Scintillation of a laser beam propagation through non-Kolmogorov strong turbulence

Atmospheric turbulence causes strong irradiance fluctuations of propagating optical wave under the severe weather conditions in long-distance free space optical communication. In this paper, the scintillation index for a Gaussian beam wave propagation through non-Kolmogorov turbulent atmosphere is derived in strong fluctuation regime, using non-Kolmogorov spectrum with a generalized power law exponent and the extended Rytov theory with a modified spatial filter function. The analytic expressions are obtained and then used to analyze the effect of power law, refractive-index structure parameter, propagation distance, phase radius of curvature, beam width and wavelength on scintillation index of Gaussian beam under the strong atmospheric turbulence. It shows that, with the increasing of structure parameter or propagation distance, scintillation index increases sharply up to the peak point and then decreases gradually toward unity at rates depending on power law. And there exist optimal value of radius of curvature and beam width for minimizing the value of scintillation index and long wavelength for mitigating the effect of non-Kolmogorov strong turbulence on link performance.     

Study of Scintillation for Infrared Laser Beam Propagating in Atmospheric Turbulence on Earth-Space Paths

On earth-space paths, by applying a modification of the Rytov method that incorporates spatial frequency filter function under strong atmosphere fluctuation conditions, a tractable model is developed for the scintillation index of infrared laser Gaussian beam wave that is valid under moderate-to-strong irradiance fluctuations. At Infrared band, based on ITU-R C ² _n model, the scintillation indexes for collimation laser beam are predicted by this analytic model. The results agree with theoretic expected scintillation. This scintillation model can be converted into a plane or a sphere wave scintillation index model on earth-space paths, and also reduced to a Gaussian beam wave model on horizontal sight paths of invariable C ² _n.     

Analysis of Inner-Scale Effect on Atmosphere Scintillation for Infrared Laser Beam Propagating on Earth-Space Paths

On Earth-space paths, based on ITU-R C_n² (h) model, by means of a modification of the Rytov method that incorporates an amplitude spatial frequency filter function under strong fluctuation conditions, considering atmospheric turbulence inner-scale, an expression is developed for the scintillation index of a visible or a near and middle infrared laser beam wave that is valid under moderate to strong irradiance fluctuations. The quantitative analyses of scintillation index are done by this analytic model for laser Gaussian collimated beam wave at visible or near and middle infrared wave band. The results agree with theoretic analysis scintillation. This scintillation model can be converted into a Gaussian beam wave model with finite inner-scale on horizontal sight paths of invariable C_n².     

Aperture-averaging effects for weak to strong scintillations in turbulent atmosphere

Under the approximations of (1) the received irradiance fluctuations of an optical wave caused by small scale turbulent eddies are multiplicatively modulated by the fluctuations caused by large scale turbulent eddies;(2) the scintillations caused by small- and large-scale eddies, respectively, are statistically independent; (3)the Rytov method for optical scintillation collected by the finite-diameter receiving aperture is valid for light wave propagation under weak to saturation fluctuation regime, we develop the applicable apertureaveraging analytic formulas in the week-to-strong-fluctuation for the scintillations of plane and spherical waves, which include the outer- and inner-scale rules of turbulence.     

General optical scintillation in turbulent atmosphere

A general expression of the scintillation index is proposed for optical wave propagating in turbulent atmosphere under arbitrary fluctuation conditions. The expression depends on extreme behaviors of the scintillation indices under both weak and strong fluctuations. The maximum scintillation index in the onset region and the corresponding Rytov index can be evaluated from the general expression. Plane and spherical waves in the cases of zero and non-zero turbulence inner scale are given as examples for illustration of the general behaviors of scintillation indices.     

Scintillation index of optical wave propagating in turbulent atmosphere

A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluctuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index are evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Fresnel size.     

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.     

Double pass wave structure function in weak to strong optical turbulence

The authors have recently published one-way horizontal path wave structure function expressions for plane, spherical, and Gaussian-beam waves. Those results are based on a modification of the Rytov approximation method and, by comparison with experimental data, are believed to be valid under all irradiance fluctuation conditions. In this paper, the earlier results are extended to the double pass case in which the received wave is reflected from a smooth target. The point target case is considered for incident plane, spherical, and Gaussian-beam waves. The finite target case is considered for an incident spherical wave with reflection from a plane mirror or a retroreflector. Comparisons are made between the results derived here, the standard Rytov approximation results, and the asymptotic results given by Banakh for conditions of strong irradiance fluctuations.     

Study on the Scintillation for Optical Wave Propagation in the Slant Path Through the Atmospheric Turbulence

Based on the theory of optical wave propagation in the slant path and the ITU-R turbulence structure constant model which is altitude dependent, the modified Rytov method, which is applicable to the optical wave propagation in the horizontal path, is extended to the propagation in the slant path. According to the spectrum model with non-zero inner scale, the scintillation index as a function of the Rytov variance is obtained from weak to strong fluctuation regions with plane wave and sphere wave incidence, respectively. Finally, the scintillation index with different zenith angles is analyzed, and comparison between the results of the modified method and experimental measurements is given and discussed in detail.     

双孔差分闪烁法测量大气湍流的理论与实验研究

根据cross-path理论, 推导出弱起伏条件下差分孔径光强起伏结构函数的精确表达式, 以此为依据, 从理论上提出测量大气湍流强度的双孔差分闪烁法. 在Kolmogorov湍流谱条件下, 分析了信标光直径和信标光高度对该方法中路径权重函数的影响. 在近地面开展了2 km路径的水平光单程传输实验, 将双孔差分闪烁法和单孔闪烁法的测量结果进行了对比. 实验结果表明: 在不同的天气条件和大气湍流状况下, 两种方法测量的折射率结构常数具有高度的一致性; 通过对折射率结构常数积分得到的球面波大气相干长度进行相关性分析, 发现两者的线性相关系数达0.96; 由此验证了双孔差分闪烁法的可行性和有效性. 该方法能够分离出主动信标双程传输的后向闪烁信息, 为主动信标准确探测大气湍流提供了一种新方法.     

高斯波束在湍流大气斜程传输中的闪烁问题研究

根据光波斜程传输理论以及随高度变化的ITU-R湍流大气结构常数模型,将水平传输的修正里托夫方法推广到了斜程传输问题中。导出了高斯波束入射时,在零内尺度湍流谱模型及考虑湍流内尺度效应和外尺度效应条件下,从弱起伏湍流区到强起伏湍流区闪烁指数随斜程里托夫方差变化的计算公式。讨论了不同传播高度、不同湍流内、外尺度对高斯波束斜程传输闪烁指数的影响。最后将有关数值计算结果与实验测量结果进行了比较和验证。     

Beam wave propagation within the second Rytov perturbation approximation

The applicability of the classical Rytov method in statistical wave propagation problems is reconsidered and expanded by demanding results that are of second order in the permittivity fluctuations, rather than limiting them to just the first Rytov perturbation approximation, as is traditionally done. It is shown that one must augment the well-known second order statistics (e.g., log-amplitude variance), as calculated from the first Rytov approximation, with first-order statistics (e.g., the average log-amplitude), as calculated from the second Rytov approximation. Thus, a complete solution is derived for the second Rytov approximation for general beam wave propagation through turbulent media, the permittivity fluctuations of which are described by the Kolmogorov-Obukhov spectrum. This then allows a complete and consistent treatment that yields the fact that the average log-amplitude is, in the general beam wave case, not equal to the additive inverse of the log-amplitude variance. This gives results from the Rytov method that are then in exact agreement with the corresponding limiting case of strong fluctuation theory, as well as a simplified analytical expression for beam wave broadening, and the correct theoretical explanation of the well-known applicability limit for the Rytov method.     

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。     

湍流大气中星载角反射器阵列回波的闪烁指数

利用Rytov方法结合ABCD传输矩阵理论, 推导了地-空-地双程湍流大气路径中单个角反射器回波在接收孔径平面上的强度协方差函数及闪烁指数公式. 根据角反射器阵列的各角反射器单元回波相位相互独立假设, 计算了接收孔径平面上的强度协方差函数、孔径平滑因子和闪烁指数, 比较分析了单个角反射器与角反射器阵列回波闪烁指数. 证明角反射器阵列不改变闪烁指数, 但大气湍流会引起光强起伏放大两倍的规律. 关键词： 大气光学 角反射器阵列 闪烁指数     

Irradiance scintillation considering finite turbulence inner scale for optical wave propagating through weak non-Kolmogorov turbulence

The turbulence inner scale plays an important role in investigating the irradiance scintillation index for optical wave propagating through atmospheric turbulence. However, previous expressions of the irradiance scintillation index, which were derived based on the general non-Kolmogorov spectral model, did not consider the influences of finite turbulence inner scale. In this study, based on the generalized exponential spectral model for non-Kolmogorov atmospheric turbulence, theoretical expressions of the irradiance scintillation index are derived for plane and spherical optical waves propagating through weak turbulence. The new expressions have considered the influences of the finite turbulence inner scale and the receiver aperture on the irradiance scintillation index. Numerical simulations are performed to analyze these parameters’ influences.     

Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum

Using a recently developed theory of scintillation that is valid under all fluctuation conditions, including the focussing and saturation regimes, we develop general models for predicting power fluctuations (or aperture averaging) over finite-size collecting apertures. Inner-scale effects are introduced using a modified atmospheric spectrum for refractive-index fluctuations that includes a high-wavenumber bump. Where comparisons can be made, these models of aperture averaging are in good agreement with previous asymptotic models and experimental data. In addition to the aperture-averaging factor, we calculate the temporal spectrum associated with power fluctuations over various aperture sizes and conditions of turbulence. These later results clearly show the transfer of power distribution from high to low frequencies as the size of the collecting aperture is increased. The transfer of power is more pronounced in the saturation regime where high frequencies (fastest fluctuations) can be averaged out even for relatively small apertures.     

大气闪烁对自适应光学校正的影响

 激光在大气湍流中长距离近水平传输时，闪烁加强，限制了常规自适应光学的校正能力。数值研究了大气闪烁对自适应光学校正的影响，拟合得到了在Fresnel数一定时，Strehl比与Rytov方差的表达式，以及Rytov方差一定时，Strehl比与Fresnel数的表达式。结果表明，在Rytov方差较小时，纯相位校正Ｓtrehl比只与Rytov方差有关；随着Rytov方差的增加，Strehl比不仅与Rytov方差有关，还与Fresnel数有关，Fresnel数越大，校正Strehl比越大；大发射和接收孔径有利于提高校正Strehl比；在一定的Rytov方差下，Stregl比随Fresnel数增大而增加，逐步趋于饱和，达到纯相位校正的极限。     

Rytov variance equivalence through extended atmospheric turbulence and an arbitrary thickness phase screen in non-Kolmogorov turbulence

An arbitrary thickness phase screen model can describe scintillation index for Gaussian beam propagating through a phase screen more accurate than thin phase screen model. To describing actual scintillation index for Gaussian beam propagating through an extended medium using a phase screen in weak non-Kolmogorov turbulence, the scintillation index and Rytov variance for arbitrary thickness phase screen model are derived. Specially, the ratio of the Rytov variances for a phase screen and extended random media is found under the assumption of equivalence in scintillation index of the two cases. The theoretical results show that the normalized Rytov variance varies with the power law of the turbulence spectrum, the relative thickness of the phase screen, the position of the phase screen, the transmitter beam parameters and the radial position at output plane. The influences of these variables are also simulated. These results will be applied to simulation of adaptive optics and laser communication.     

Propagation of a Gaussian-beam wave through a random phase screen

Tractable analytic expressions are developed for a variety of basic statistical quantities involving a Gaussian-beam wave propagating through a random medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, it is well known that the statistics in the receiver plane are in close agreement with those associated with a plane wave propagating through an extended random medium between input and output planes. For a similar comparison between a phase screen and extended turbulence in the case of a Gaussian-beam wave at the input plane, the present analysis reveals that the phase screen must be positioned between input and output planes differently from the plane-wave case, the position being dependent upon the Fresnel ratio of the Gaussian beam. The analytic results developed in this paper for the thin phase screen model are based on the Kolmogorov power-law spectrum for refractive-index fluctuations and the Rytov approximation. Extension of these results to multiple phase screens is also discussed.     

漂移对聚焦高斯光束闪烁影响的数值模拟

 采用非自适应坐标变换对聚焦高斯光束在湍流大气中的传输进行了数值模拟,结果显示轴闪烁指数并没有出现如Rytov理论所预言的随初始光束半径的增大而明显减小的现象,其原因在于Rytov近似理论未考虑大尺度湍涡产生的漂移效应对闪烁的贡献。对比数值模拟结果与漂移理论结果以及相关实验结果,三者相吻合,表明未考虑漂移效应的Rytov近似理论不能完全准确地描述聚焦光束的闪烁特征,在研究聚焦光束的闪烁时,应当考虑漂移的影响。