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

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.