Two-frequency radiative transfer: Maxwell equations in random dielectrics

Abstract

The paper addresses the space-frequency correlations of electromagnetic waves in general random, bianisotropic 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 are 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 chiral, uniaxial, and gyrotropic media are examined. For the unpolarized wave in an isotropic medium the 2f-RT equations reduces to the 2f-RT equation previously derived in part I of this research [J. Opt. Soc. Am. A24, 2248 (2007)]. A similar Fokker-Planck-type equation is derived from the scalar 2f-RT equation for the birefringent media.