论文标题
与远程相关性的随机介质中的近后波传播
Paraxial wave propagation in random media with long-range correlations
论文作者
论文摘要
我们使用随机扰动的折射指数研究近端波方程，该指数可以模拟湍流介质中波束的传播。随机扰动是一个固定和各向同性过程，具有一般形式的协方差，或者可能是可集成的。我们将注意力集中在非整合情况上，该情况与具有远程相关性的随机扰动相对应，这与通过多云湍流气氛传播有关。该分析是在向前散射近似的高频方向上进行的。它揭示了波场的随机化是多尺度的：波前的行进时间是在繁殖的短距离内随机分配的，并且可以通过分数的布朗运动来描述。在随机行进时间范围内观察到的波场会受到长距离的随机扰动的影响，并且由标准布朗尼场驱动的Schroedinger-type方程描述。我们使用这些结果来量化散射如何导致波场的空间和光谱成分以及源发出的脉冲的变形。这些是通过湍流气氛与脉冲激光束进行成像和可用空间通信等应用的重要问题。我们还将结果与光学文献中使用的结果进行了比较，该结果基于湍流的Kolmogorov模型。
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of the covariance that may be integrable or not. We focus attention mostly on the non-integrable case, which corresponds to a random perturbation with long-range correlations, that is relevant for propagation through a cloudy turbulent atmosphere. The analysis is carried out in a high-frequency regime where the forward scattering approximation holds. It reveals that the randomization of the wave field is multiscale: The travel time of the wave front is randomized at short distances of propagation and it can be described by a fractional Brownian motion. The wave field observed in the random travel time frame is affected by the random perturbations at long distances, and it is described by a Schroedinger-type equation driven by a standard Brownian field. We use these results to quantify how scattering leads to decorrelation of the spatial and spectral components of the wave field and to a deformation of the pulse emitted by the source. These are important questions for applications like imaging and free space communications with pulsed laser beams through a turbulent atmosphere. We also compare the results with those used in the optics literature, which are based on the Kolmogorov model of turbulence.
