High-frequency beam propagation in complex random structures

Ray trajectories, as has been shown in the recently formulated Stochastic Geometrical Theory of Diffraction (SGTD), play an important role in determining the propagation properties of high-frequency wave fields and their paired measures. As in the case of deterministic GTD, the main concern is the construction of high frequency asymptotic propagators relating the values of the random field and its statistical measures at some observation plane to their source (actual or virtual) distributions at the initial plane. We start with the parabolic approximation performed in local coordinates around the curved ray path connecting a source with an arbitrarily located observer in the deterministic background medium. The solution strategy involves the ray-centered coordinates for a typical ray with extraction of the average phase accumulation along that ray. We present a reference wave method to obtain an approximate solution of the parabolic wave equation in a homogeneous background random medium. These solutions are further applied for modeling propagation of a directional beam in a waveguide with randomly varying interior. We show that statistical propagation characteristics can be modeled in terms of stochastic rays and guided modes.