Elegant Laguerre-Gaussian beam in a turbulent atmosphere

Paraxial propagation of an elegant Laguerre-Gaussian beam (ELGB) in a turbulent atmosphere is investigated in detail. Analytical formulae for the average intensity and effective beam size of an ELGB in a turbulent atmosphere are derived based on the extended Huygens-Fresnel integral. The average intensity and spreading properties of an ELGB in a turbulent atmosphere are studied numerically and compared with those of a standard Laguerre-Gaussian beam (SLGB). Our results indicate that the propagation properties of an ELGB in a turbulent atmosphere are much different from its properties in free space, and are closely related to its beam parameters and the structure constant of the atmospheric turbulence. The ELGB with higher mode orders is less affected by the turbulence. The SLGB spreads more rapidly than the ELGB in a turbulent atmosphere under the same conditions. Our results will be useful in long-distance free-space optical communications. ©2010 Elsevier Science B.V. All rights reserved.     

Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere

Cylindrical vector (CV) partially coherent beam was introduced (Dong et al. Opt Express 19:5979–5992, 2011) and generated (Wang et al. Appl Phys Lett 100:051108, 2012) recently. In this paper, we derive the realizability conditions for a CV partially coherent beam, and we derive the analytical formula for the cross-spectral density matrix of a CV partially coherent beam propagating in turbulent atmosphere based on the extended Huygens-Fresnel formula. The statistical properties, such as the average intensity, the complex degree of coherence and the degree of polarization of a CV partially coherent beam in turbulent atmosphere are studied in detail and compared with those in free space. It is found that the statistical properties of a CV partially coherent beam in turbulent atmosphere are much different from those in free space, and are affected by the initial beam parameters.     

Spectral properties of partially coherent azimuthally polarized beam in a turbulent atmosphere

In this paper, based on the extended Huygens–Fresnel integral formula, the analytical expression for the beam coherence-polarization (BCP) matrix of the partially coherent azimuthally polarized (PCAP) beams propagating in turbulent atmosphere has been derived. The distribution of the spectral density, the spectral degree of polarization, the spectral degree of coherence and the spectral degree of cross-polarization of the PCAP beams propagating in turbulent atmosphere with different coherences in the source are investigated in detail. It is shown by numerical results and analysis that the distribution of the spectral properties of the PCAP beam will change on propagation in a turbulent atmosphere, and this change is dependent upon the degree of coherence of the source beam and atmospheric turbulence. It is also shown that even through the source beam is chosen as δ_gxx ≠ δ_gyy the distribution of the spectral density, the spectral degree of polarization, the spectral degree of coherence and the spectral degree of cross-polarization in the far field tends to symmetrical profile.     

Propagation properties of a non-circular partially coherent flat-topped beam in a turbulent atmosphere

The propagation of partially coherent flat-topped (PCFT) beams with non-circular symmetries in a turbulent atmosphere is investigated and an analytical formula for the average intensity is derived. Detailed analyses of PCFT beams in a turbulent media led to the derivation of analytical formulae. These formulae demonstrated that higher-order PCFT beams are less broadened in comparison with those with smaller orders and also demonstrated that PCFT beams with smaller correlation lengths are more broadened than the others. The Strehl ratio for PCFT beams is also calculated and the results show that PCFT beams with a higher order of flatness and smaller correlation length are less affected in turbulent media.     

Propagation properties of radially polarized partially coherent beam in turbulent atmosphere

On the basis of the extended Huygens–Fresnel integral formula, analytical propagation formulae for radially polarized partially coherent beam propagating in turbulent atmosphere are derived, and some analyses are illustrated by numerical examples. It is shown that the structure constant of turbulent atmosphere and the initial coherence length have significant influence on the degree of polarization and coherence for radially polarized partially coherent beam.     

高斯谢尔光束通过湍流大气漫射目标的散射统计

基于广义惠更斯菲涅耳原理分析了高斯谢尔光束通过湍流大气漫射目标的散射统计特性。假定相位结构函数起主导作用,根据高斯谢尔光束的交叉密度函数,推导了散斑场的互相干函数表达式,进而得出接收面处的散斑尺寸大小和强湍流起伏的时延协方差函数表达式。数值分析了源相干长度、波长、湍流强度对互相干函数的影响。对理想漫射目标,接收面的散斑尺寸大小由束腰宽度、源相干长度和湍流强度确定,随着湍流强度的增加,散斑尺寸变小;在弱湍流区,散斑尺寸由源相干长度决定,当湍流增强时,散斑尺寸大小逐渐趋于一致。     

高斯谢尔光束通过湍流大气漫射目标的散射统计

基于广义惠更斯菲涅耳原理分析了高斯谢尔光束通过湍流大气漫射目标的散射统计特性。假定相位结构函数起主导作用,根据高斯谢尔光束的交叉密度函数,推导了散斑场的互相干函数表达式,进而得出接收面处的散斑尺寸大小和强湍流起伏的时延协方差函数表达式。数值分析了源相干长度、波长、湍流强度对互相干函数的影响。对理想漫射目标,接收面的散斑尺寸大小由束腰宽度、源相干长度和湍流强度确定,随着湍流强度的增加,散斑尺寸变小;在弱湍流区,散斑尺寸由源相干长度决定,当湍流增强时,散斑尺寸大小逐渐趋于一致。     

Partially coherent aberrated beam propagating in a turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the propagation formulate for partially coherent aberrated beam in a turbulent atmosphere has been derived. Then the propagation of such beams in the turbulent atmosphere has been studied in great detail. It is found that beams with spherical aberration spread more rapidly than those without spherical aberration. It is also found that the beam spreads more rapidly for a stronger turbulence or a source with lower coherence. In addition, some explanation to those results is also given.     

Degree of polarization for single-photon beam in a turbulent atmosphere

The polarization fluctuations of single-photon beam propagation through the slant path turbulent atmosphere are studied. The Stokes operators and the degree of polarization of single-photon beam in a turbulent atmosphere are obtained. It is shown by analytical calculations, that the quantum degree of polarization of linearly polarization light is a decrease function of the atmospheric turbulence strength and the propagation distance for lower detection photon number.     

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.     

Effect of spatial coherence on the scintillation properties of a dark hollow beam in turbulent atmosphere

With the help of a tensor method, we derive an explicit expression for the on-axis scintillation index of a circular partially coherent dark hollow (DH) beam in weakly turbulent atmosphere. The derived formula can be applied to study the scintillation properties of a partially coherent Gaussian beam and a partially coherent flat-topped (FT) beam. The effect of spatial coherence on the scintillation properties of DH beam, FT beam and Gaussian beam is studied numerically and comparatively. Our results show that the advantage of a DH beam over a FT beam and a Gaussian beam for reducing turbulence-induced scintillation increases particularly at long propagation distances with the decrease of spatial coherence or the increase of the atmospheric turbulence, which will be useful for long-distance free-space optical communications.     

Aperture averaging beam-wander of multi-Schell quantization beam in a turbulent atmosphere

We study the effects of the mode number of the multi-Schell Gaussian model beams on aperture averaging wander of quantization Gaussian beams propagating through weak turbulence fluctuation channel. The results demonstrate that there is an optimal sub-Schell beam number M_opt, in here the beam wander is minimum. Because of the beam spreading of turbulence and vacuum diffraction, and aperture smoothing effect of the multi-beam jitter, the impact of zenith angle of channel and turbulent outer scale on the beam wander is tiny. The beam wander of the multi-Schell Gaussian model beams is increased as the increasing of the wavelength λ.     

Propagation of a decentered astigmatic partially coherent beam in a turbulent atmosphere

Propagation properties of a decentered general astigmatic partially coherent beam (i.e., decentered twisted anisotropic Gaussian Schell-model beam) in a turbulent atmosphere are investigated. Analytical formulas for the cross-spectral density and decentered parameter of a decentered astigmatic partially coherent beam propagating in a turbulent atmosphere are derived. Irradiance properties of a decentered astigmatic partially coherent beam in a turbulent atmosphere are studied graphically, and are found to be quite different from its properties in free space.     

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.