Coupled paraxial wave equations in random media in the white-noise regime

TL;DR

This paper derives coupled paraxial wave equations in a random medium within the white-noise regime, analyzing reflection and transmission phenomena using stochastic Schrödinger equations and Wigner distributions.

Contribution

It introduces a new coupled system of random Schrödinger equations for wave propagation in random media in the white-noise, paraxial regime, linking wave statistics to transport equations.

Findings

Derived coupled stochastic Schrödinger equations for wave fields.

Established transport equations for Wigner distributions and autocorrelations.

Analyzed enhanced backscattering phenomenon using the Wigner distribution.

Abstract

In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schr\"{o}dinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation functions are determined by a closed system of transport equations. The Wigner distribution is then used to describe the enhanced backscattering phenomenon for the reflected field.