two problems: (1) computation of complex-valued beam times and amplitudes in Cartesian (x,z) coordinates, and (2) limiting computations to only those (x,z) coordinates within a region where beam amplitudes are significant. The first problem can be reduced to a particular instance of a class of closest-point problems in computational geometry, for which efficient solutions, such as the Delaunay triangulation, are well known. Delaunay triangulation of sampled points along a ray enables the efficient location of that point on the raypath that is closest to any point (x,z) at which beam times and amplitudes are required. Although Delaunay triangulation provides an efficient solution to this closest point problem, a simpler solution, also presented in this paper, may be sufficient and more easily extended for use in 3-D Gaussian beam migration. The second problem is easily solved by decomposing the subsurface image into a coarse grid of square cells. Within each cell, simple and efficient loops over (x,z) coordinates may be used. Because the region in which beam amplitudes are significant may be difficult to represent with simple loops over (x,z) coordinates, I use recursion to move from cell to cell, until entire region defined by the beam has been covered. Benchmark tests of a computer program implementing these solutions suggest that the cost of Gaussian hewn migration is comparable to that of migration via explicit depth extrapolation in the frequency-space domain. For the data sizes and computer programs tested here, the explicit method was faster. However, as data size was increased, the computation time for Gaussian beam migration grew more slowly than that for the explicit method.
One method to uniformize LD Gaussian beam
NASA Astrophysics Data System (ADS)
Liu, Xu
2001-10-01
The uniformization of Gaussian beam intensity is necessary in many applications. In active night-vision, monitoring targets especially requires this. IR semiconductor laser is widely used in the area because of its low power-consumption and small size. But the effects of the product are restrained due to system output Gaussian beam of ununiform intensity. The essay discusses a former system design and then gives an improved experimental scheme with some exciting results. The previous structure was as follows. High power SQW-LD beam was coupled to a plastic optical fiber (POF) directly, and then output through a lens. With its angle varied, targets ranged from 60 to 100 meters can be monitored. But unfortunately there were interference speckles folded on the target. An experimental system based on the thoughts of fiber transmission and complex filter was designed to improve the distribution of Gaussian beam intensity, with the result that the relatively well-distributed beam was got. Laser wavefront propagated through a very small pinhole whose diameter was 20 micrometers or so. The pinhole acted as an amplitude filter. Then the beam was coupled directly into a multi-mode quartz fiber whose core/cladding layer diameter parameter was 50/125micrometers . It conveyed laser beam about 200 mm. At the end of the fiber, several phase plates stood. Laser beam transmitted through the fiber was then phase-filtered and at last beam-expanded by a lens to illuminate the target. The more plates you used, the more uniform the illuminated picture was on condition the beam intensity was so strong that the CCD device could respond to.
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. PMID:9729853
Migration by the Kirchhoff, slant stack, and Gaussian beam methods
Hale, D.
1992-08-01
Gaussian beam migration offers features that are unmatched by any other single depth migration method. Unfortunately, computer algorithms for Gaussian beam migration are more complicated and difficult to understand that those for most other methods. One way to simplify Gaussian beam migration is to understand how it is related to other methods that may be more familiar. In particular, Gaussian beam migration is similar to Kirchhoff integral migration. It is also similar to the phase-shift (or slant stack) migration method. In a sense, the Gaussian beam approach to depth migration is to combine the best of these more familiar methods to obtain an efficient, robust, and flexible method for seismic imaging.
Migration by the Kirchhoff, slant stack, and Gaussian beam methods
Hale, D.
1992-01-01
Gaussian beam migration offers features that are unmatched by any other single depth migration method. Unfortunately, computer algorithms for Gaussian beam migration are more complicated and difficult to understand that those for most other methods. One way to simplify Gaussian beam migration is to understand how it is related to other methods that may be more familiar. In particular, Gaussian beam migration is similar to Kirchhoff integral migration. It is also similar to the phase-shift (or slant stack) migration method. In a sense, the Gaussian beam approach to depth migration is to combine the best of these more familiar methods to obtain an efficient, robust, and flexible method for seismic imaging.
Gaussian beam decomposition of high frequency wave fields
Tanushev, Nicolay M. Engquist, Bjoern; Tsai, Richard
2009-12-10
In this paper, we present a method of decomposing a highly oscillatory wave field into a sparse superposition of Gaussian beams. The goal is to extract the necessary parameters for a Gaussian beam superposition from this wave field, so that further evolution of the high frequency waves can be computed by the method of Gaussian beams. The methodology is described for R{sup d} with numerical examples for d=2. In the first example, a field generated by an interface reflection of Gaussian beams is decomposed into a superposition of Gaussian beams. The beam parameters are reconstructed to a very high accuracy. The data in the second example is not a superposition of a finite number of Gaussian beams. The wave field to be approximated is generated by a finite difference method for a geometry with two slits. The accuracy in the decomposition increases monotonically with the number of beams.
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
Beam-Beam Simulations with the Gaussian Code TRS
Matter, Regina S.
2000-06-26
The authors have summarized the main features of the beam-beam simulation code TRS and presented two sample applications to the PEP-II collider. The code has been successfully tested against analytic results and against other simulation codes whenever such comparisons are meaningful. The soft-gaussian approximation is believed to represent reliably incoherent beam-beam effects. The code has been used to perform studies for the PEP-II collider. For example, simulated tune scans reveal undesirable operating points due to beam blowup from synchrotron sidebands. The dynamical beta effect, clearly seen in these simulations, also influences the choice of a working point. The code has been used to establish the adequate beam separation at the parasitic collision points [24], and has been applied to the proposed muon collider [25], including the effects from the instability of the muon.
Propagation of Gaussian beams through a modified von Karman phase screen
NASA Astrophysics Data System (ADS)
Whitfield, Erica M.; Banerjee, Partha P.; Haus, Joseph W.
2012-10-01
Gaussian beam propagation through a thin screen and an extended random media has been studied using a beam propagation method. We use the modified von Karman spectrum model to describe the phase screen statistics. The scintillation index is analyzed as a function of the structure constant, phase screen location, the initial width and curvature of the Gaussian beam, etc. The numerical simulations are extended using a pair of Gaussian beams. We examine the interference of the beams and measure the fringe visibility at the target. The results are correlated with the scintillation index.
Optimizing Electromagnetically Induced Transparency Signals with Laguerre-Gaussian Beams
NASA Astrophysics Data System (ADS)
Holtfrerich, Matthew; Akin, Tom; Krzyzewski, Sean; Marino, Alberto; Abraham, Eric
2016-05-01
We have performed electromagnetically induced transparency in ultracold Rubidium atoms using a Laguerre-Gaussian laser mode as the control beam. Laguerre-Gaussian modes are characterized by a ring type transverse intensity profile and carry intrinsic orbital angular momentum. This angular momentum carried by the control beam can be utilized in optical computing applications which is unavailable to the more common Gaussian laser field. Specifically, we use a Laguerre-Gaussian control beam with a Gaussian probe to show that the linewidth of the transmission spectrum can be narrowed when compared to a Gaussian control beam that has the same peak intensity. We present data extending this work to compare control fields in both the Gaussian and Laguerre-Gaussian modes with constant total power. We have made efforts to find the optical overlap that best minimizes the transmission linewidth while also maintaining signal contrast. This was done by changing the waist size of the control beam with respect to the probe. The best results were obtained when the waist of a Laguerre-Gaussian control beam is equal to the waist of the Gaussian probe resulting in narrow linewidth features.
Gaussian beam diffraction in weakly anisotropic inhomogeneous media
NASA Astrophysics Data System (ADS)
Kravtsov, Yu. A.; Berczynski, P.; Bieg, B.
2009-08-01
Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.
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.
Beam wander of J 0- and I 0-Bessel Gaussian beams propagating in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Çil, C. Z.; Eyyuboğlu, H. T.; Baykal, Y.; Korotkova, O.; Cai, Y.
2010-01-01
Root mean square (rms) beam wander of J 0-Bessel Gaussian and I 0-Bessel Gaussian beams, normalized by the rms beam wander of the fundamental Gaussian beam, is evaluated in atmospheric turbulence. Our formulation is based on the first and the second statistical moments obtained from the Rytov series. It is found that after propagating in atmospheric turbulence, the collimated J 0-Bessel Gaussian and the I 0-Bessel Gaussian beams have smaller rms beam wander than that of the Gaussian beam, regardless of the choice of Bessel width parameter. However, the extent of such an advantage depends on the chosen width parameter, Gaussian source size, propagation distance and the wavelength. Focusing at finite distances of the considered beams causes the rms beam wander to decrease sharply at the propagation distances equal to the focusing parameter.
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. PMID:27534506
Sharpness changes of gaussian beams induced by spherically aberrated lenses
NASA Astrophysics Data System (ADS)
Piquero, G.; Mejías, P. M.; Martínez-Herrero, R.
1994-04-01
Sharpness changes of the spatial profile of a gaussian beam induced by spherically aberrated lenses are investigated in terms of the so-called kurtosis parameter. It is shown both theoretically and experimentally that, after a single aberrated lens, it is possible to get flatter and sharper beam intensity distributions than the input gaussian beam depending on the plane where the field is observed. Agreement between analytical and experimental results is discussed.
Scintillation advantages of lowest order Bessel-Gaussian beams
NASA Astrophysics Data System (ADS)
Eyyuboğlu, H. T.; Baykal, Y.; Sermutlu, E.; Cai, Y.
2008-08-01
For a weak turbulence propagation environment, the scintillation index of the lowest order Bessel-Gaussian beams is formulated. Its triple and single integral versions are presented. Numerical evaluations show that at large source sizes and large width parameters, when compared at the same source size, Bessel-Gaussian beams tend to exhibit lower scintillations than the Gaussian beam scintillations. This advantage is lost however for excessively large width parameters and beyond certain propagation lengths. Large width parameters also cause rises and falls in the scintillation index of off-axis positions toward the edges of the received beam. Comparisons against the fundamental Gaussian beam are made on equal source size and equal power basis.
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. PMID:19770925
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.
Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media
NASA Astrophysics Data System (ADS)
Berczynski, Pawel
2012-08-01
The method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.
Diffraction of a Gaussian Beam by a Spherical Obstacle
NASA Technical Reports Server (NTRS)
Lock, James A.; Hovenac, Edward A.
1993-01-01
The Kirchhoff integral for diffraction in the near-forward direction is derived from the exact solution of the electromagnetic boundary value problem of a focused Gaussian laser beam incident on a spherical particle. The diffracted intensity in the vicinity of the particle is computed and the way in which the features of the diffraction pattern depend on the width of the Gaussian beam is commented on.
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.
Single-beam interference from plain Gaussian and OAM wavefronts
NASA Astrophysics Data System (ADS)
Popov, S.; Favier, M.
2016-03-01
We implement an SLM to generate laser beams of variable orbital angular momentum, also referred as Laguerre- Gaussian beams. Input beam polarization takes into account a local birefringence of each pixel of the SLM. We identify the beam polarization eigenstates allowing generate L-G beams of different order via matching variable birefringence of every separate pixels. Zero-order beam passing through the SLM can interact with a generated OAM beam to create an interference pattern. Experimental results demonstrate good agreement with simulations.
Quality changes of gaussian beams propagating through axicons
NASA Astrophysics Data System (ADS)
Piquero, G.; Mejías, P. M.; Martínez-Herrero, R.
1994-02-01
The beam quality parameter of gaussian fields propagating through axicons is investigated. A simple analytical formula is derived for the output quality parameter in terms of the input beam width, refractive index of the axicon material and the angle of the axicon wedge.
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.
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.
Vector treatment of second-harmonic generation produced by tightly focused vignetted Gaussian beams
NASA Astrophysics Data System (ADS)
Asatryan, Ara A.; Sheppard, Colin J. R.; de Sterke, C. Martijn
2004-12-01
We present a fast and accurate method to calculate the vector-field distribution of a focused Gaussian beam. This method is applied to calculate the second harmonic that is generated by such a beam from a sample in the undepleted pump approximation. These calculations can be used to model second-harmonic imaging in an optical microscope with a wide aperture.
Second- and third-harmonic generation with vector Gaussian beams
NASA Astrophysics Data System (ADS)
Carrasco, Silvia; Saleh, Bahaa E. A.; Teich, Malvin C.; Fourkas, John T.
2006-10-01
We consider second-harmonic generation (SHG) and third-harmonic generation (THG) in a nonlinear optical crystal illuminated by a vector Gaussian beam, i.e., a Gaussian beam in which the axial component of the excitation field is considered. This component exhibits twice the Gouy phase shift of the transverse component and vanishes at points on the beam axis. Harmonic generation stemming from this component exhibits a unique dependence on geometrical factors associated with the location and focusing of the beam relative to the location of the crystal. Using the first Born approximation (undepleted fundamental beam), we derive analytical formulas for the quantities that characterize these geometrical factors for a nonlinear optical crystal described by an arbitrary nonlinear susceptibility tensor, for both SHG and THG and for all polarization components. We also determine the efficiencies of these processes as functions of the geometry of the experimental arrangement for phase-matched crystals as well as for crystals of infinite length.
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.
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.
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.
Schaub, S A; Lock, J A; Naqwi, A A
1998-11-20
We present a generalized theoretical model for the response of the phase/Doppler (P/D) measurement system to light scattered by cylindrical fibers. This theoretical model is valid for arbitrary fiber diameters and refractive indices, for Gaussian incident beams, and it accounts for arbitrary fiber orientations, fiber positions, and effects that are due to the two-dimensional receivers. The generalized P/D computer model (GPDCM) is the extension of an earlier study by the authors, combining past P/D simulation methodology with recent developments in modeling light scattering by tilted cylindrical fibers. A fortran computer program that implements the GPDCM theoretical development was written and tested against known P/D results and physical expectations. To illustrate the capabilities of the GPDCM, we present computation results, comparing the effect of fiber tilt, fiber position, and receiver aperture on the performance of P/D systems configured in backscatter and sidescatter arrangements. Calculations show that the effects of fiber tilt and position are most pronounced in the backscatter P/D arrangement, resulting in broadening of the measured phase distribution. The calculated mean phase shifts, however, were found to be essentially independent of the above factors. Computational results also showed that the effect of fiber tilt and position on phase-distribution measurements can be reduced through proper choice of aperture shape and by imposition of threshold criteria on measurable signal characteristics such as the amplitude ratio and visibilities. The GPDCM provides a computational tool that will be valuable in the design, optimization, and evaluation of P/D fiber measurement systems. PMID:18301627
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 χ0. 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.
Beam width evolution of astigmatic hollow Gaussian beams in highly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Yang, Zhen-Feng; Jiang, Xue-Song; Yang, Zhen-Jun; Li, Jian-Xing; Zhang, Shu-Min
We investigate the beam width evolution of astigmatic hollow Gaussian beams propagating in highly nonlocal nonlinear media. The input-power-induced different evolutions of the beam width are illustrated: (i) the beam widths in two transverse directions are compressed or broadened at the same time; (ii) the beam width in one transverse direction keeps invariant, and the other is compressed or broadened; (iii) furthermore, the beam width in one transverse direction is compressed, whereas it in the other transverse direction is broadened.
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).
Revisit on dynamic radiation forces induced by pulsed Gaussian beams.
Wang, Li-Gang; Chai, Hai-Shui
2011-07-18
Motivated by the recent optical trapping experiments using ultra-short pulsed lasers [Opt. Express 18, 7554 (2010); Appl. Opt. 48, G33 (2009)], in this paper we have re-investigated the trapping effects of the pulsed radiation force (PRF), which is induced by a pulsed Gaussian beam acting on a Rayleigh dielectric sphere. Based on our previous model [Opt. Express 15, 10615 (2007)], we have considered the effects arisen from both the transverse and axial PRFs, which lead to the different behaviors of both velocities and displacements of a Rayleigh particle within a pulse duration. Our analysis shows that, for the small-sized Rayleigh particles, when the pulse has the large pulse duration, it might provide the three-dimensional optical trapping; and when the pulse has the short pulse duration, it only provides the two-dimensional optical trapping with the axial movement along the pulse propagation. When the particle is in the vacuum or in the situation with the very weak Brownian motion, the particle can always be trapped stably due to the particle's cumulative momentum transferred from the pulse, and only in this case the trapping effect is independent of pulse duration. Finally, we have predicted that for the large-sized Rayleigh particles, the pulse beam can only provide the two-dimensional optical trap (optical guiding). Our results provide the important information about the trapping mechanism of pulsed tweezers. PMID:21934801
BER of Gaussian beam propagation in non-Kolmogorov turbulent atmosphere on slant path
NASA Astrophysics Data System (ADS)
Yang, Rui-ke; Chen, Yuan; Hou, Jie; Chen, Hui
2013-08-01
The propagation characteristic of a Gaussian beam through turbulent atmosphere have been studied in the past several years. The main advantage of Gaussian beam wave model is that the infinite plant wave and a spherical wave are being included. Non-Kolmogorov spectrum can describe generalized turbulent atmosphere environment. The propagation properties of Gaussian beam propagating through the turbulent atmosphere described by non-Kolmogorov spectrum are studied on slant path. The scintillation index is analyzed with the Gaussian beam of different turbulent strength, zenith angle, φ , and the spectral exponent, α, of non-Kolmogorov, respectively. The effect of the turbulent structure constant on the ground on sicntillation is notable. The scintillation index reduces remarkably with zenith angle and structure parameter decrease. At weak turbulenc, scintillation index increases as spectral exponent decreases. The bit error rate (BER) of a Gaussian beam propagating in non-Kolmogorov atmospheric turbulence channel is estimated on Earth-space slant path. By comparing the effect of the spectral power with the structure constant on BER at moderate and strong turbulence, the effect of the spectral power change on BER is small. With turbulence weakening , at the order of 10-15m-2/3 , the relative effect of the spectral power on BER is gradually increase. Hence, at the small structure constant on the ground, or weak turbulence, the effect of the turbulent spectral power on BER is required to take into account.
Interaction of Airy-Gaussian beams in Kerr media
NASA Astrophysics Data System (ADS)
Peng, Yulian; Peng, Xi; Chen, Bo; Zhou, Meiling; Chen, Chidao; Deng, Dongmei
2016-01-01
We study the interaction of the Airy-Gaussian (AiG) beams by using the numerical simulations with the split-step Fourier method. The results show that the single breathers and breather pairs can be formed in the condition with interaction. The breathers can be formed with the enough intensity of interactive beams. By adjusting the parameters of amplitude, interval, phase and χ0, we find that the interaction of the two beams is the strongest with in-phase and out-of-phase cases, especially in the shorter distance. Moreover, both the interaction intensity and the location, the interaction happens, can be changed by adjusting the distribution factor χ0 of the beams. It is notable that the various propagation directions of the beams can be obtained by changing the phase, at the same situation, when the interval of the two beams becomes narrower, the phase plays an important role of controlling the direction of the accelerated spot.
Spatial properties of coaxial superposition of two coherent Gaussian beams.
Boubaha, Boualem; Naidoo, Darryl; Godin, Thomas; Fromager, Michael; Forbes, Andrew; Aït-Ameur, Kamel
2013-08-10
In this paper, we explore theoretically and experimentally the laser beam shaping ability resulting from the coaxial superposition of two coherent Gaussian beams (GBs). This technique is classified under interferometric laser beam shaping techniques contrasting with the usual ones based on diffraction. The experimental setup does not involve the use of some two-wave interferometer but uses a spatial light modulator for the generation of the necessary interference term. This allows one to avoid the thermal drift occurring in interferometers and gives a total flexibility of the key parameter setting the beam transformation. In particular, we demonstrate the reshaping of a GB into a bottle beam or top-hat beam in the focal plane of a focusing lens. PMID:23938430
Use of complex source points to simplify Gaussian beam synthesis
NASA Astrophysics Data System (ADS)
Forsythe, Stephen
2002-11-01
It is often desirable to generate the acoustic field due to a so-called Gaussian beam. One way to do this is to use the free-space Greens function for the acoustic field and to sum small area sources over a circular plate with the appropriate shading for the desired Gaussian beam. For very high frequencies and narrow beams, the computation time to give an accurate sum can be large when calculating the sum for many points in the acoustic field. An alternate approach comes from the use of a single point source with complex coordinates R=Xr+iXi,Yr+iYi,Zr+iZi. When this complex source point is used in the free-space Greens function, the formal expressions for pressure and particle velocity can be used if careful attention is paid to the interpretation of the complex distance, r, that arises in the exp(ikr)/r. The singularity is no longer a single point in the case of a complex source, but a circular disk. The far field of a complex source point is a good approximation to a Gaussian beam. Several computational uses of the technique will be demonstrated. [Work supported by ONR.
ABCD matrix for weakly apertured Gaussian beams in the far field.
Wang, S; Bernabeu, E; Alda, J
1991-05-01
When a Gaussian beam is weakly diffracted by a circular aperture it can be approximated by another Gaussian beam with slightly different properties in the far field. In this Technical Note, using the relationship between these two Gaussian beams, before and after the aperture, an ABCD matrix is defined for cascaded laser systems. PMID:20700323
NASA Astrophysics Data System (ADS)
Zou, Qihui; Hu, Qianhuan; Guo, Jie; Duan, Xi; Tong, Shihong
2015-10-01
Based on the Fresnel-Kirchhoff diffraction integral and Fourier transform, the propagation equation and its Fourier spectrum for ultra-short chirped pulsed Gaussian beams diffracted by Gaussian aperture are derived in dispersive medium, and the frequency-domain analytical electric field are presented. The effects of relative aperture, transmission distance and chirp parameter on the axial spectral properties are illustrated with numerical calculation results, and the variations of off-axis power spectrum with relative aperture, transmission distance and off-axis radius are given. It is found that the axial power spectrum of ultra-short chirped pulsed Gaussian increases with increasing relative aperture, the axial spectral blue-shift increases and approaches an asymptotic value associated with chirp parameter and propagation distance. The axial spectra of ultra-short chirped pulsed Gaussian become broadened with increasing the absolute value of the chirp parameter. With increasing off-axis radius, the off-axis power spectrum reduce rapidly, and the distribution of spectra shifts to the left. The off-axis spectral redshift increases with increasing off-axis radius.
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.
Gras, S.; Blair, D. G.; Ju, L.
2010-02-15
To reduce the thermal noise in the future generation of gravitational wave detectors, flat-top beams have been proposed to replace conventional Gaussian beams, so as to obtain better averaging over the Brownian motion of the test masses. Here, we present a detailed investigation of the unwanted opto-acoustic interactions in such interferometers, which can lead to the phenomenon of parametric instability. Our results show that the increased overlap of the Mesa beams with the test masses leads to approximately 3 times as many unstable modes in comparison to a similar interferometer with Gaussian beams.
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-01
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. PMID:27607713
Mutual interaction between parallel Gaussian electromagnetic beams in plasmas
Sodha, Mahendra Singh; Agarwal, Sujeet Kumar; Sharma, Ashutosh
2006-10-15
In this paper, the interaction between two Gaussian electromagnetic beams in a plasma has been investigated, when the axes of the two beams are initially (z=0) parallel along the z axis in the x-z plane; the beams are initially propagating in the z direction. For the three types of nonlinearities (viz., collisional, ponderomotive, and relativistic) the dielectric function has been expressed as a function of the irradiances of the two beams; this expression for the dielectric function has been substituted in the wave equation and a solution of the resulting nonlinear equation obtained in the paraxial approximation. The paraxial approximation is justified since the phenomena of interest occur when the beams are initially close ({radical}(2)x{sub 0}{<=}r{sub 0}). Further, the absorption of the beam in the plasma has been neglected, which is justified when the electron collision frequency is much less than the frequencies of the beams. Second-order coupled ordinary differential equations have been obtained for the distance between the centers of the beams and the beam widths in the x and y directions as a function of the distance of propagation along the z axis. The equations have been solved numerically for a range of parameters and a discussion of the results is presented.
Gaussian Mixture Model of Heart Rate Variability
Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario
2012-01-01
Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386
Transmission of a Gaussian beam by a Fizeau interferential wedge.
Stoykova, Elena
2005-12-01
Analysis of transmission of a finite-diameter Gaussian beam by a Fizeau interferential wedge is presented. The fringe calculation is based on angular spectrum expansion of the complex amplitude of the incident wave field. The developed approach is applicable to any beam diameter and wedge thickness at any distance from the wedge and yields as a boundary case the fringes at plane-wave illumination. The spatial region of resonant transmission on the wedge surface is given by the width of the transmitted peak for plane-wave illumination. At higher coating reflectivity, the direction of the transmitted beam is deviated with respect to that of the incident beam. Evaluation of the spectral response based on the spectral width of the transmitted power curve is introduced as more realistic for a correct description of the application of a Fizeau wedge as an interferential selector in laser resonators. PMID:16396037
Light steering of Air-Gaussian beam in Nonlocal Nonlinear Medium
NASA Astrophysics Data System (ADS)
Chen, Ran; Zhang, Xiaping
2016-07-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results show that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Espesically, by tuning the phase difference between the two beams, we can steer the centre of the bound AiG beams in nonlocal nonlinear media.
Bound states of breathing Airy-Gaussian beams in nonlocal nonlinear medium
NASA Astrophysics Data System (ADS)
Zhang, Xiaping
2016-05-01
With a nonlocal model, we investigate the propagation dynamics of a single Airy-Gaussian (AiG) beam and their interaction in one-dimensional condition by means of direct numerical simulations. With the split-step Fourier method, numerical results shows that nonlocality can support periodic intensity distribution of AiG beams leading to the formation of stable bound states. Especially, by tuning the phase difference between the two beams, we can steer the center of the bound AiG beams in nonlocal nonlinear media.
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing
2016-08-01
Rytov theory was employed to establish the transmission model for the optical vortices carried by Bessel-Gaussian (BG) beams in weak anisotropic turbulence based on the generalized anisotropic von Karman spectrum. The influences of asymmetry anisotropic turbulence eddies and source parameters on the signal orbital angular momentum (OAM) mode detection probability of partially coherent BG beams in anisotropic turbulence were discussed. Anisotropic characteristics of the turbulence could enhance the OAM mode transmission performance. The spatial partially coherence of the beam source would increase turbulent aberration's effect on the optical vortices. BG beams could dampen the influences of the turbulence because of their nondiffraction and self-healing characteristics. PMID:27505641
Schimpf, Damian N; Putnam, William P; Grogan, Michael D W; Ramachandran, Siddharth; Kärtner, Franz X
2013-07-29
We derive solutions for radially polarized Bessel-Gauss beams in free-space by superimposing decentered Gaussian beams with differing polarization states. We numerically show that the analytical result is applicable even for large semi-aperture angles, and we experimentally confirm the analytical expression by employing a fiber-based mode-converter. PMID:23938719
Optimal focusing conditions of lenses using Gaussian beams
NASA Astrophysics Data System (ADS)
Franco, Juan Manuel; Cywiak, Moisés; Cywiak, David; Mourad, Idir
2016-07-01
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. 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.
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.
Modelling of sub-wavelength THz sources as Gaussian apertures.
Lin, Hungyen; Fumeaux, Christophe; Fischer, Bernd Michael; Abbott, Derek
2010-08-16
The THz emission point on a nonlinear electro-optical crystal for generating broadband THz radiation is modeled as a radiating Gaussian aperture. With the wavelengths of the infrared pump beam being much smaller than the wavelength components of the generated THz pulse, a THz sub-wavelength radiating aperture with Gaussian profile is effectively created. This paper comprehensively investigates Gaussian apertures in focused THz radiation generation in electro-optical crystals and illustrates the breakdown of the paraxial approximation at low THz frequencies. The findings show that the shape of the radiation pattern causes a reduction in detectable THz radiation and hence contributes significantly to low signal-to-noise ratio in THz radiation generation. Whilst we have demonstrated the findings on optical rectification in this paper, the model may apply without a loss of generality to other types of apertures sources in THz radiation generation. PMID:20721154
Secondary diffraction of diffracted Gaussian beam of laser radiation
NASA Astrophysics Data System (ADS)
Vasil'Ev, Yu. V.; Kozar', A. V.; Matyunin, A. V.
2011-10-01
The diffraction of a narrow Gaussian beam of laser radiation on mutually perpendicular edges of crossed, superimposed sharp wedge-shaped blades (safety razors) has been studied. The diffraction pattern observed on a flat screen behind the blades comprises a very bright central spot, which exhibits the structure of a "light network" with rectangular cells, and four groups of narrow bright bands that expand from the central spot toward the periphery and form a rectangular cross. The spatial frequency of light-field modulation on the screen can be controlled by varying the distance from the blades to screen.
Hermite-Gaussian beams with self-forming spiral phase distribution
NASA Astrophysics Data System (ADS)
Zinchik, Alexander A.; Muzychenko, Yana B.
2014-05-01
Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).
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.
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). PMID:26480441
Optical fibers as beam shapers: from Gaussian beams to optical vortices.
Rodrigues Ribeiro, Rita S; Dahal, Pabitra; Guerreiro, Ariel; Jorge, Pedro; Viegas, Jaime
2016-05-15
This Letter reports a new method for the generation of optical vortices using a micropatterned optical fiber tip. Here, a spiral phase plate (2π phase shift) is micromachined on the tip of an optical fiber using a focused ion beam. This is a high resolution method that allows milling the fibers with nanoscale resolution. The plate acts as a beam tailoring system, transforming the fundamental guided mode, specifically a Gaussian mode, into the Laguerre-Gaussian mode (LG_{01}), which carries orbital angular momentum. The experimental results are supported by computational simulations based on the finite-difference time-domain method. PMID:27176946
Self-trapped elliptical super-Gaussian beam in cubic-quintic media
NASA Astrophysics Data System (ADS)
Jana, Soumendu; Singh, Ajitpal; Porsezian, K.; Mithun, T.
2014-12-01
We find self-trapped propagation of elliptical super-Gaussian beam in cubic-quintic nonlinear media. The soliton beam preserves its shape and size during propagation in Kerr media. Both defocusing and focusing quintic nonlinearities are considered. In a cubic (focusing)-quintic (defocusing) media breather like beam propagation with intriguing beam width oscillation is observed. The influence of beam ellipticity, super-Gaussian nature and quintic nonlinearity on self-trapping has been studied. A formula for critical power for self-focusing has been derived and it readily agrees with the results obtained by variational method. In Kerr and focusing quintic media beam collapse occurs quicker for higher order super-Gaussian beam. The critical power of self-focusing in defocusing (focusing) quintic medium prominently increases (decreases) with increasing strength of quintic nonlinearity. This variation rate is greater for higher order super Gaussian beam. A beam with greater ellipticity requires larger power for self-trapping.
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.
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.
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).
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. PMID:26906582
NASA Astrophysics Data System (ADS)
Xiang, Ning-Jing; Wu, Zhen-Sen; Guo, Qiu-Fen; Wang, Ming-Jun
2015-09-01
The extended Huygens-Fresnel principle is used to develop a formulation for the backscattered intensity enhancement of a Gaussian Schell-model source beam through a weak turbulence. The results are shown that backscattered intensity enhancement factor of the reflected GSM beam is concerned with the coherence length of source, the wavelength, the size of target and wave structure function. In addition, the closed-form expressions can interpret backscattered intensity enhancement of plane and spherical wave scattered from a diffuse target. The results are illustrated by examples and compared with the previous work.
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.
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.
Propagation characteristics of a Gaussian laser beam in plasma with modulated collision frequency
NASA Astrophysics Data System (ADS)
Wang, Ying; Yuan, Chengxun; Zhou, Zhongxiang; Gao, Ruilin; Li, Lei; Du, Yanwei
2012-08-01
The propagation characteristics of a Gaussian laser beam in cold plasma with the electron collision frequency modulated by laser intensity are presented. The nonlinear dynamics of the ponderomotive force, which induce nonlinear self-focusing as opposed to spatial diffraction, are considered. The effective dielectric function of the Drude model and complex eikonal function are adopted in deriving coupled differential equations of the varying laser beam parameters. In the framework of ponderomotive nonlinearity, the frequency of electron collision in plasmas, which is proportional to the spatial electron density, is strongly interrelated with the laser beam propagation characteristics. Hence, the propagation properties of the laser beam and the modulated electron collision frequency distribution in plasma were studied and explained in depth. Employing this self-consistent method, the obtained simulation results approach practical conditions, which is of significance to the study of laser-plasma interactions.
Gaussian beam decomposition of high frequency wave fields using expectation-maximization
Ariel, Gil; Engquist, Bjoern; Tanushev, Nicolay M.; Tsai, Richard
2011-03-20
A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.
Extension of filament propagation in water with Bessel-Gaussian beams
NASA Astrophysics Data System (ADS)
Kaya, G.; Kaya, N.; Sayrac, M.; Boran, Y.; Strohaber, J.; Kolomenskii, A. A.; Amani, M.; Schuessler, H. A.
2016-03-01
We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.
NASA Astrophysics Data System (ADS)
Wagner, F. R.; Melninkaitis, A.; BatavičiutÄ--, G.; Gouldieff, C.; Smalakys, L.; Beaudier, A.; Natoli, J.-Y.
2015-11-01
Damage induced by nanosecond laser in optical materials can often be attributed to the presence of laser damage precursor in the material. The presence of these precursors within dielectric optics can be successfully described by so called distributed defect ensembles. The physical parameters of these precursor presence models can be deduced by fitting experimental laser damage probability data. For a degenerate defect ensemble these parameters are the precursor threshold and the precursor density in the sample. To deduce precursor densities correctly it is essential to consider the real shape of laser beam that often deviates from Gaussian or hat-top models. To address these issues we discuss a new fitting procedure that minimizes significant errors in the deduced model parameters using experimental beam profile images. We suggest two methods: Defining a Gaussian replacement beam or using a numerical approximation of the surface over threshold (SOT) of the real beam. Both methods are discussed at the example of a degenerate damage precursor population but apply to any type of damage precursor population.
Refractive turbulence effects on truncated Gaussian beam heterodyne lidar
NASA Technical Reports Server (NTRS)
Murty, R.
1984-01-01
A monostatic heterodyne lidar performance model is formulated to study the combined effects of beam truncation and refractive turbulence in the weak scintillation regime. The results show that there is a loss of signal power due to beam truncation and coherence loss, but there is also an enhancement of signal power due to log-amplitude covariance in suitable conditions of long paths with weak turbulence.
NASA Astrophysics Data System (ADS)
Berczyński, Paweł; Kravtsov, Yury A.; Żeglinski, Grzegorz
2008-09-01
The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.
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
Closed laser-beam trajectories in plano-spherical resonators with Gaussian apertures
Malyutin, A A
2008-02-28
The closed trajectories of a Gaussian beam in plano-spherical degenerate and nondegenerate resonators with two Gaussian apertures (with two pump regions with the Gaussian distribution of the gain) are described analytically and the existence conditions are found for such trajectories. It was assumed that Gaussian apertures (gain regions) were located in the plane of a flat mirror at equal distances on both sides of the resonator axis and the size of apertures restricted their action by the corresponding half-plane. (beams, resonators)
Extended laser filamentation in air generated by femtosecond annular Gaussian beams
NASA Astrophysics Data System (ADS)
Feng, Z. F.; Li, W.; Yu, C. X.; Liu, X.; Liu, J.; Fu, L. B.
2015-03-01
Extending the longitudinal range of plasma channels produced by femtosecond annular (ring) Gaussian beams in atmosphere is numerically investigated. We find that the length of a stable plasma channel induced by the annular Gaussian beam, comparing with a Gaussian beam under the same initial condition, has a significant improvement, which can be well understood from two aspects. The dynamic complementation caused by the optical system composing of an axicon and a diverging lens can extend the plasma channel greatly, and the special initial transverse distribution of ring-Gaussian pulse leads to pulse splitting and redistribution of the pulse energy before the formation of optical filament. The ultrashort ring-Gaussian beam perhaps offers a new and an efficient route towards the generation of extended optical filament.
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
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.
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.
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.
Shaping the beam profile of an elliptical Gaussian beam by an elliptical phase aperture
NASA Astrophysics Data System (ADS)
Wen, Wei; Wu, Gaofeng; Song, Kehui; Dong, Yiming
2013-03-01
Based on the generalized Collins integral formula, an analytical paraxial propagation formula for an elliptical Gaussian beam (EGB) passing through an astigmatic ABCD optical system with an elliptical phase aperture is derived by use of a tensor method. As an application example, we study the propagation properties of an EGB passing through an elliptical aperture in free space. It is found that the elliptical phase aperture can be used for shaping the beam profile of an EGB, which is useful in many applications, such as free space optical communication and material thermal processing. The elliptical phase aperture induced changes of the propagation factors of an EGB are also analyzed.
A unifying review of linear gaussian models.
Roweis, S; Ghahramani, Z
1999-02-15
Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model. We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models. PMID:9950734
Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma
NASA Astrophysics Data System (ADS)
Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.
2016-07-01
Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.
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. PMID:27140133
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.
Diffractive properties of obstructed vector Laguerre-Gaussian beam under tight focusing condition.
Vyas, Sunil; Niwa, Masato; Kozawa, Yuichi; Sato, Shunichi
2011-07-01
Diffractive and focusing properties of vector Laguerre-Gaussian beams with obstacle are investigated under tight focusing conditions. Using vector diffraction theory, intensity and polarization distributions near the focus at different orthogonal planes are calculated and analyzed for vector Laguerre-Gaussian beams. It is observed that the beam is able to compensate the distortion produced by obstacles when the size of the obstacle is small. The structural changes in the polarization distribution are not the same in different orthogonal planes. The polarization characteristics of the beam show a significant change when the size of the obstacle is large. A comparative study of the focusing and diffractive properties of vector Laguerre-Gaussian and vector Bessel-Gaussian beams has also been performed. PMID:21734737
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : Z^2to{Z}} a probability proportional to {exp(-β {H}(η))}, where {β} is the inverse-temperature and {{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Llog log L}}. The key is a large deviation estimate for the height at the origin in {{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
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.
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
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.
OPTICAL SOLITONS: Excitation of two-dimensional soliton matrices by fundamental Gaussian beams
NASA Astrophysics Data System (ADS)
Borovkova, O. V.; Chuprakov, D. A.; Sukhorukov, Anatolii P.
2005-01-01
The excitation of two-dimensional periodic structures of fields of the first and second radiation harmonics due to the modulation instability of fundamental Gaussian beams is studied in a medium with a quadratic nonlinearity. The distances are found at which soliton matrix structures with a specified period are formed and destroyed. Optical gratings formed due to nonlinear aberration of broad Gaussian beams are considered.
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
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. PMID:26470046
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. PMID:27411135
Propagation properties of quantized Laguerre-Gaussian beams in atmospheric turbulence
NASA Astrophysics Data System (ADS)
Saito, Aya; Tanabe, Ayano; Kurihara, Makoto; Hashimoto, Nobuyuki; Ogawa, Kayo
2016-03-01
Effect of scintillations is serious problems in optical systems which require the atmospheric propagation, the optimization of optical system to minimize the effects of scintillation have been examined using the simulation of propagation in atmospheric turbulence. The analytic studies of scintillation index of LG beams show that LG beams have less scintillation than Gaussian beams. However, in these researches, the diameter of receiving aperture was set as point receiver without considering the effects of aperture averaging, which is phenomenon that reduced scintillations over finite aperture. In this paper, considering size of a receiving aperture, the propagation losses and the scintillation index of LG beams are simulated. Also, for practical applications, propagation properties of "quantized" LG(5,1) beams simulated. As a result of the examination, the propagation losses and the scintillation index of LG beams is smaller than those of Gaussian beams. By applying LG beams for optical wireless communications, it is expected to improve better the effect of scintillations than using Gaussian beams. The result is that the scintillation index of quantized LG beams is equal to those of LG beams, and it suggested that quantized LG beams can be treat the quantized LG beams the same as LG beams.
NASA Astrophysics Data System (ADS)
Ruffato, G.; Carli, M.; Massari, M.; Romanato, F.
2015-03-01
The work of design, fabrication and characterization of spiral phase plates for the generation of Laguerre-Gaussian (LG) beams with non-null radial index is presented. Samples were fabricated by electron beam lithography on polymethylmethacrylate layers over glass substrates. The optical response of these phase optical elements was measured and the purity of the experimental beams was investigated in terms of Laguerre-Gaussian modes contributions. The farfield intensity pattern was compared with theoretical models and numerical simulations, while the expected phase features were confirmed by interferometric analyses. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order Laguerre-Gaussian beams. A novel application consisting in the design of computer-generated holograms encoding information for light beams carrying phase singularities is shown. A numerical code based on iterative Fourier transform algorithm has been developed for the computation of the phase pattern of phase-only diffractive optical element for illumination under LG beams. Numerical analysis and preliminary experimental results confirm the applicability of these devices as high-security optical elements.
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…
Procedures for the measurement of the extinction cross section of one particle using a Gaussian beam
NASA Astrophysics Data System (ADS)
Bosch, Salvador; Sancho-Parramon, Jordi
2016-09-01
Two procedures for the measurement of the extinction cross section (ECS) of one particle using a slightly focused Gaussian beam have been introduced and numerically tested. While the first one relies on previously introduced ideas and has close connection with the optical theorem, the second procedure is new and is mostly related with light measurements where the detector collects much of the energy of the incident beam. Both procedures prove to be valid and somehow complementary up to particle sizes of the order of the beam waist, thus enlarging the capability of simple measurement set-ups based on Gaussian beams for the estimation of the ECS of one particle.
Smirnov, V N; Strokovsky, G A
1993-05-20
The diffraction pattern in the penumbra region from a metallic cylinder of radius p illuminated by a focused Gaussian beam waist of the half-width w approximately rho is experimentally studied. The observed correlation of band structure distortions in the diffraction pattern with calibrated deformations of the Gaussian beam by an opaque obstacle (which is called a label) is considered to be anomalous from the viewpoint of wave (interference) phenomena. The alternative (corpuscular) interpretation of diffracted light distribution, which is represented as a bundle of partially overlapping noninterfering beams propagating in discrete directions and preserving geometric similarity to the disturbed incident beams, is discussed. PMID:20820447
The intensity distribution of hollow Gaussian beams focused by a lens with spherical aberration
NASA Astrophysics Data System (ADS)
Alkelly, Abdu A.; Al-Nadary, H.; Alhijry, Ibraheem A.
2011-01-01
We developed an expression that describes the hollow Gaussian beams (HGBs) passing through a spherically aberrated lens by using the Collins formula. The radial intensity distribution in both spherical aberration SA free lens, lens that exhibits relatively large in both positive spherical aberration PSA, and negative spherical aberration NSA is calculated. Numerical calculations are made and the results show that the PSA and NSA have a strong influence on the intensity distribution especially at the focus. The study showed remarkable results for which there is no hollow Gaussian beam at a large NSA along the optical axis at the focus. In addition, we found that the DSS, and wr of focused hollow Gaussian beams in the focal region depend not only on the beam radius, and beam order; but also on the spherical aberration.
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.
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.
Fiber coupling efficiency for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.
Zhai, Chao; Tan, Liying; Yu, Siyuan; Ma, Jing
2015-06-15
Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidence and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using the method of effective beam parameters and a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the fiber coupling efficiency for a Gaussian-beam wave has been derived for a horizontal path in both weak and strong fluctuation regimes. And then the influence of spectral power law variations on the fiber coupling efficiency has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence. PMID:26193506
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.
On the relaxation of semi-Gaussian and K-V beams to thermal equilibrium
Lund, S.M.; Barnard, J.J.; Miller, J.M.
1995-05-02
A beam propagating in a continuous, linear focusing channel tends to relax to a thermal equilibrium state. We employ nonlinear conservation constraints to theoretically analyze changes in quantities that characterize both an initial semi-Gaussian beam with a matched rms beam envelope and a K-V beam under a relaxation to thermal equilibrium. Results from particle-in-cell simulations are compared to the theoretical predictions.
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. PMID:27140138
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. PMID:27128076
The Gaussian beam mode analysis of off-axis aberrations in long wavelength optical systems
NASA Astrophysics Data System (ADS)
Finn, T. J.; Trappe, N.; Murphy, J. A.; Withington, S.
2008-03-01
An issue of major concern in the design of long wavelength systems is optical aberration or distortion, which can be particularly severe in off-axis systems. Aberrations occur in both lenses and mirrors and in this paper we present a novel method capable of modelling off-axis mirror configurations. Aberrations degrade fundamental receiver coupling coefficients such as aperture efficiency while increasing spillover power losses. For single pixel instruments this will lead to much longer integration times and the possibility of stray light. For imaging arrays the aberrations cause a departure from perfect point imaging by increasing coupling to array detectors located at angles further off the bore sight of the telescope. This paper verifies a matrix-based scheme using Gaussian beam mode analysis (GBMA) for predicting aberrations from off-axis mirrors. The applied technique was originally described in (S. Withington, A. Murphy, G. Isaak, Representation of mirrors in beam waveguides as inclined phase transforming surfaces, Infrared Phys. Tech. 36(3) (1995) 723-734. [1]) and in this paper we exploit the theory and validate the approach with a series of examples using off-axis conic sections. We present the predictions for both a fundamental Gaussian and a scalar horn field illuminating various off-axis mirror configurations including different angles of incidence. A commercially available physical optics (PO) software package, GRASP8™, is used to validate the accuracy of these scalar GBMA predictions.
Gaussian beam in two-photon fluorescence imaging of rat brain microvessel
Shi, Lingyan; Rodríguez-Contreras, Adrián; Alfano, Robert R.
2014-01-01
Abstract. The critical optical properties of a Gaussian laser beam in two-photon or multiphoton fluorescence imaging, including the beam spot size, depth of focus, and intensity profile, are investigated for spatially locating nanoscale solutes in and surrounding the microvessels of rat brain. PMID:25490048
NASA Astrophysics Data System (ADS)
Zhao, Chengliang; Huang, Kaikai; Lu, Xuanhui
2010-03-01
The properties of Bessel-Gaussian beams (BGBs) and Bessel beams (BBs) propagating through a fractional Fourier transform (FRT) optical system have been investigated. The analytical transformation formulae for BBs and BGBs propagation through a FRT optical system are derived based on definition of the FRT in the cylindrical coordinate system. By using the derived formula, numerical examples are illustrated.
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.
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.
Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram
NASA Astrophysics Data System (ADS)
Lu, Yang; Jiang, Bo; Lü, Shuchao; Liu, Yongqi; Li, Shasha; Cao, Zheng; Qi, Xinyuan
2016-03-01
We generate various kinds of arrays of Gaussian vortex, Bessel and Airy beams, respectively, with digital phase holograms (DPH) based on the fractional-Talbot effect by using the phase-only spatial light modulator (SLM). The linear and nonlinear transmissions of these beam arrays in strontium barium niobate (SBN) crystal are investigated numerically and experimentally. Compared with Gaussian vortex arrays, Bessel and Airy beam arrays can keep their patterns unchanged in over 20 mm, realizing non-diffracting transmission. The Fourier spectra (far-field diffraction patterns) of the lattices are also studied. The experimental results are in good agreement with the numerical simulations.
Gaussian Process Modeling of Protein Turnover.
Rahman, Mahbubur; Previs, Stephen F; Kasumov, Takhar; Sadygov, Rovshan G
2016-07-01
We describe a stochastic model to compute in vivo protein turnover rate constants from stable-isotope labeling and high-throughput liquid chromatography-mass spectrometry experiments. We show that the often-used one- and two-compartment nonstochastic models allow explicit solutions from the corresponding stochastic differential equations. The resulting stochastic process is a Gaussian processes with Ornstein-Uhlenbeck covariance matrix. We applied the stochastic model to a large-scale data set from (15)N labeling and compared its performance metrics with those of the nonstochastic curve fitting. The comparison showed that for more than 99% of proteins, the stochastic model produced better fits to the experimental data (based on residual sum of squares). The model was used for extracting protein-decay rate constants from mouse brain (slow turnover) and liver (fast turnover) samples. We found that the most affected (compared to two-exponent curve fitting) results were those for liver proteins. The ratio of the median of degradation rate constants of liver proteins to those of brain proteins increased 4-fold in stochastic modeling compared to the two-exponent fitting. Stochastic modeling predicted stronger differences of protein turnover processes between mouse liver and brain than previously estimated. The model is independent of the labeling isotope. To show this, we also applied the model to protein turnover studied in induced heart failure in rats, in which metabolic labeling was achieved by administering heavy water. No changes in the model were necessary for adapting to heavy-water labeling. The approach has been implemented in a freely available R code. PMID:27229456
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.
The Gouy phase anomaly for harmonic and time-domain paraxial Gaussian beams
NASA Astrophysics Data System (ADS)
Nowack, Robert L.; Kainkaryam, Sribharath M.
2011-02-01
The Gouy phase anomaly resulting from the focusing of wave solutions is illustrated using 2-D paraxial Gaussian beams. For harmonic Gaussian beams, this gives rise to a continuous variation of the Gouy phase as a function of propagation distance. This is in contrast to the discontinuous phase anomaly at caustics for ray solutions. However, as the beam-width of a Gaussian beam at a focus gets smaller, the Gouy phase anomaly becomes more concentrated near the focus and approaches that of the ray solution. The Gouy phase for a harmonic Gaussian beam is first illustrated in a homogeneous medium, and then in a quadratic velocity waveguide where the beam can pass through multiple focus points. However for multiple focus points, care must be taken to ensure that the phase remains continuous. Finally, an example is shown of the Gouy phase for a time-domain signal using a Gabor wavelet. This is validated using the finite difference method, and illustrates the progressive phase advance of a time-domain signal modifying the pulse shape with distance. Intuitively, as a wave solution gets `squeezed' at a focus, it `squirts' forward by slightly increasing its apparent speed in the propagation direction and modifying the pulse shape. However, this is a phase advance and not a group or energy advance and does not violate causality. Nonetheless, this could potentially influence the interpretation of travel-times using correlation techniques when using sources that generate beamed signals, for example from transducer sources in the laboratory.
Effects of astigmatic aberration in holographic generation of Laguerre-Gaussian beam
NASA Astrophysics Data System (ADS)
Wada, Atsushi; Miyamoto, Yoko; Ohtani, Takumi; Nishihara, Noboru; Takeda, Mitsuo
2001-05-01
The Laguerre-Gaussian (LG) beam is an optical beam with a phase singularity that propagates along its axis. We have previously reported the fabrication of blazed transmission phase holograms to generate beams with phase singularities. A common problem encountered in the generation of a phase singularity with high charge is that the singularity tends to split into m individual charge 1 singularities, where m is the charge of the original singularity. We have found through numerical simulation that astigmatic aberration can cause a higher-charge phase singularity to split. We have also found that strong astigmatic aberrations make the resulting beam close to a Hermite-Gaussian beam rather than an LG beam. Experimental investigation of these phenomena agree with the numerical simulation.
On the interference of two Gaussian beams and their ABCD matrix representation.
Arain, Muzammil A; Mueller, Guido
2009-10-12
Gaussian beam propagation is well described by the q-parameter and the ABCD matrices. A variety of ABCD matrices are available that represent commonly occurring scenarios/components in optics. One important phenomenon that has not been studied in detail is the interference of two optical beams with different q-parameters undergoing interference. In this paper, we describe the effect of interference of two Gaussian beams. We derive an ABCD matrix for the addition of two beams that takes into account both the amplitude and phase difference between two beams. This ABCD matrix will help greatly in determining the propagation of beams inside complex interferometers and finding the solutions for the coupled cavity Eigenmodes. PMID:20372655
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.
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.
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.
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
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.
Cheng, Mingjian; Guo, Lixin; Zhang, Yixin
2015-12-14
Analytic expression of the receiver-aperture-averaged scintillation index (SI) was derived for Gaussian-beam waves propagating through non-Kolmogorov maritime atmospheric environment by establishing a generalized maritime atmospheric spectrum model. The error performance of an intensity-modulated and direct-detection (IM/DD) free-space optical (FSO) system was investigated using the derived SI and log-normal distribution. The combined effects of non-Kolmogorov power-law exponent, turbulence inner scale, structure parameter, propagation distance, receiver aperture, and wavelength were also evaluated. Results show that inner scale and power-law exponent obviously affect SI. Large wavelength and receiver aperture can mitigate the effects of turbulence. The proposed model can be evaluated ship-to-ship/shore FSO system performance. PMID:26699050
Gaussian Beam Propagation in a Kerr Type Metamaterial Medium Using ABCD Matrix Method
NASA Astrophysics Data System (ADS)
Keshavarz, A.; Naseri, M.
2016-08-01
In this paper, a split step ABCD matrix method is suggested to investigate Gaussian beam propagation in a Kerr type metamaterial medium. This method is based on dividing the medium interval into subsequent steps. Meanwhile, Gaussian beam profile in every step is obtained by finding the ABCD matrix of that particular step, and is used to find the ABCD matrix of the next step. Results of the suggested matrix method have been compared with the results of numerical split-step Fourier method for a Kerr medium, which indicates a good agreement. Then, we use the ABCD matrix to investigate Gaussian beams propagation in a Kerr type metamaterial, which is also in agreement with pervious results by other methods.
NASA Astrophysics Data System (ADS)
Jimenez, Jose Ramón; González Anera, Rosario; Jiménez del Barco, Luis; Hita, Enrique; Pérez-Ocón, Francisco
2005-01-01
We provide a correction factor to be added in ablation algorithms when a Gaussian beam is used in photorefractive laser surgery. This factor, which quantifies the effect of pulse overlapping, depends on beam radius and spot size. We also deduce the expected post-surgical corneal radius and asphericity when considering this factor. Data on 141 eyes operated on LASIK (laser in situ keratomileusis) with a Gaussian profile show that the discrepancy between experimental and expected data on corneal power is significantly lower when using the correction factor. For an effective improvement of post-surgical visual quality, this factor should be applied in ablation algorithms that do not consider the effects of pulse overlapping with a Gaussian beam.
Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system.
Gao, Yan-Qi; Zhu, Bao-Qiang; Liu, Dai-Zhong; Lin, Zun-Qi
2009-10-01
The generalized analytical expression for the propagation of flat-topped multi-Gaussian beams through a misaligned apertured ABCD optical system is derived. Using this analytical expression, the propagation characteristics of flat-topped multi-Gaussian beams through a spatial filter are investigated. The analytical formula of the electric field distribution in the focal plane is also derived for revealing the effects of the misalignment parameters clearly. It is found that different misalignment parameters have different influences on the electric field distributions of the beam focus spot and the output beam characteristics. The intensity distribution of the beam is mainly determined by the misalignment matrix element E, and the phase distribution is affected by the misalignment matrix elements G and E. PMID:19798391
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
On focusing of a ring ripple on a Gaussian electromagnetic beam in a plasma
Misra, Shikha; Mishra, S. K.
2008-09-15
In this communication the authors have investigated the focusing of a ring ripple on a Gaussian electromagnetic beam propagating in a plasma, considering each of the three kinds of basic nonlinearities, namely, ponderomotive, collisional, and relativistic. In this analysis, the electric field profile of the propagating beam is assumed to be composed of the radial electric field distribution of the Gaussian beam as well as that of the ring ripple; a paraxial like approach has been adopted to analyze the characteristics of the propagation. Thus, one considers a unique dielectric function for the beam propagation and a radial field sensitive diffraction term, appropriate to the vicinity of the maximum of the irradiance distribution of the ring ripple. Further, the variation of the phase associated with the beam on account of the r independent terms in the eikonal has also been accounted for.
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
Vacuum electron acceleration driven by a tightly focused radially polarized Gaussian beam.
Dai, Lin; Li, Jian-Xing; Zang, Wei-Ping; Tian, Jian-Guo
2011-05-01
Electron acceleration in vacuum driven by a tightly focused radially polarized Gaussian beam has been studied in detail. Weniger transformation method is used to eliminate the divergence of the radially polarized electromagnetic field derived from the Lax series approach. And, electron dynamics in an intense radially polarized Gaussian beam is analyzed by using the Weniger transformation field. The roles of the initial phase of the electromagnetic field and the injection angle, position and energy of electron in energy gain of electron have been studied in detail. PMID:21643185
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
NASA Astrophysics Data System (ADS)
Wu, Rongrong; Cheng, Kaixuan; Liu, Xiaozhou; Liu, Jiehui; Mao, Yiwei; Gong, Xiufen
2014-10-01
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.
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.
NASA Astrophysics Data System (ADS)
Berczynski, P.
2013-09-01
The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak absorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.
NASA Astrophysics Data System (ADS)
Liu, Jianfeng; Gong, Jinhui; Liu, Kan; Zhang, Xinyu; Xie, Changsheng
2011-11-01
A special software is constructed effectively for reconstructing the fine phase distribution of the diffracted Gaussian laser beams in the terahertz frequency range, according to common diffraction theory. The fine surface microrelief patterns of the elements, which originate from the simple patterns in photomask and further etched onto the surface of {100}- oriented silicon wafer by a low cost and rapid method, are created by the software above according to the phase distribution designed. Being different with the traditional silicon diffractive lenses fabricated by multiple level processes, the elements produced by the method introduced by us can transfer common Gaussian beams into desired images through created fine patterns over the surface of the elements. Two typical type of diffractive elements, which are used to transform common Gaussian laser beams in terahertz frequency into highly focused spot or so-called common focus, and the desired figure of the "umber one", are designed and fabricated. For testing the element, the LASER SIEIR 50 of Coherent Company is used to generate common Gaussian laser beams (the diameter of the beams is 10mm), and the PYROCAM THERE of Spiricon Company is also used to display the images acquired. Experimental results show that the elements can be used to form needed light fields and expected images, respectively.
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. PMID:24180754
Gaussian-Schell analysis of the transverse spatial properties of high-harmonic beams
NASA Astrophysics Data System (ADS)
Lloyd, David T.; O’Keeffe, Kevin; Anderson, Patrick N.; Hooker, Simon M.
2016-07-01
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.
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
2-D Gaussian beam imaging of multicomponent seismic data in anisotropic media
NASA Astrophysics Data System (ADS)
Protasov, M. I.
2015-12-01
An approach for true-amplitude seismic beam imaging of multicomponent seismic data in 2-D anisotropic elastic media is presented and discussed. Here, the recovered true-amplitude function is a scattering potential. This approach is a migration procedure based on the weighted summation of pre-stack data. The true-amplitude weights are computed by applying Gaussian beams (GBs). We shoot a pair of properly chosen GBs with a fixed dip and opening angles from the current imaging point towards an acquisition system. This pair of beams is used to compute a true-amplitude selective image of a rapid velocity variation. The total true-amplitude image is constructed by superimposing selective images computed for a range of available dip angles. The global regularity of the GBs allows one to disregard whether a ray field is regular or irregular. P- and S-wave GBs can be used to handle raw multicomponent data without separating the waves. The use of anisotropic GBs allows one to take into account the anisotropy of the background model.
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
Focusing of Gaussian beam passed under small angle to optical axis of uniaxial crystal
NASA Astrophysics Data System (ADS)
Ivanov, M. O.; Shostka, N. V.
2016-07-01
We showed both experimentally and analytically, the effect of focusing of a Gaussian beam propagated under small angle ϕ with respect to the optical axis of a uniaxial crystal, on the generation of a bottle beam. At ϕ = 0° two foci that correspond to ordinary and extraordinary parts of a beam form a closed 3D structure of a bottle beam. At this point, the beam, in the foci points, has radially and azimuthally aligned polarizations. Increasing the value of ϕ leads to dramatic changes in the intensity and polarization structure of a bottle beam. Starting from the value of ϕ = ±2° the closed 3D symmetric structure of a bottle beam breaks down. At ϕ = ±5° both beams are focused at the same transverse plane, while its polarization evolves to x- and y-linear. With a further increase in angle ϕ two foci ‘switch’ their spatial positions and move further away.
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.
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.
Propagation characteristics of a non-uniformly Hermite-Gaussian correlated beam
NASA Astrophysics Data System (ADS)
Song, Zhenzhen; Liu, Zhengjun; Zhou, Keya; Sun, Qiongge; Liu, Shutian
2016-01-01
We introduce a new kind of partially coherent beam, non-uniformly Hermite-Gaussian correlated beam, by employing a non-uniformly Hermite function to modulate the spectral degree of coherence. The evolution of such scalar beam on propagation in free space and turbulent atmosphere are investigated. It is demonstrated that the spectral intensity distributions exhibit extraordinary propagation characteristics, such as self-focusing and laterally shifted intensity maxima. The position of the maximum intensity and the intensity profile can be controlled by the order of the Hermite function. The results can be useful in free-space optical communications and beam shaping.
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.
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
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)
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.
Synthesis of partially polarized Gaussian Schell-model sources
NASA Astrophysics Data System (ADS)
Piquero, G.; Gori, F.; Romanini, P.; Santarsiero, M.; Borghi, R.; Mondello, A.
2002-07-01
An experimental procedure for the synthesis of a class of partially polarized Gaussian Schell-model sources is proposed. The experimental set-up is based on Mach-Zenhder interferometer. This kind of sources give rise to not only a coherence degree and intensity profile that are both Gaussian but also a Gaussian local degree of polarization in each plane upon free propagation. Measurements of the local degree of polarization and the intensities in the far field are presented. It is shown that from these measurements some characteristic parameters of the source can be obtained.
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.
Low coherence interferometry modelling using combined broadband Gaussian light sources
NASA Astrophysics Data System (ADS)
Jansz, Paul; Wild, Graham; Richardson, Steven; Hinckley, Steven
2012-02-01
Using a Low Coherence Interferometry (LCI) model, a comparison of broadband single-Gaussian and multi-Gaussian light sources has been undertaken. For single-Gaussian sources, the axial resolution improved with source bandwidth, confirming the coherence length relation that resolution for single Gaussian sources improves with increasing spectral bandwidth. However, narrow bandwidth light sources resulted in interferograms with overlapping strata peaks and the loss of individual strata information. For multiple-Gaussian sources with the same bandwidth, spectral side lobes increased, reducing A-scan reliability to show accurate layer information without eliminating the side lobes. The simulations show the conditions needed for resolution of strata information for broadband light sources using both single and multiple Gaussian models. The potential to use the model to study LCI and OCT light sources, optical delays and sample structures can better characterise these LCI and OCT elements. Forecasting misinformation in the interferogram, may allow preliminary corrections. With improvements to the LCI-OCT model, more applications are envisaged.
Gaussian-to-top-hat beam shaping: an overview of parameters, methods, and applications
NASA Astrophysics Data System (ADS)
Homburg, O.; Mitra, T.
2012-02-01
Direct laser patterning of various materials is today widely used in several micro-system production lines like inkjet printing, solar cell technology, flat-panel display production, LEDs, OLEDs, semiconductors and medicine. Typically single-mode solid state lasers and their higher harmonics (e. g. 266, 355, 532 and 1064 nm) are used especially for machining of holes and grooves. The striking advantages of flat top intensity distributions compared to Gaussian beam profiles with respect to the efficiency and quality of these processes were already demonstrated. Here we will give an overview of parameters, methods and applications of Gaussian-to-top-hat beam shaping. The top hat field size can start from about 30 μm with no upper size limitation in the far field of the optics. Beam shaping for various wavelengths were realized with field geometries of squares, rectangles and circles. With LIMO's compact Gaussian-to-top-hat converter an inhomogeneity better than 5% contrast was reached. Special focus is put on the integration of Gaussian-to-top-hat beam shapers in fast scanning systems employing Galvo mirrors and a specially developed f-Theta lens to avoid destruction of the top hat profile within the scan field. Results with a 50x50μm2 top hat size (inhomogeneity down to <10%) in a scan area of 156x156mm² are presented. The minimal distortions of the top hat observed within the scan area make LIMO's compact Gaussian-to-top-hat converter excellently suited for industrial scanning applications, e.g. for the processing of solar panels.
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.
Spin-controlled orbital motion in tightly focused high-order Laguerre-Gaussian beams.
Cao, Yongyin; Zhu, Tongtong; Lv, Haiyi; Ding, Weiqiang
2016-02-22
Spin angular momentum can contribute to both optical force and torque exerted on spheres. Orbit rate of spheres located in tightly focused LG beams with the same azimuthal mode index l is spin-controlled due to spin-orbit coupling. Laguerre-Gaussian beams with high-order azimuthal mode are used here to study the orbit rate of dielectric spheres. Orbit rates of spheres with varying sizes and refravtive indices are investigated as well as optical forces acting on spheres in LG beams with different azimuthal modes. These results would be much helpful to investigation on optical rotation and transfer of spin and orbital angular momentum. PMID:26906996
Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media
NASA Astrophysics Data System (ADS)
Chen, Chidao; Peng, Xi; Chen, Bo; Peng, Yulian; Zhou, Meiling; Yang, Xiangbo; Deng, Dongmei
2016-05-01
We investigate the propagation of an Airy-Gaussian vortex (AiGV) beam in free space and Kerr media. It is interesting to see that the beam will perform self-healing and main lobe focusing both in free space and Kerr media when the vortex locates at the center of the plane. By controlling the number of the topological charge, the beam distribution factor χ 0 and the position of the vortex, we can control the intensity distribution of the AiGV beam in the out plane both in free space and Kerr media. It is found that when the vortex is close to the center of the plane, it has a strong effect on the intensity distribution of the beam. When the beam propagates in the number of the topological charge, the partial collapse will take place even with low initial input power. We find that the main lobe focusing contributes to this partial collapse.
Generating a Bessel-Gaussian beam for the application in optical engineering
Chu, Xiuxiang; Sun, Quan; Wang, Jing; Lü, Pin; Xie, Wenke; Xu, Xiaojun
2015-01-01
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. PMID:26690264
Generating a Bessel-Gaussian beam for the application in optical engineering.
Chu, Xiuxiang; Sun, Quan; Wang, Jing; Lü, Pin; Xie, Wenke; Xu, Xiaojun
2015-01-01
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. PMID:26690264
Automatic image equalization and contrast enhancement using Gaussian mixture modeling.
Celik, Turgay; Tjahjadi, Tardi
2012-01-01
In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The algorithm uses the Gaussian mixture model to model the image gray-level distribution, and the intersection points of the Gaussian components in the model are used to partition the dynamic range of the image into input gray-level intervals. The contrast equalized image is generated by transforming the pixels' gray levels in each input interval to the appropriate output gray-level interval according to the dominant Gaussian component and the cumulative distribution function of the input interval. To take account of the hypothesis that homogeneous regions in the image represent homogeneous silences (or set of Gaussian components) in the image histogram, the Gaussian components with small variances are weighted with smaller values than the Gaussian components with larger variances, and the gray-level distribution is also used to weight the components in the mapping of the input interval to the output interval. Experimental results show that the proposed algorithm produces better or comparable enhanced images than several state-of-the-art algorithms. Unlike the other algorithms, the proposed algorithm is free of parameter setting for a given dynamic range of the enhanced image and can be applied to a wide range of image types. PMID:21775265
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.
Strong terahertz generation by optical rectification of a super-Gaussian laser beam
NASA Astrophysics Data System (ADS)
Kumar, Subodh; Kishor Singh, Ram; Sharma, R. P.
2016-06-01
Terahertz (THz) generation by optical rectification of a laser beam having spatially super-Gaussian and temporally Gaussian intensity profile is investigated when it is propagating in a pre-formed rippled density plasma. The quasi-static ponderomotive force which is generated due to the variation in intensity of laser pulse leads to a nonlinear current density in the direction transverse to the direction of propagation which drives a radiation. The frequency of this radiation falls in the THz range if the pulse duration of the laser is chosen suitably. The density ripple provides the phase matching. The yield of generated THz has been compared when the phase matching is exact and when there is slight mismatch of phases. The variation in the intensity of the generated THz with the index of super-Gaussian pulse has also been studied.
Investigation of Anderson localization in disordered heterostructures irradiated by a Gaussian beam
NASA Astrophysics Data System (ADS)
Ardakani, Abbas Ghasempour
2016-02-01
The propagation of a Gaussian beam through a one-dimensional disordered media is studied. By employing the transfer matrix method, the localization length as a function of frequency is calculated for different values of transverse coordinate r. It is demonstrated that the localization length significantly depends on r in different frequency ranges. This result is in contrast to those reported for a plane wave incident on disordered structures in which the localization length is transversely constant. For some frequency regions, the peak of localization length is red-shifted and becomes smaller with increasing the transverse coordinate. At some frequencies, the system is in the localized state for particular values of r, while at other r values the system is in the extend regime at the same frequencies. It is observed that the quality of localization at each frequency depends on r. To quantify the localization behavior of the whole Gaussian beam, a modified localization length is defined in terms of the input and output powers of the Gaussian beam where the dependence of Anderson localization on the transverse coordinate is considered. It is suggested that this modified localization length is used in experiments performed for study of wave propagation in one-dimensional random media under illumination of laser beams.
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.
Design and analysis of diffractive optical elements for flattening of single modal Gaussian beams
NASA Astrophysics Data System (ADS)
Yin, Kewei; Huang, Zhiqiang; Lin, Wumei; Xing, Tingwen
2012-10-01
A design method of diffractive optical element is presented for converting a single modal Gaussian beam into a flat-top beam in the far field of the source. The design is based on geometrical method and modified Gerchberg-Saxton method. Geometrical method derives from the conservation of energy and the constant optical path length. This method could supply initial phase distribution of the modified Gerchberg-Saxton method. To find the optimization design results, the modified Gerchberg-Saxton method is important to choose the feedback factor to increase the convergent speed. In addition, tolerances and limitations of such elements result in a reduction of the diffraction efficiency and as a result of stray light. Further study indicates that deviation of the laser wavelength, incident beam, and observation plane can greatly influence flat-top beam shaping quality. On the basis of theoretical and experimental results, limitations for the application of diffractive beam shaping elements are investigated.
Geometrical representation of Gaussian beams propagating through complex paraxial optical systems.
Andrews, L C; Miller, W B; Ricklin, J C
1993-10-20
Geometric relations are used to study the propagation environment of a Gaussian beam wave propagating through a complex paraxial optical system characterized by an ABCD ray matrix in two naturally linked complex planes. In the plane defined by beam transmitter parameters Ω(o) and Ω, the propagation path is described by a ray line similar to the ray line in the y? diagram method, whereas the path in the plane of beam receiver parameters θ and Λ is described by a circular arc. In either plane the amplitude, phase, spot size, and radius of curvature of the Gaussian beam are directly related to the modulus and argument of the complex number designating a particular transverse plane along the propagation path. These beam parameters also lead to simple geometric relations for locating the beam waist, Rayleigh range, focal plane, and sister planes, which share the same radius of curvature but have opposite signs. Combined with the paraxial wave propagation technique based on a Huygens-Fresnel integral and complex ABCD ay matrices, this geometric approach provides a new and powerful method for the analysis and design of laser systems. PMID:20856413
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. PMID:23842364
Log-amplitude variance for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.
Tan, Liying; Du, Wenhe; Ma, Jing; Yu, Siyuan; Han, Qiqi
2010-01-18
In the past decades, both the increasing experimental evidences 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, using 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 log-amplitude variances for a Gaussian-beam wave are derived in the weak-fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the effect of spectral power-law variations on the log-amplitude fluctuations of Gaussian-beam wave. PMID:20173865
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.
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. PMID:23481721
Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis
2013-02-01
Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented. PMID:23385926
The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise
NASA Astrophysics Data System (ADS)
Guo, Qin; Sun, Zhongkui; Xu, Wei
2016-05-01
The anti-tumor model with correlation between multiplicative non-Gaussian noise and additive Gaussian-colored noise has been investigated in this paper. The behaviors of the stationary probability distribution demonstrate that the multiplicative non-Gaussian noise plays a dual role in the development of tumor and an appropriate additive Gaussian colored noise can lead to a minimum of the mean value of tumor cell population. The mean first passage time is calculated to quantify the effects of noises on the transition time of tumors between the stable states. An increase in both the non-Gaussian noise intensity and the departure from the Gaussian noise can accelerate the transition from the disease state to the healthy state. On the contrary, an increase in cross-correlated degree will slow down the transition. Moreover, the correlation time can enhance the stability of the disease state.
Light scattering of a Laguerre-Gaussian vortex beam by a chiral sphere.
Qu, Tan; Wu, Zhen-Sen; Shang, Qing-Chao; Li, Zheng-Jun
2016-04-01
Since the development of the generalized Lorenz-Mie theory, electromagnetic scattering by arbitrary beams has drawn growing interest. The Laguerre-Gaussian (LG) vortex beam is well known for its orbital angular momentum. With the aim of investigating the analytical solution to the scattering of a chiral sphere by a LG vortex beam, particular attention is paid to the expansion expression of the LG vortex beam. The expansion coefficients are derived based on the expansion of a Hermite Guassian beam as the LG vortex beam can be expressed as the superposition of Hermite Guassian modes. The numerical results of the incident beam expansion coefficients convergence and the scattered field comparison with the reference prove the validity of the theoretical analysis and computation codes. The results reveal that there exists an optimal sphere size for the maximum scattered field which is determined by the topological charge, beam waist radius, and beam center position. The investigation could provide a foundation for the optical manipulation of chiral particles by a LG vortex beam. PMID:27140753
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.
Chen, Chunyi; Yang, Huamin; Tong, Shoufeng; Lou, Yan
2016-04-01
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. PMID:27136990
Gaussian beam diffraction in inhomogeneous media: solution in frame of complex geometrical optics
NASA Astrophysics Data System (ADS)
Kravtsov, Yu. A.; Berczynski, P.
2005-09-01
The method of paraxial complex geometrical optics is presented to describe Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like media. The method modifies and specifies the results by Babic' (1968), Kirpichnikova (1971), Cerveny, Popov, Psencik (1982), Cerveny (1983, 2001), Timofeev (1995) and Pereverzev (1996) as applied to the optical problems. The method of paraxial complex geometrical optics reduces the problem of Gaussian beam diffraction in inhomogeneous media to the solution of the system of the ordinary differential equations of first order, which can be readily calculated numerically by the Runge-Kutta method. Thereby the paraxial complex geometrical optics radically simplifies description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. By the way of example the known analytical solution for Gaussianbeam diffraction both in a free space and in lens-like medium (Bornatici, Maj 2003) are presented. It is pointed out, that the method of paraxial complex geometrical optics turns out to be equivalent to the solutions of the abridged parabolic wave equation.
Demonstration of CNOT gate with Laguerre Gaussian beams via four-wave mixing in atom vapor.
Cao, Mingtao; Yu, Ya; Zhang, Liyun; Ye, Fengjuan; Wang, Yunlong; Wei, Dong; Zhang, Pei; Guo, Wenge; Zhang, Shougang; Gao, Hong; Li, Fuli
2014-08-25
We present an experimental study of controlled-NOT (CNOT) gate through four-wave mixing (FWM) process in a Rubidium vapor cell. A degenerate FWM process in a two level atomic system is directly excited by a single diode laser, where backward pump beam and probe beam are Laguerre Gaussian mode. By means of photons carrying orbital angular momentum, we demonstrate the ability to realize CNOT gate with topological charges transformation in this nonlinear process. The fidelity of CNOT gate for a superposition state with different topological charge reaches about 97% in our experiment. PMID:25321227
Kaur, Sukhdeep; Sharma, A. K.; Salih, Hyder A.
2009-04-15
Second harmonic generation of a right circularly polarized Gaussian electromagnetic beam in a magnetized plasma is investigated. The beam causes Ohmic heating of electrons and subsequent redistribution of the plasma, leading to self-defocusing. The radial density gradient, in conjunction with the oscillatory electron velocity, produces density oscillation at the wave frequency. The density oscillation beats with the oscillatory velocity to produce second harmonic current density, giving rise to resonant second harmonic radiation when the wave frequency is one-third of electron cyclotron frequency. The second harmonic field has azimuthal dependence as exp(i{theta}). The self-defocusing causes a reduction in the efficiency of harmonic generation.
NASA Astrophysics Data System (ADS)
Stilgoe, Alexander B.; Nieminen, Timo A.; Rubinsztein-Dunlop, Halina
2015-12-01
Non-paraxial theories of wave propagation are essential to model the interaction of highly focused light with matter. Here we investigate the energy, momentum and propagation of the Laguerre-, Hermite- and Ince-Gaussian solutions (LG, HG, and IG) of the paraxial wave equation in an apertured non-paraxial regime. We investigate the far-field relationships between the LG, HG, and IG solutions and the vector spherical wave function (VSWF) solutions of the vector Helmholtz wave equation. We investigate the convergence of the VSWF and the various Gaussian solutions in the presence of an aperture. Finally, we investigate the differences in linear and angular momentum evaluated in the paraxial and non-paraxial regimes. The non-paraxial model we develop can be applied to calculations of the focusing of high-order Gaussian modes in high-resolution microscopes. We find that the addition of an aperture in high numerical aperture optical systems does not greatly affect far-field properties except when the beam is significantly clipped by an aperture. Diffraction from apertures causes large distortions in the near-field and will influence light-matter interactions. The method is not limited to a particular solution of the paraxial wave equation. Our model is constructed in a formalism that is commonly used in scattering calculations. It is thus applicable to optical trapping and other optical investigations of matter.
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. PMID:27409428
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.
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.
Yuan, Qiong-kun; Wu, Zhen-sen; Li, Zheng-jun
2010-06-01
An analytical solution to the scattering of an off-axis Gaussian beam obliquely incident on a uniaxial anisotropic sphere is obtained in the particle-centered system. Based on the local approximation to the off-axis beam shape coefficients and the coordinate rotation theory, the off-axis obliquely incident Gaussian beam is expanded with the spherical vector wave functions in the primary coordinate of the uniaxial anisotropic sphere. The internal fields of the uniaxial anisotropic sphere are proposed in the integrating form of the spherical vector wave functions by introducing the Fourier transform. By matching the fields on the boundary and solving matrix equations, the expansion coefficients are analytically derived. The influences of the beam waist center positioning and the obliquely incident angles, as well as the permittivity tensors on the far scattered field distributions, are numerically presented. The correctness of the theory is verified by comparing our numerical results in special cases with results from the references and with calculations by other algorithms. PMID:20508716
Bayesian Gaussian Copula Factor Models for Mixed Data
Murray, Jared S.; Dunson, David B.; Carin, Lawrence; Lucas, Joseph E.
2013-01-01
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The models in this paper are implemented in the R package bfa.1 PMID:23990691
Gaussian modelling and Schmidt modes of SPDC biphoton states
NASA Astrophysics Data System (ADS)
Fedorov, M. V.; Mikhailova, Yu M.; Volkov, P. A.
2009-09-01
A double-Gaussian model and the Schmidt modes are found for the biphoton wavefunction characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses: short, long and intermediately long.
Robust Gaussian Graphical Modeling via l1 Penalization
Sun, Hokeun; Li, Hongzhe
2012-01-01
Summary Gaussian graphical models have been widely used as an effective method for studying the conditional independency structure among genes and for constructing genetic networks. However, gene expression data typically have heavier tails or more outlying observations than the standard Gaussian distribution. Such outliers in gene expression data can lead to wrong inference on the dependency structure among the genes. We propose a l1 penalized estimation procedure for the sparse Gaussian graphical models that is robustified against possible outliers. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its own likelihood. An efficient computational algorithm based on the coordinate gradient descent method is developed to obtain the minimizer of the negative penalized robustified-likelihood, where nonzero elements of the concentration matrix represents the graphical links among the genes. After the graphical structure is obtained, we re-estimate the positive definite concentration matrix using an iterative proportional fitting algorithm. Through simulations, we demonstrate that the proposed robust method performs much better than the graphical Lasso for the Gaussian graphical models in terms of both graph structure selection and estimation when outliers are present. We apply the robust estimation procedure to an analysis of yeast gene expression data and show that the resulting graph has better biological interpretation than that obtained from the graphical Lasso. PMID:23020775
Optical trapping by Laguerre-Gaussian beams: Far-field matching, equilibria, and dynamics
NASA Astrophysics Data System (ADS)
Kiselev, Alexei D.; Plutenko, Dmytro O.
2016-07-01
By using the method of far-field matching we obtain the far-field expressions for the optical (radiation) force exerted by Laguerre-Gaussian (LG) light beams on a spherical (Mie) particle and study the optical-force-induced dynamics of the scatterer near the trapping points represented by the equilibrium (zero-force) positions. The regimes of linearized dynamics are described in terms of the stiffness matrix spectrum and the damping constant of the ambient medium. Numerical analysis is performed for both nonvortex and optical-vortex LG beams. For the purely azimuthal LG beams, the dynamics is found to be locally nonconservative and is characterized by the presence of conditionally stable equilibria (unstable zero-force points that can be stabilized by the ambient damping). We also discuss effects related to the Mie resonances (maxima of the internal field Mie coefficients) that under certain conditions manifest themselves as the points changing the trapping properties of the particles.
Scattering of an anisotropic sphere by an arbitrarily incident Hermite-Gaussian beam
NASA Astrophysics Data System (ADS)
Qu, Tan; Wu, Zhensen; Shang, Qingchao; Li, Zhengjun; Bai, Lu; Li, Haiying
2016-02-01
An analytic theory for the scattering of an off-axis Hermite-Gaussian (HG) beam obliquely incident on an anisotropic sphere is developed. Based on the complex-source-point method and coordinate rotation theory, a general expansion expression for an arbitrarily incident HG beam in terms of Spherical Vector Wave Functions (SVWFs) is derived, and its convergence is numerically discussed. By introducing the Fourier transformation, the internal field expressions of the anisotropic sphere are represented. With the continuous tangential boundary conditions applied, the unknown scattering coefficients are solved. The theory and code are verified from the comparisons between the degenerated cases using our theory and those in the references. Two eigenmodes inside the uniaxial anisotropic sphere are characterized. The influences of beam mode, oblique incident angles, permittivity and permeability tensors, and sphere radius on the scattered field are analyzed numerically. The scattering intensity distributions on uniaxial anisotropic sphere in xoz and yoz plane are enantiomorphous for on-axis oblique illumination.
NASA Astrophysics Data System (ADS)
Guo, Jianjun; Guo, Banghong; Fan, Ronghua; Zhang, Wenjie; Wang, Yu; Zhang, Litao; Zhang, Panpan
2016-03-01
We demonstrate, theoretically and experimentally, a new method to measure high-order topological charges (TCs) of Laguerre-Gaussian vortex beams, including the magnitude and the sign, by analyzing the interference intensity patterns. The magnitude is determined by analyzing the interference intensity patterns between the vortex beam and its conjugate beam, and using an improved Mach-Zehnder interferometer with a dove prism. Counting the number of interference bright petals attests to the magnitude of high-order TCs through half of the bright petal number. After the TC is modulated by a spiral phase plate, the sign is acquired by comparing the counting results of two charge-coupled devices. Just by this method, we have been able to measure both the magnitude and the sign of the TCs up to l=±90. Our experimental results are in good agreement with the numerical simulations.
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. PMID:27505642
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.
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.
A Model for Gaussian Perturbations of Graphene
NASA Astrophysics Data System (ADS)
Dodson, C. T. J.
2015-11-01
Graphene consists nominally of a regular planar hexagonal carbon lattice monolayer. However, its structure experiences perturbations in the presence of external influences, whether from substrate properties, thermal or electromagnetic fields, or ambient fluid movement. Here we give an information geometric model to represent the state space of perturbations as a Riemannian pseudosphere with scalar curvature close to -1/2. This would allow the representation of a trajectory of states under a given ambient or process change, so opening the possibility for geometrically formulated dynamical models to link structural perturbations to the physics.
The influence of oceanic turbulence on the spectral properties of chirped Gaussian pulsed beam
NASA Astrophysics Data System (ADS)
Liu, Dajun; Wang, Yaochuan; Wang, Guiqiu; Yin, Hongming; Wang, Jinren
2016-08-01
Based on the extended Huygens-Fresnel principle, the spectral behaviors of a chirped Gaussian pulsed beam propagating in oceanic turbulence are illustrated. The influence of the parameters of oceanic turbulence (the rate of dissipation of turbulent kinetic energy per unit mass of fluid, rate of dissipation of mean-square temperature, relative strength of temperature and salinity fluctuations), relative position parameter and propagation distance on the spectra shift is analysed and given by numerical examples. The research results have the potential application in underwater wireless laser communication and remote sensing.