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.     

The wave structure function in weak to strong fluctuations: an analytic model based on heuristic theory

The Rytov perturbation method can be used to derive analytic expressions governing statistical quantities of an optical wave propagating through the Earth's atmosphere. It is generally accepted that the validity of these expressions is restricted to the weak fluctuation regime, and that the wave structure function for plane and spherical waves obtained via the Rytov method is valid in all fluctuation regimes, for sufficiently small separation distances. Data from experimental results for the wave structure function as a function of the fluctuation strength for a fixed value of the separation distance indicate that the Rytov method does not accurately model the behaviour of the wave structure function in moderate to strong fluctuation regimes. This is similar to what is observed for the scintillation index. Recently, however, it was shown that the integral definition of the scintillation index obtained via the Rytov perturbation yields analytic expressions that are valid in all fluctuation regimes when a filter function is applied to the atmospheric spectrum. The underlying physical theory is that as the wave propagates, intermediate refractive index scale sizes fail to refract or diffract the beam. Hence, these scale sizes do not contribute to the scintillation index. In this paper, we investigate the results of applying this concept to the wave structure function. Specifically, we apply a filter function to the atmospheric spectrum and develop analytic expressions for the wave structure function for plane, spherical and Gaussian beam waves using the Rytov perturbation method. It is shown that in weak fluctuations these expressions yield similar results to standard expressions obtained where no filter function is applied. However, in moderate to strong fluctuations, these new expressions predict a decrease in the value of the wave structure function as compared to the standard expressions, following the trend of the experimental data presented by Gurvich.

(Some figures in this article are in colour only in the electronic version)     

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.     

Collisions and turbulence in optical rogue wave formation

We discuss optical rogue wave generation in terms of collisions and turbulence processes. Simulations of picosecond pulse propagation in optical fibres show rogue soliton generation from either third-order dispersion or Raman scattering independently. Simulations of rogue soliton emergence with dispersive perturbation in the long-distance limit are also presented.     

Passive scalar in a random wave field: the weak turbulence approach

We consider the evolution of a passive scalar advected by a velocity field which is a superposition of random linear waves. An equation for the average concentration of the passive scalar is derived (in the limit of small molecular diffusion) using the weak turbulence methodology. In addition to the enhanced diffusion, this equation contains the correction to the (Stokes) drift. Both of these terms have the fourth order with respect to wave amplitudes. The formulas for the coefficients of turbulent diffusion and turbulent drift are derived.     

强湍流区的光束漂移

 基于修正Rytov理论,导出了适应于强湍流起伏区的光束漂移方差表达式,分析了湍流外尺度、有效散射区域尺度和光束束腰对光束漂移的影响,并与实验结果进行了比较。结果表明,相对于基于指数模型的光束漂移方差表达式,基于修正Rytov理论给出的表达式的计算结果能更好地与实验结果吻合。当光束束腰大于有效散射区域尺度时,不发生饱和效应,导出的表达式与传统理论给出的表达式一致;当光束束腰小于有效散射区域尺度时,光束漂移的幅度不随Rytov方差的增大而明显变化。     

Angle-of-arrival fluctuations in moderate to strong turbulence

Based on the modified spectrum, the analytic expressions for the variance and normalized covariance of angle-of-arrival (AOA) fluctuations are presented, which are applicable to the weak and strong regimes. The experimental data of AOA fluctuations validate the new derived expressions in weak and strong regimes. The results show that the receiving aperture D, outer scale and cell scale larger than the scattering disc S contribute significantly to the AOA fluctuations, and contributions from the small-scale turbulence are negligible. For the case of 4S/D\ll 1, the receiving aperture dominates low-pass filtering effects and the new displacement variances are in good agreement with the results from the old weak-fluctuation theory. For the case of 4S/D\gg 1, the scattering disc dominates the low-pass filtering effects and the new displacement variances depart from the results from the old weak-fluctuation theory.     

Adaptive detection technique for optical wireless communication over strong turbulence channels

Optical wireless communication (OWC) systems use the atmosphere as a propagation medium, so the atmospheric turbulence effects lead to fading related with signal intensity. The received signal of OWC over strong turbulence channels is assumed to be a mixture of K-distributed fading and Gaussian distributed thermal noise. Second-order spectral analysis is unable to separately estimate the mixed signal. In order to mitigate the fading induced by turbulence, the decision threshold-updating algorithm based on second and higher order cumulants is proposed and is able to operate in an unknown turbulence environment. The performance of the adaptive processing scheme has been evaluated by means of Monte Carlo simulations. Simulation results show the improvement of the bit error rate (BER) performance.     

Hamiltonian structure for Alfvén wave turbulence equations

A hamiltonian formulation using a noncanonical Poisson bracket is presented for a nonlinear fluid system that includes reduced magnetohydrodynamics and the Hasegawa-Mima equation as limiting cases. Nonlinear integral invariants for the system are found to be in the kernel of the noncanonical Poisson bracket. This Poisson bracket is given a Lie algebraic interpretation.     

海洋湍流中光波特征参量和短期光束扩展的研究

Nikishov等建立的海洋湍流功率谱模型中,假设了海水有着稳定的分层.但是,实际海水通常不是稳定分层的,温度与盐度的涡流扩散率是不相等的.2017年,Elamassie等建立了考虑这些因素的更合理的海洋湍流功率谱模型.湍流介质中光波空间相干长度等基本特征参量在表征湍流强度和光传输相位校正技术等方面起着重要作用.本文基于Elamassie海洋湍流功率谱模型,重新推导出了海洋湍流中光波结构函数、光波空间相干长度和Fried参数的解析公式,并校验了所得公式的正确性.研究发现：当温度变化引起的光学湍流占主导地位时,Nikishov海洋湍流功率谱模型把湍流强度低估了;当盐度变化引起的光学湍流占主导地位时,Nikishov海洋湍流功率谱模型把湍流强度高估了.基于Elamassie海洋湍流功率谱模型,本文推导出了高斯光束短期光束扩展的半解析公式,并验证了其正确性.研究还表明：海水稳定分层与否,短期光束扩展差异很大.本文研究结果对水下湍流环境中的光通信、成像和传感等应用具有重要意义.     

大气弱湍流下星地光链路衰落特性影响因素分析

研究了弱湍流条件下星地光通信链路的衰落概率、平均衰落次数以及平均衰落时间3个重要参数的统计特性,并通过数值仿真分析了链路天顶角、光波长以及接收机海拔高度对链路衰落特性的影响。结果表明:减小天顶角和提高接收机探测灵敏度可以改善链路的衰落特性;1.55 m激光较0.85 m、1.06 m激光更适合于星地光通信;地面接收机应尽量建在2 000 m以上的高海拔地区。     

Kolmogorov spectra in one-dimensional weak turbulence

In this article, we report the results of our numerical simulation of a one-dimensional modified MMT model, which includes the processes of “one-to-three” wave interactions. We show that this model, with properly chosen parameters, behaves according to the weak-turbulence theory. In particular, it demonstrates the validity of the Kolmogorov spectrum over a wide range of wave numbers.