Space-frequency correlation of classical waves in disordered media: high-frequency and small scale asymptotics

TL;DR

This paper develops a two-frequency radiative transfer theory for classical waves in disordered media, deriving a Fokker-Planck-like equation for the space-frequency correlation and analyzing its asymptotic behavior at high frequencies and small scales.

Contribution

It introduces a rigorous 2f-RT framework with a closed-form equation for the 2f-Wigner distribution, revealing scaling laws and sub-transport-mean-free-path behavior.

Findings

Derivation of a Fokker-Planck-like equation for 2f-WD

Scaling laws for spatial spread, coherence length, and bandwidth

Analytical solution for sub-transport-mean-free-path regime

Abstract

Two-frequency radiative transfer (2f-RT) theory is developed for geometrical optics in random media. The space-frequency correlation is described by the two-frequency Wigner distribution (2f-WD) which satisfies a closed form equation, the two-frequency Wigner-Moyal equation. In the RT regime it is proved rigorously that 2f-WD satisfies a Fokker-Planck-like equation with complex-valued coefficients. By dimensional analysis 2f-RT equation yields the scaling behavior of three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. The sub-transport-mean-free-path behavior is obtained in a closed form by analytically solving a paraxial 2f-RT equation.