激光大气传输湍流扰动仿真技术

为了研究激光大气传输时湍流效应对激光应用技术的影响,对湍流扰动的仿真进行了分析。介绍了在实验室内进行激光大气传输湍流扰动研究的数值仿真技术和仿真系统。阐述了快速傅里叶变换（FFT）和Zernike多项式两种湍流扰动数值仿真方法,并且对比了两种方法的优劣。利用物理相位屏搭建了实物湍流仿真系统,介绍了其理论模型并进行了仿真实验,对激光经湍流系统传输后的光强能量分布进行了研究分析。结果显示,室内湍流仿真系统能够准确地模拟弱起伏条件下湍流对激光传输的影响。     

Beam propagation factor of partially coherent elegant Hermite-cosh-Gaussian beam through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and the second moments of the Wigner distribution function, an analytical expression for the propagation factors of partially coherent elegant Hermite-cosh-Gaussian beams (EHChGB) in non-Kolmogorov is derived. The M² factor of partially coherent EHChGB through non-Kolmogorov turbulence is studied analytically and numerically. The results show that partially coherent EHCHGB with higher beam order and longer wavelengths is less affected by non-Kolmogorov turbulence.     

Angle-of-arrival fluctuations for wave propagation through non-Kolmogorov turbulence

Recently the increasing experimental evidences have shown that atmospheric turbulence statistics does not obey Kolmogorov’s power spectrum model in portions of the troposphere and stratosphere. These experiments have prompted the investigations of optical wave propagation through atmospheric turbulence described by non-classical power spectra. In this paper, using an original approach and considering a non-Kolmogorov power spectrum which uses a generalized power law instead of constant standard power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the variances of the angle-of-arrival fluctuations of the plane and spherical waves are derived in weak turbulence for a horizontal path. The concise closed-form expressions are obtained and used to analyze the influence of spectral power law variation on the angle-of-arrival fluctuations.     

The effect of non-Kolmogorov turbulence on the propagation of cosh-Gaussian beam

The propagation of cosh-Gaussian beam in turbulence with different power spectral density of refractive index is investigated. By using the expansion of mutual coherence function in Taylor series, analytical expression for the average intensity is presented. With the help of this expression, the intensity profiles with different parameters are analyzed. Relative errors of the analytical expression are studied, and the effects of power spectral density on beam spreading and evolvement are discussed in details. It shows that the analytical expression should provide reasonable approximations to study the propagation of cosh-Gaussian in non-Obukhov-Kolmogorov turbulence.     

Beam propagation factor of radial Gaussian-Schell model beam array in non-Kolmogorov turbulence

The analytical expression for the beam propagation factor (M²-factor) of a radial Gaussian-Schell model (GSM) beam array propagating in non-Kolmogorov turbulence is derived. The influences of beam number, ring radius and generalized exponent on the M²-factor are investigated. The results indicate that the M²-factor has great dependence on the generalized exponent and the beam number. Moreover, there is an optimum ring radius, which leads to a minimum M²-factor and increases with increase in beam number. Further, the M²-factor for the superposition of the intensity is larger than that for the superposition of the cross-spectral density function (CSDF). However, the M²-factor for the superposition of the intensity is less sensitive to the turbulence than that for the superposition of the CSDF.     

Effect of non-Kolmogorov turbulence on beam spreading in satellite laser communication

In the past half a century, satellite laser communication has caught the attention of scientists due to its distinct advantages in comparison with conventional satellite microwave communication. For ground-to-satellite and satellite-to-ground data links, the atmosphere is a part of the communication channel; thus, atmospheric turbulence severely degrades the performance of satellite laser communication systems. In general, the Kolmogorov turbulence model is used to study the effect of atmosphere turbulence on satellite laser communications since it has been confirmed by numerous direct measurements of temperature and humidity fluctuations in the atmospheric boundary layer. However, increasing experimental evidence and theoretical investigations have shown that the Kolmogorov theory is sometimes inadequate to describe atmospheric statistics properly, in particular, in some domains of the atmosphere. We analyze the joint influence of Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the spot size associated with the uplink and downlink propagation channels for a satellite laser communication system in the geosynchronous orbit, using a power spectrum of non-Kolmogorov turbulence with power law ?5 that describes the refractiveindex fluctuations in the atmosphere above 6 km and considering the combined power spectrum of Kolmogorov and non-Kolmogorov turbulence. Before this analysis, we study the joint influence of the Kolmogorov turbulence from the ground to 6 km and non-Kolmogorov turbulence above 6 km on the scintillation indices of laser beams.     

Beam propagation factor of partially coherent Hermite-Gaussian beams through non-Kolmogorov turbulence

Based on extended Huygens-Fresnel principle, an analytical expression of M² factor for partially coherent Hermite-Gaussian (PCHG) beams through non-Kolmogorov turbulence is obtained. Our results show that M² factor of PCHG beams depends on coherence length, beam order m, wavelength, exponent value α, outer scale L₀ and inner scale l₀. The impact of the exponent's variation on the M² factor is analyzed in detail. When the propagation distance fixed, the M² factor of PCHG beams has a maximum for alpha values lower than 11/3.     

Annular beam scintillations in non-Kolmogorov weak turbulence

In a weakly turbulent atmosphere governed by the non-Kolmogorov spectrum, the on-axis scintillation index is formulated and evaluated when the incidence is an annular Gaussian type. When the power law of the non-Kolmogorov spectrum is varied, the scintillation index first increases, and reaches a peak value, then starts to decrease, and eventually approaches zero. The general trend is that when turbulence has a non-Kolmogorov spectrum with power law larger than the Kolmogorov power law, the scintillation index values become smaller. For all power laws, collimated annular Gaussian beams exhibit smaller scintillations when compared to pure Gaussian beams of the same size. Intensity fluctuations at a fixed propagation distance diminish for the non-Kolmogorov spectrum with a very large power law, irrespective of the focal length and the thickness of optical annular Gaussian sources.     

部分相干光在大气湍流中传输的闪烁指数

实验测量了不同空间相干度的部分相干光在实际大气湍流中传输的闪烁指数。结果表明:随着入射光空间相干度的降低,闪烁随光传输距离增长而增加的趋势变得缓慢,甚至出现减小的情况。此外,与完全相干光的闪烁指数随着径向距离的增加而增加不同,部分相干光的闪烁指数沿着光斑径向距离的增加不一定增加,而有可能出现降低。相干度越低,该效应越明显。     

部分相干光在大气湍流中传输的闪烁指数

实验测量了不同空间相干度的部分相干光在实际大气湍流中传输的闪烁指数。结果表明：随着入射光空间相干度的降低,闪烁随光传输距离增长而增加的趋势变得缓慢,甚至出现减小的情况。此外,与完全相干光的闪烁指数随着径向距离的增加而增加不同,部分相干光的闪烁指数沿着光斑径向距离的增加不一定增加,而有可能出现降低。相干度越低,该效应越明显。     

基于拉盖尔-高斯光束的通信系统在非Kolmogorov湍流中传输的系统容量

涡旋波束在大气湍流中的传输有非常重要的理论研究和实际应用意义. 本文基于利托夫近似和广义惠更斯-菲涅耳原理, 推导出拉盖尔-高斯(LG)光束在非Kolmogorov湍流中斜程传输时的螺旋谱, 并进一步推导出系统的容量. 对基于LG光束的通信系统容量进行了数值计算, 并对指数参数、光束波长、天顶角、湍流内尺度、外尺度、结构常数对系统容量的影响进行了分析比较. 本文的结论能够为LG光束在非Kolmogorov湍流中的通信提供一定的参考价值. 关键词： 拉盖尔-高斯光束 非Kolmogorov湍流 平均容量     

Average capacity of free-space optical systems for a partially coherent beam propagating through non-Kolmogorov turbulence

The performance of partially coherent free-space optical links is investigated in the moderate to strong fluctuation regime of non-Kolmogorov turbulence. The expressions for large- and small-scale log-irradiance flux variance are obtained in non-Kolmogorov turbulence. By employing the gamma-gamma distribution of irradiance fluctuations, the effects of spatial coherence of the source, index of non-Kolmogorov spectrum, and size of the receiver on channel capacity for horizontal links are discussed. Results show that channel capacity presents fluctuating behaviors with the variation of alpha for longer links and increases for alpha values higher than 11/3.     

光束在强湍流区中传播的到达角起伏

 基于修正Rytov理论，导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式，分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用，随着Rytov方差的增加到达角起伏趋于饱和；高频功率谱的下降速度随着散射盘尺度的增加而增加。     

光束在强湍流区中传播的到达角起伏

基于修正Rytov理论,导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式,分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用,随着Rytov方差的增加到达角起伏趋于饱和;高频功率谱的下降速度随着散射盘尺度的增加而增加。     

Scintillation optimization of radial Gaussian beam array propagating through Kolmogorov turbulence

The analytical expression for scintillation index of radial Gaussian beam array with coherent combination based on Kolmogorov power-law spectrum in the horizontal path is derived. The influences of the beam number and ring radius on the scintillation index are studied. The results show that the scintillation index can be reduced by increasing beam number and an optimum ring radius is proved to exist. Further, the optimum ring radius greatly depends on the source size and exists only in a certain range of the source size determined by the propagating distance. Additionally, the scintillation index distributions at the receiver greatly depend on the source size.     

Further analysis of scintillation index for a laser beam propagating through moderate-to-strong non-Kolmogorov turbulence based on generalized effective atmospheric spectral model

A new expression of the scintillation index(SI) for a Gaussian-beam wave propagating through moderate-to-strong non-Kolmogorov turbulence is derived, using a generalized effective atmospheric spectrum and the extended Rytov approximation theory. Finite inner and outer scale parameters and high wave number "bump" are considered in the spectrum with a generalized spectral power law in the range of 3–4, instead of the fixed classical Kolmogorov power law of 11/3. The obtained SI expression is then used to analyze the effects of the spectral power law and the inner scale and outer scale on SI under various non-Kolmogorov fluctuation conditions. These results will be useful in future investigations of optical wave propagation through atmospheric turbulence.     

Average intensity of flattened Gaussian beam in non-Kolmogorov turbulence

Based on the extended Huygens-Fresnel principle and the first-order approximation of wave structure function, an analytical expression for the average intensity of flattened Gaussian beam (FGB) in non-Kolmogorov turbulence has been derived. The variations of normalized intensity with some parameters, such as wave coherence length, Fresnel number, waist width and the order of FGB are investigated in detail.     

Scintillation index of the Gaussian beams propagated through the paths with strong turbulence

Theoretical and experimental studies of the local statistical characteristics of Gaussian beams propagated through the paths with strong turbulence were carried out and their results are presented. It is ascertained that the applicability of the scintillation index meanings are substantially limited for the assessment of the performance quality of the optical data transmitting channels. On the basis of the experimental data got under different propagation conditions the peculiarities of the localized intensity distributions and those of the scintillation index are revealed.     

Scintillation behavior of cos, cosh and annular Gaussian beams in non-Kolmogorov turbulence

For a non-Kolmogorov spectrum, scintillation aspects of cos, cosh and annular Gaussian beams are investigated. The appropriate mathematical formulation is developed, the derived scintillation index is evaluated and its variation is plotted in graphs. We find that, when the values of the power coefficient of the spectrum are just above 3, low scintillation is encountered, then as the power coefficient is increased, rises will occur with a peak being reached around 3.21. From there onwards, scintillation will drop, as the power coefficient approaches a value of 5. For extreme off-axis positions, there will be slight increases in scintillation at high power coefficient values. At points near on-axis and when the beams have small width sizes, cosh Gaussian beam having a bigger displacement parameter will offer the lowest scintillation. At large width sizes, this advantage will switch to the side of the cos Gaussian beam. In this study, the variation of scintillation with other sources and propagation parameters is examined as well.     

Spiral spectrum of Airy-Schell beams through non-Kolmogorov turbulence

Based on the geometrical optics approximation, we analyze the effects of non-Kolmogorov turbulence on the spiral spectrum of the orbital angular momentum(OAM) of Airy-Schell beams. Our numerical results of Airy—Schell beams on the horizontal path show that the beam spreading due to diffraction is smaller for shorter wavelengths, a smaller OAM quantum number, a larger radius of the main ring, and a higher arbitrary trans?verse scale in weak turbulence. The oscillation frequency of the mode probability density of Airy-Schell beams in the radial direction is much lower than that of Hankel-Bessel beams. The mode probability densities of Airy—Schell and Hankel-Bessel beams are remarkably dependent on the wavelength and OAM quantum num?ber. In order to improve the mode probability density, Airy-Schell beams with shorter wavelengths and lower OAM quantum numbers may be the better choice, which is diametrically opposite to Hankel-Bessel beams. Our research provides a reasonable basis for selecting light sources and precise tracking.