Coupled paraxial wave equations in random media in the white-noise regime
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.
Keywords
Cite
@article{arxiv.0903.0449,
title = {Coupled paraxial wave equations in random media in the white-noise regime},
author = {Josselin Garnier and Knut Sølna},
journal= {arXiv preprint arXiv:0903.0449},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AAP543 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)