Derivation of a one-way radiative transfer equation in random media

Liliana Borcea and Josselin Garnier
Phys. Rev. E 93, 022115 – Published 9 February 2016

Abstract

We derive from first principles a one-way radiative transfer equation for the wave intensity resolved over directions (Wigner transform of the wave field) in random media. It is an initial value problem with excitation from a source which emits waves in a preferred, forward direction. The equation is derived in a regime with small random fluctuations of the wave speed but long distances of propagation with respect to the wavelength, so that cumulative scattering is significant. The correlation length of the medium and the scale of the support of the source are slightly larger than the wavelength, and the waves propagate in a wide cone with an opening angle less than 180, so that the backward and evanescent waves are negligible. The scattering regime is a bridge between that of radiative transfer, where the waves propagate in all directions, and the paraxial regime, where the waves propagate in a narrow angular cone. We connect the one-way radiative transfer equation with the equations satisfied by the Wigner transform of the wave field in these regimes.

  • Received 22 October 2015
  • Revised 5 January 2016

DOI:https://doi.org/10.1103/PhysRevE.93.022115

©2016 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsInterdisciplinary Physics

Authors & Affiliations

Liliana Borcea*

  • Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043, USA

Josselin Garnier

  • Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13, France

  • *borcea@umich.edu
  • garnier@math.univ-paris-diderot.fr

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Issue

Vol. 93, Iss. 2 — February 2016

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