Influence of turbulence on the beam propagation factor of Gaussian Schell-model array beams

The analytical expression for the beam propagation factor (M²-factor) of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the M²-factor of GSM array beams depends on the beam number, the relative beam separation distance, the beam coherence parameter, the type of beam superposition, and the strength of turbulence. The turbulence results in an increase of the M²-factor. However, for the superposition of the intensity the M²-factor is less sensitive to turbulence than that for the superposition of the cross-spectral density function. The M²-factor of GSM array beams is larger than that of the corresponding Gaussian array beams. However, the M²-factor of GSM array beams is less affected by turbulence than that of the corresponding Gaussian array beams. For the superposition of the cross-spectral density function a minimum of the M²-factor of GSM array beams may appear in turbulence, which is even smaller than that of the corresponding single GSM beams.     

Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

双曲余弦高斯列阵光束在湍流大气中的光束传输因子

本文推导出了双曲余弦高斯(ChG)列阵光束在湍流大气中的光束传输因子( M ^{2因子)的解析公式,并采用相对 M 2因子研究了湍流对 M 2因子的影响.研究表明,在湍流大气中 M 2因子不再是一个传输不变量,湍流使得 M 2因子增大.非相干合成情况下, M 2因子随着传输距离、光束参数、相对子光束间距和子光束数目的增大而增大.相干合成情况下, M 2因子随光束参数和相对子光束间距的增大呈现振荡上升.相干合成情况下的 M 2因子比 关键词： M2因子)')" href="#">光束传输因子(M2因子) 光束质量 双曲余弦高斯列阵光束 大气湍流}     

Long-distance propagation of pseudo-partially coherent Gaussian Schell-model beams in atmospheric turbulence

Propagation properties of spatially pseudo-partially coherent Gaussian Schell-model beams through the atmo- spheric turbulence over a long-distance uplink path are studied by numerical simulation. A linear coordination trans-formation is introduced to overcome the window effect and the loss-of-resolution problem. The beam spreading, beam wandering, and intensity scintillation as functions of turbulence strength, source correlation length, and change frequency of random phase that models the partial coherence of the source are analyzed. It is found that the beam spreading and the intensity scintillation of the partially coherent beam are less affected by the turbulence than those of the coherent one, but it suffers from a more severe diffractive effect, and the change frequency of random phase has no evident influence on it. The beam wandering is insensitive to the variation of source correlation length, and decreases firstly then goes to a fixed value as the change frequency increases.     

Propagation invariants of twisted Gaussian Schell-model beams

The second-order moments method is used to study the M² factor and intrinsic astigmatism of twisted Gaussian Schell-model (GSM) beams. It is shown that the M² factor of twisted GSM beams defined by the determinate of the 4×4 variance matrix is a propagation invariant and is independent of the beam twist, whereas the twist affects the intrinsic astigmatism of twisted GSM beams.     

矩形分布高斯-谢尔模型列阵光束的等效曲率半径

 推导出矩形分布高斯-谢尔模型（GSM）列阵光束通过湍流大气传输的等效曲率半径的解析表达式。研究表明,等效曲率半径由湍流强度、GSM列阵光束参数及光束的叠加方式等因素共同确定。湍流使得等效曲率半径减小,但湍流对交叉谱密度函数叠加时等效曲率半径的影响要比光强叠加时大。在自由空间中,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径要比光强叠加时的大。但是,随着湍流的增强,交叉谱密度函数叠加时GSM列阵光束的等效曲率半径可以大于、等于或小于光强叠加时的等效曲率半径。此外,若光束相干参数和子光束数目越大,则等效曲率半径受湍流的影响越大。GSM列阵光束的等效曲率半径受湍流的影响比高斯列阵光束要小。     

The aperture effect on the propagation of partially polarized Gaussian Schell-model beams

Based on the beam coherence-polarization (BCP) matrix approach and propagation law of partially coherent beams, the propagation of partially polarized Gaussian Schell-model (PGSM) beams through an aperture is studied. Numerical calculation results are given to illustrate the propagation-induced polarization changes and irradiance distribution of PGSM beams for the apertured case.     

Spectral shifts of Gaussian Schell-model beams in passage through an astigmatic lens

Starting from the propagation law of partially coherent light, a closed-form expression for the spectrum of Gaussian Schell-model (GSM) beams propagating through an astigmatic lens is derived, which enables us to study the dependence of spectral shift of GSM beams on the astigmatism of the lens and spatial coherence of GSM beams both analytically and numerically. A comparison with the aberration-free case is made, and shows that the astigmatism affects the spectral behavior of GSM beams. Two special cases of the full coherence and incoherence are discussed and illustrated physically.     

Focal shift of partially polarized Gaussian Schell-model beams

A detailed study of the focal shift of partially polarized Gaussian Schell-model (PGSM) beams is made on the basis of the beam coherence-polarization (BCP) matrix approach. It is shown that, apart from the Fresnel number and truncation parameter, the focal shift of PGSM beams depends on the angle of polarizer and the ratio of degree of spatial coherence.     

Propagation properties of partially polarized Gaussian Schell-model beams through an astigmatic lens

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.     

高斯-谢尔模型列阵光束的远场发散角和远场辐射强度

推导出了高斯-谢尔模型（GSM）列阵光束通过自由空间传输其二阶矩束宽、远场发散角和远场辐射强度的解析表达式,并给出了GSM列阵光束与高斯光束具有相同远场发散角的条件.研究表明,具有相同远场发散角的GSM列阵光束与对应的高斯光束并不具有相同的远场辐射强度分布,这一特性与单束GSM光束的差异很大. 关键词： 高斯-谢尔模型列阵光束 远场发散角 远场辐射强度     

On-axis spectral shifts and spectral switches of Gaussian Schell-model beams focused by an astigmatic aperture lens

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.     

Spectral changes of vector Gaussian Schell-model beams passing through an aperture lens

On the basis of the polarization matrix and propagation equation of the cross-spectral density matrix, the spectral changes in the focal plane of vector Gaussian Schell-model (GSM) beams focused by an aperture lens are studied, where the influence of correlation and polarizer on the behavior of the spectral switch is stressed. It is found that the critical position u_c, spectral minimum S_min, and transition height Δ of the spectral switch depend on the auto-correlation but do not depend on the cross-correlation of GSM beams if there is no polarizer. However, in the presence of the polarizer u_c, S_min and Δ depend on both auto- and cross-correlations. The polarizer affects the spectral switch of vector GSM beams, whereas it does not affect the spectral switch of scalar GSM beams.     

大气湍流对多色高斯-谢尔模型光束扩展的影响

基于广义惠更斯-菲涅耳原理,采用Rytov相位结构函数二次近似和硬边窗口函数的复高斯展开法,推导了受光阑限制的多色高斯-谢尔模型(GSM)光束在大气湍流中的二阶矩束宽公式。研究表明:二阶矩束宽随着大气湍流折射率结构常数、源光谱带宽和光束传输距离的增加而增大,随着光束截断参数和光束相干参数的增加而减小;并且,当源光谱带宽越大、光束截断参数和光束相干参数越小,则湍流对受光阑限制的多色GSM光束扩展的影响就越小。关键词:      

Polarization properties of nonparaxial partially polarized Gaussian Schell-model beams

The polarization properties of nonparaxial partially polarized Gaussian Schell-model (PGSM) beams are studied. Based on the beam coherence-polarization matrix, the propagation formula of the degree of polarization for the nonparaxial PGSM beams is derived. The paraxial approximation is dealt with as special cases of our general results. Some conditions that limit the choice of the parameters are established. The sufficiency condition of polarization invariance in propagation for the nonparaxial PGSM beams is derived. By using the derived formulae, the propagation properties of the degree of polarization for the nonparaxial PGSM beam in free space are illustrated and analyzed with numerical examples. Some detailed comparisons of the obtained results with the paraxial results are made.     

Influence of oceanic turbulence on propagation characteristics of Gaussian array beams

Based on the power spectrum of oceanic turbulence proposed by Nikishov, the influence of oceanic optical turbulence on propagation of Gaussian array beams is studied in detail by using five propagation characteristic parameters (i.e., mean-squared beam width, Rayleigh range, turbulence distance, power in the bucket and Strehl ratio). It is shown that the influence of oceanic optical turbulence on propagation of laser beams becomes stronger as τ (ratio of temperature to salinity contribution to the refractive index spectrum) and χ_T (rate of dissipation of mean-squared temperature) increase and ɛ (rate of dissipation of kinetic energy per unit mass of fluid) decreases, which is in agreement with the further analysis of oceanic turbulence shown in this paper. Furthermore, it is concluded that propagation of laser beams is more affected by oceanic optical turbulence in abyssal region than that in active region or oceanic surface.     

Changes in polarization of Gaussian Schell-model beams and partially polarized Gaussian Schell-model beams through a polarization grating

The polarization properties of Gaussian Schell-model (GSM) beams and partially polarized Gaussian Schell-model (PGSM) beams passing through a polarization grating (PG) are studied based on the beam coherence-polarization (BCP) matrix formulism, where the finite size of the PG is considered. Detailed numerical calculation results are given and compared with the previous work.