涡旋光束在湍流大气中的传输特性

根据广义的惠更斯-菲涅耳原理, 研究了涡旋光束在湍流大气中的传输特性。研究结果表明, 涡旋光束在湍流大气中传输时, 截面光强会从空心分布转化为高斯分布。光束所带的拓扑电荷数以及大气湍流均会影响光强分布的变化。研究结果还表明, 涡旋光束能够抑制大气湍流对光束扩展的影响, 这一现象得到了实验上的证实。通过杨氏双缝干涉的方法, 还研究了涡旋光束经过湍流大气传输后的拓扑电荷数。研究发现, 涡旋光束经过湍流大气后, 拓扑电荷数将发生波动。     

Propagation of cylindrical vector beams in a turbulent atmosphere

<正>Based on the extended Huygens-Presnel principle,the propagation of cylindrical vector beams in a turbulent atmosphere is investigated.The intensity distribution and the polarization degree of beams on propagation are studied. It is found that the beam profile has a Gaussian shape under the influence of the atmospheric turbulence,and the polarization distribution shows a dip in the cross section as the beam propagates in the turbulent atmosphere.It is also found that the beam profile and the polarization distribution are closely related to beam parameter and atmospheric turbulence.     

Propagation of a phase-locked circular dark hollow beams array in a turbulent atmosphere

The propagation of phase-locked circular dark hollow beams array in a turbulent atmosphere is studied. An analytical expression for the average intensity distribution at the receiving plane is obtained based on the extended Huygens-Fresnel principle. The effects of turbulence, dark parameter and beam order of the beams array on the intensity pattern are studied and analyzed. It is found that the intensity pattern of the phase-locked circular dark hollow beams array will evolve from a multiple-spot-pattern into a Gaussian beam spot under the isotropic influence of the turbulence. The intensity pattern of beam array with a larger dark parameter and beam order evolves into the Gaussian-shape faster with increasing propagation distance.     

Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere

The characteristics of partially coherent Bessel-Gaussian beams propagating in turbulent atmosphere are investigated. Based on the extended Huygens–Fresnel principle, the influence of topological charges and coherence of the source on the intensity and the degree of coherence in the received plane are considered. The influence of atmospheric turbulence on beam profile and coherence in the received plane is also analyzed. It is found that a Bessel-Gaussian shaped intensity distribution will eventually transform into a Gaussian distribution after propagating in turbulent atmosphere. Meanwhile, topological charges, coherence of the source and atmospheric turbulence will also influence the propagation characterizations of the beams.     

Propagation of partially coherent double-vortex beams in turbulent atmosphere

Based on the extended Huygens–Fresnel principle, we study the propagation properties of partially coherent double-vortex beams in turbulent atmosphere. The intensity distribution of the beams on propagation and the influence of the characteristic parameters are investigated in great detail. It is shown that when the beams propagate in turbulent atmosphere, the intensity distributions are of double-ring structure near the source plane, but they will experience change, which are determined by the topological charges, the spatial coherence, source beam width and atmospheric turbulence. These results may have applications in space optical communication.     

Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere

The propagation and spreading of a Hermite–Laguerre–Gaussian (HLG) beam in a turbulent atmosphere has been investigated. Based on the extended Huygens–Fresnel integral and some mathematical techniques, analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of an HLG beam in a turbulent atmosphere are derived, respectively. The average intensity distribution and the spreading properties of HLG beams in a turbulent atmosphere are numerically demonstrated. Upon propagation in a turbulent atmosphere, the central lobes in the beam spot of the HLG beam will evolve into the dominant lobes, and the peripheral lobes around the central lobes will evolve into the subdominant lobes. The influences of the additional angle parameter and the transversal mode numbers on the propagation of HLG beams in a turbulent atmosphere are also discussed. As the coherence length of the turbulence is determined by the propagation distance, the effect of the additional angle parameter on the effective beam size is related to the propagation distance. The kurtosis parameter generally increases with increasing the additional angle parameter. The influence of the transversal mode numbers on the kurtosis parameter is related to the additional angle parameter and the propagation distance. According to the practical need of free-space optical communications and remote sensing, the HLG beam in a turbulent atmosphere can be controlled by choice of the additional angle parameter and the transversal mode numbers.     

部分相干光束经过湍流大气传输研究进展

相较于相干光束,部分相干光束经过湍流大气传输能够有效地抑制湍流引起的光束展宽、光斑漂移及光强闪烁等扰动效应,在自由空间光通信、激光雷达和激光遥感等方面有重要的应用前景.近年来,部分相干光束湍流大气传输研究受到越来越多学者的关注.本文回顾了部分相干光束在湍流大气中传输特性研究的发展历程、理论基础及常用的理论方法,介绍了处理光束经过湍流大气传输的相位屏数值模拟方法,以及如何把该方法运用到处理部分相干光束传输.     

Propagation of modified Bessel-Gaussian beams in turbulence

We investigate the propagation characteristics of modified Bessel-Gaussian beams traveling in a turbulent atmosphere. The source beam formulation comprises a Gaussian exponential and the summation of modified Bessel functions. Based on an extended Huygens–Fresnel principle, the receiver plane intensity is formulated and solved down to a double integral stage. Source beam illustrations show that modified Bessel-Gaussian beams, except the lowest order case, will have well-like shapes. Modified Bessel-Gaussian beams with summations will experience lobe slicing and will display more or less the same profile regardless of order content. After propagating in turbulent atmosphere, it is observed that a modified Bessel-Gaussian beam will transform into a Bessel-Gaussian beam. Furthermore it is seen that modified Bessel-Gaussian beams with different Bessel function combinations, but possessing nearly the same profile, will differentiate during propagation. Increasing turbulence strength is found to accelerate the beam transformation toward the eventual Gaussian shape.     

一维线阵离轴高斯光束通过湍流大气的传输特性

研究了一维(1D)线阵离轴高斯光束通过湍流大气的传输特性，推导出了其光强传输方程. 研究表明，1D线阵离轴高斯光束通过湍流大气传输经历了三个阶段，即在近场其光强分布为类似于入射光的锯齿状分布，随着传输距离的增加逐渐变为平顶分布，最后在远场成为类高斯分布. 湍流的增强会使光束传输经历三阶段的进程加快. 并且，湍流使得不同子光束数的1D线阵离轴高斯光束的归一化光强分布相接近. 此外，子光束数越多的1D线阵离轴高斯光束受到湍流的影响越小；1D线阵离轴高斯光束较高斯光束受到湍流的影响要小. 关键词： 一维(1D)线阵离轴高斯光束 湍流大气 传输特性     

Propagation properties of radial partially coherent flat-topped array beams in a turbulent atmosphere

With the help of the tensor method, the analytical expression for the cross-spectral density of the radial partially coherent flat-topped array (RPCFTA) beams propagating in a turbulent atmosphere is derived, where the correlated superposition and uncorrelated superposition are considered. The average intensity, the spatial coherence properties and power in bucket (PIB) of these kinds of beams are investigated in detail. It is shown by numerical results and analysis that the average intensity and the spatial coherence of the correlated or uncorrelated RPCFTA beams will change on propagation and this change is dependent upon the correlation of the source's beamlets and atmospheric turbulence. In addition, the comparisons of the average intensity and the spatial coherence between the correlated and the uncorrelated RPCFTA beams propagating both in turbulent atmosphere and in free space are also given, and some interesting results are obtained. The laser power of focus ability of the single PCFT beam is worse than that of the correlated RPCFTA beam and but better than that of the uncorrelated RPCFTA beam when propagation distance in turbulent atmosphere is far-field plane.     

部分相干Airy光束在大气湍流中的光强演化

为了利用Airy光束的无衍射、自恢复和自弯曲特性抑制大气湍流效应,实现远距离无线光通信,对部分相Airy光束在大气湍流中传输时的光强演化进行了研究.利用高斯-谢尔模型的交叉谱密度函数、广义惠更斯-菲涅尔原理以及Rytov相位近似法,推导了部分相干Airy在湍流大气中平均光强的表达式.分别从传播距离、湍流强度等方面对光强分布的影响进行了模拟仿真,并对光束自身参数对光强分布的影响进行了相关实验验证.结果表明:随着传播距离的增加,部分相干Airy光束的旁瓣逐渐衰减,主瓣逐渐扩散;在传播足够远时,其旁瓣逐渐消失,主瓣逐渐演化为高斯分布.仿真和实验结果一致表明光束的截断因子越小、特征长度和相干长度越长,光束的光强分布保持越完整.     

Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.     

Propagation characteristics of higher-order annular Gaussian beams in atmospheric turbulence

The propagation characteristics of higher-order annular Gaussian (HOAG) beams in turbulence are investigated. From a HOAG source plane excitation, the average intensity of the receiver plane is developed analytically. This formulation is verified against the previously derived HOAG beam solution in free space. The graphical outputs indicate that, upon traveling in turbulent atmosphere, the HOAG beam will undergo different stages of evolution. At intermediate propagation distances, it will attempt to concentrate the energy near the origin. In this process, the appearance of the single higher-order primary beam will be encountered. Eventually HOAG originated beam will become a pure Gaussian beam after propagating an excessive distance in the turbulent medium.     

Propagation of Helmholtz-Gauss beams in weak turbulent atmosphere

Based on the Rytov approximation of light propagation in weak turbulent atmosphere,the closed-form expressions of field and average irradiance of each one of the four fundamental families of Helmholtz-Gauss (HzG)beams:cosine-Gauss beams,stationary Mathieu-Gauss beams,stationary parabolic-Gauss beams,and Bessel-Gauss beams,which are propagating in weak turbulent atmosphere,are obtained.The results show that the field and average irradiance can be written as the product of four factors:complex amplitude depending on the z-coordinate only,a Ganssian beam.a factor of complex phase perturbation induced by atmospheric turbulence,and a complex scaled version of the transverse shape of the non-diffracting beam.The effect of weak atmospheric turbulence on irradiance distribution of the HzG beam can be ignored.     

大气湍流中部分相干聚焦涡旋光束的传输特性

基于广义惠更斯-菲涅耳原理和相位结构函数的平方近似,研究了部分相干高斯-谢尔模型涡旋光束被聚焦后在大气湍流中的传输特性,得到了焦平面上光强解析表达式.利用该表达式,详细研究了该类光束在大气湍流中传输焦平面上的光强分布特性.结果表明：在大气湍流中,随着传输距离的增加,涡旋光束的奇异性逐渐降低.对于拓扑荷大的以及空间相干长度较长的涡旋光束,光束奇异性的保持相对要好.在一定的焦距长度和湍流大气条件下,我们可以通过调整光源的拓扑荷和相干长度控制焦面光强分布和焦斑大小.另外,有一定拓扑荷的涡旋光束可以在一定程度上降低大气湍流对传输光束焦面光强分布的影响.     

湍流大气中高斯谢尔光束的波前位错

在Rytov近似下,通过引入短期统计平均位错位置的概念,研究了高斯谢尔光束通过近地面弱湍流大气传播时,波前圆形位错形成和位错位置与湍流大气起伏强度和传播距离等参数间的关系.基于湍流大气中平行和交叉双光束的简化近似传输模型,研究了湍流大气中传播高斯谢尔光束波前位错位置与大气湍流强度、传输距离等参数间的相关机制.在远小于光波位相起伏周期的条件下,分别得出了束径不同同轴双光束和交叉双光束传播情况下波前圆位错位置的湍流系综统计平均理论关系.所得结果表明,同轴平行光束干涉和交叉光束干涉所产生的光束波前位错受大气湍流强度、传输距离等参数调制的规律是不同的.     

非均匀拉盖尔-高斯关联光束及其传输特性

提出了一种新型特殊关联部分相干光束即非均匀拉盖尔-高斯关联光束,其在x和y方向上的关联结构函数分别为非均匀关联和拉盖尔-高斯关联函数.基于广义惠更斯-菲涅耳衍射积分公式,推导了这种光束交叉谱密度函数在自由空间以及大气湍流中的传输式,并计算了该光束经过自由空间和湍流大气传输的光强分布和关联结构函数分布演化特性.研究发现,该光束光强分布在传输过程中展现出自聚焦、自偏移和自分裂等奇异特性,同时发现控制关联结构函数参数可以有效地降低湍流大气的影响.关联结构调控为操控光束传输行为提供了一种新颖而有效的手段,在大气激光通信、微粒操控等领域具有重要的应用前景.     

Power coupling of Gaussian vortex beam propagation through an optical system with the Cassegrain-telescope receiver in turbulent atmosphere

Model of Gaussian vortex beam propagation through an optical system with the Cassegrain-telescope receiver in turbulent atmosphere is established. With this model, the analytical formulas of the average intensity distribution at the receiver plane are derived, and the influences of the optical topological charge, the propagation distance and the turbulence strength are numerically analyzed. These studies show that optical power at the receiver plane concentrates in an annular area, which is suitable for power coupling by the Cassegrain-telescope receiver; the optical topological charge of the vortex source need to be optimized to access the most power coupling. Under the H-V 5/7 turbulence model, power coupling efficiencies of the optical system with different parameters are calculated. Results show that in comparison with the Gaussian beams, Gaussian vortex beams have great advantages in power coupling of optical systems with the Cassegrain-telescope receivers in turbulent atmosphere, which can be a new attractive application of the vortex beams.     

Propagation analysis of flattened circular Gaussian beams with a misaligned circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with a misaligned circular aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel formula. From the study and numerical calculation, the effects of aperture parameters on the propagation properties of flattened Gaussian beams in turbulent atmosphere have been illuminated. The results show that angle misalignments and lateral displacements of aperture create unsymmetrical average intensity distribution at any cross section. The intensity distributions are much more sensitive to the lateral displacement than to the angle misalignments. And the propagation properties of different flattened Gaussian beams in turbulent atmosphere are also compared.     

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.