Multi-Gaussian Schell-model vortex beam

Multi-Gaussian Schell-model (MGSM) beam was introduced recently (Sahin and Korotkova, 2012 [34], and Korotkova et al., 2012 [35]). In this paper, multi-Gaussian Schell-model vortex (MGSMV) beam is introduced as a natural extension of MGSM beam. The explicit expression for the cross-spectral density of a MGSMV beam propagating through a stigmatic ABCD optical system is derived and the focusing properties of a MGSMV beam are studied in detail. It is found that we can shape the focused beam profile by varying the initial beam parameters, which will be useful in material thermal processing and particle trapping.     

Tight focusing of J0-correlated Gaussian Schell-model beam through high numerical aperture

Based on the vectorial Debye diffraction theory, the tight focusing of a linearly polarized J₀-correlated Gaussian Schell-model (JGSM) beam through high numerical aperture (NA) is investigated. The components of intensity distributions as well as the 3D degree of polarization of light at the focal plane are depicted by numerical integrations, respectively. It is shown that intensity distributions as well as the degree of polarization of focused field not only strongly depend on the global correlation length of the JGSM beam but also relate to the focusing parameter of NA. It is also indicated that the weight of the longitudinal intensity component would enhance in the focal plane, as long as either the correlation length of the JGSM beam or the focusing parameter of NA increases.     

Experimental observation of lensless coincidence fractional Fourier transform with a Gaussian Schell-model beam

A modified lensless optical system for implementing coincidence fractional Fourier transform (FRT) is proposed, and the conditions for the optical system to implement the coincidence FRT with incoherent or partially coherent light are discussed. Furthermore, we report the experimental observation of lensless coincidence FRT of an object (double slits) with a typical partially coherent beam - Gaussian Schell-model (GSM) beam. The experimental results are analyzed and agree reasonably well with the theoretical results.     

Hollow Gaussian Schell-model beam and its propagation

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

Spectral shift of a stochastic electromagnetic Gaussian Schell-model beam in a Gaussian cavity

Spectral changes of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam interacting with a Gaussian cavity are investigated. It is shown that the spectral shift is mainly determined by the degree of polarization of the initial beam and by the parameters of the cavity. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.     

Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam

The concept of the degree of paraxiality introduced recently for monochromatic fields is extended to the domain of stochastic electromagnetic fields. Analytical expression for the degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is derived. Numerical results show that the degree of paraxiality of an EGSM beam is determined by the degree of polarization, r.m.s. widths of the spectral densities and of the correlation functions of its source. Degree of paraxiality of an EGSM beam after passing through a linear polarizer is also analyzed. Our results show that one can modulate the degree of paraxiality of an EGSM beam by a linear polarizer.     

Propagation properties of a partially polarized electromagnetic twist anisotropic Gaussian Schell-model beam in turbulent atmosphere

Based on the extended Huygens-Fresnel integral formula, analytical formulae for the elements of cross-spectral density matrix of partially polarized electromagnetic twist anisotropic Gaussian Schell-model (TAGSM) beam propagating in turbulent atmosphere can been derived by a tensor method. Our main attention was focus on the effect of the atmospheric turbulence, twist parameters and partial coherence on the spectral degree of polarization, the spectral degree of coherence and the spectral density. Numerical calculation results and analysis are given.     

Propagation of a twisted anisotropic Gaussian Schell-model beam beyond the paraxial approximation

With the help of a tensor method, an analytical nonparaxial propagation formula for a twisted anisotropic Gaussian Schell-model (GSM) beam in free space is derived based on the generalized Raleigh-Sommerfeld diffraction integral. The far-field nonparaxial propagation expression for a twisted anisotropic GSM beam is also derived. The paraxial approximation is dealt with as a special case of our general result. Our numerical results show that the nonparaxial propagation properties of a twisted anisotropic GSM beam are closely related to the initial beam parameters (i.e., twist factor, transverse spot width matrix, coherence width matrix and wavelength) and the propagation distance. Our formulae provide a convenient and powerful way for studying the paraxial and nonparaxial propagation of an isotropic or anisotropic GSM beam with or without twist phase in free space.     

Evolution of the degree of polarization of an electromagnetic Gaussian Schell-model beam in a Gaussian cavity

The interaction of an electromagnetic Gaussian Schell-model (EGSM) beam with a Gaussian cavity is analyzed. In particular, the evolution of the degree of polarization of the EGSM beam is investigated. The results show that the behavior of the degree of polarization depends on both the statistical properties of the source that generates the EGSM beam and the parameters of the cavity.     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

Angular momentum density of a Gaussian vortex beam

The Gaussian vortex beam is assumed to be linearly polarized.The analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral formulae.The propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric field.By employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is derived.The three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference plane.The effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are investigated.To acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge increases.This research is useful to the optical trapping,the optical guiding,and the optical manipulation.     

Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam

Based on classical theory of optical coherence and polarization, coincidence fractional Fourier transform (FRT) with a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is investigated. Dependences of the quality and visibility of the coincidence FRT pattern of an object on the degree of polarization and correlation coefficients of the EGSM beam are studied numerically. It is shown that the quality and visibility of the coincidence FRT pattern of an object are determined by the polarization and coherence of the EGSM beam together.     

Tight focusing properties of linearly polarized Gaussian beam with a pair of vortices

The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane.     

Off-axis Gaussian Schell-model beam and partially coherent laser array beam in a turbulent atmosphere

The propagation of an off-axis Gaussian Schell-model (GSM) beam in a turbulent atmosphere is investigated based on the extended Huygens-Fresnel integral formula. Analytical formulae for the cross-spectral density and corresponding partially coherent complex curvature tensor of an off-axis GSM beam propagating in a turbulent atmosphere are derived. Based on these formulae, the propagation properties of such kind of beam in a turbulent atmosphere are investigated in detail. Furthermore, the methods are extended to investigate the propagation properties of a partially coherent laser array beam in a turbulent atmosphere. The properties of an off-axis GSM beam and a partially coherent laser array beam in a turbulent atmosphere are closely related with the beam parameters and the structure constant of the turbulent atmosphere.     

Intensity distribution properties of Gaussian vortex beam propagation in atmospheric turbulence

By using wave optics numerical simulation, the intensity-hole effect, beam spreading and wandering properties of Gaussian vortex beam propagation in atmospheric turbulence are investigated quantitatively. It is found that an intensity hole in the center of the beam pattern appears gradually as a Gaussian vortex beam propagates. The size of the intensity hole increases with the increase of the topological charge of the vortex phase. However, the intensity hole could to some extent be filled with optical energy by atmospheric turbulence, especially in strong turbulence. The radius of the intensity hole first decreases and then increases with the growth of turbulence strength. The effective radius of vortex beam with larger topological charge is greater than with a smaller topological charge. But the topological charge has no evident influence on beam wandering.     

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

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

高斯涡旋光束的光束传输因子和峭度参数

基于强度二阶矩定义, 导出了高斯涡旋光束光束传输因子即M² 因子的解析表达式, 高斯涡旋光束的M² 因子唯一取决于拓扑电荷数n. 数值计算表明, 高斯涡旋光束的M² 因子随着拓扑电荷数n的增大而增大. 基于强度高阶矩, 还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式, 高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D. 在自由空间传输时, 高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ. 自由空间传输时, 高斯涡旋光束峭度参数的变化规律为: 峭度参数随参数δ的增大先减小而后趋向于一最小值, 随拓扑电荷数n的增大而减小. 这一研究有助于高斯涡旋光束的实际应用.     

Spectral properties of apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model beam propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical formulas are derived for the cross-spectral density matrix of an apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model (ETAGSM) beam propagating in a turbulent atmosphere by use of a tensor method. Spectral properties of apertured ETAGSM beam are closely related with the strength of atmospheric turbulence, the aperture widths and the beam's parameters, etc. Our main attention was focused on the influence of the aperture widths, atmospheric turbulence, twist parameters and partial coherence on the spectral properties (including spectral degree of polarization, the spectral degree of coherence and the spectral density) of apertured ETAGSM beam propagating in turbulent atmosphere. Numerical calculation results and analysis are given.     

左手材料平板对傍轴高斯光束聚焦特性分析

在傍轴近似下,推导出了左手材料平板聚焦系统的传输矩阵,并利用ABCD定律得到了高斯光束在左手材料中和经过平板透镜聚焦后的传输公式。高斯光束在左手材料内部和像空间的传输公式的研究表明:像高斯光束和物高斯光束束腰大小一致,即左手材料平板透镜实际上对高斯光束没有聚焦作用。研究同时表明左手材料平板对高斯光束的聚焦与几何光学成像规律完全一致,而不存在一般透镜聚焦时的焦移效应。