Enhanced and specular backscattering in random media

We study scalar waves probing a heterogeneous medium whose parameters are modeled in terms of a statistically isotropic random field. The medium is terminated by an oblique interface at one end (the bottom) and pressure release type boundary conditions at the other end (the top). The tilt of the (bottom) interface is relatively small so that the dominant contributions to the wave field are confined to a paraxial tube. This study generalizes the basic formulation in terms of Itô-Schrödinger equations in a one-dimensional deterministic background, describing the macrostructure, to the one in which the background is more complicated. It provides the first step toward the analysis of scattered waves in general background media modulated by a random microstructure. We discuss in detail the enhanced backscattering phenomenon or weak localization in this setting, with a tilted interface imbedded in the random medium, and find that the backscattering cone does not depend on the tilt. We also find that the enhanced backscattering phenomenon is not affected by the replacement of a specular interface with a diffusive interface.