Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended

TL;DR

This paper develops a two-frequency Wigner distribution approach to analyze the coherence of polarized electromagnetic waves in complex disordered media, deriving new radiative transfer equations applicable to various anisotropic and birefringent materials.

Contribution

It introduces a simplified 2f-Wigner distribution and derives closed-form Wigner-Moyal and radiative transfer equations for polarized waves in complex media, extending previous models to more general anisotropic cases.

Findings

Derived 2f-RT equations for coherence matrices in complex media.

Simplified the 2f-Wigner distribution for polarized waves.

Applied the framework to isotropic, chiral, uniaxial, and gyrotropic media.

Abstract

The paper addresses the two-point correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian, positive- or negative-definite matrices. A simplified version of the two-frequency Wigner distribution (2f-WD) for polarized waves is introduced and the closed form Wigner-Moyal equation is derived from the Maxwell equations. In the weak-disorder regime with an arbitrarily varying background the two-frequency radiative transfer (2f-RT) equations for the associated $2\times 2$ coherence matrices are derived from the Wigner-Moyal equation by using the multiple scale expansion. In birefringent media, the coherence matrix becomes a scalar and the 2f-RT equations take the scalar form due to the absence of depolarization. A paraxial approximation is developed for spatialy anisotropic media. Examples of isotropic, chiral, uniaxial and gyrotropic media are discussed.