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

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

2009-03-03

arxiv.org/abs/0903.0449v1

Annals of Applied Probability 2009, Vol. 19, No. 1, 318-346

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP543 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP543

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.

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