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

TL;DR

This paper derives a one-way radiative transfer equation for wave intensity in random media, bridging radiative transfer and paraxial regimes, accounting for cumulative scattering over long distances.

Contribution

It introduces a first-principles derivation of a one-way wave intensity equation in random media, applicable to a wide cone of propagation angles.

Findings

Derivation of a one-way radiative transfer equation from first principles.

The equation applies in a regime with small fluctuations and long propagation distances.

Connection established between this equation and existing wave equations in related regimes.

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 opening angle less than $180^o$, 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 transport equation with the equations satisfied by the Wigner transform of the wave field in these regimes.