Two-Frequency Radiative Transfer. II: Maxwell Equations in Random Dielectrics

TL;DR

This paper develops a mathematical framework using two-frequency Wigner distributions to describe electromagnetic wave correlations in complex random media, deriving radiative transfer equations that generalize classical models for various anisotropic and birefringent materials.

Contribution

It introduces the 2f-Wigner distribution and derives new two-frequency radiative transfer equations for complex media, extending classical models to anisotropic and birefringent materials.

Findings

Derived 2f-RT equations for isotropic and birefringent media.

Showed reduction to classical equations like Chandrasekhar's and Fokker-Planck.

Examined specific media such as chiral, uniaxial, and gyrotropic.

Abstract

The paper addresses the space-frequency correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian matrices. The two-frequency Wigner distribution (2f-WD) for polarized waves is introduced to describe the space-frequency correlations and the closed form Wigner-Moyal equation is derived from the Maxwell equations. Two-frequency radiative transfer (2f-RT) equations is then derived from the Wigner-Moyal equation by using the multiple scale expansion. For the simplest isotropic medium, the result coincides with Chandrasekhar's transfer equation. In birefringent media, the 2f-RT equations take the scalar form due to the absence of depolarization. A number of birefringent media such as the chiral, uniaxial and gyrotropic media are examined. For the unpolarized wave in the isotropic medium the 2f-RT equations reduces to the Fokker-Planck equation previously derived in Part I. A similar Fokker-Planck equation is derived from the scalar 2f-RT equation for the birefringent media.