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We study the propagation of high-frequency electromagnetic waves in randomlyheterogeneous bianisotropic media with dissipative properties. For that purposewe consider randomly fluctuating optical responses of such media withcorrelation lengths comparable to the typical wavelength of the waves. Althoughthe fluctuations are weak, they induce multiple scattering over longpropagation times and/or distances such that the waves end up travelling inmany different directions with mixed polarizations. We derive the dispersionand evolution properties of the Wigner measure of the electromagnetic fields,which describes their angularly-resolved energy density in this propagationregime. The analysis starts from Maxwell's equations with general constitutiveequations. We first ignore the random fluctuations of the optical response andobtain uncoupled transport equations for the components of the Wigner measureon the different propagation modes (polarizations). Then we use a multi-scaleexpansion of the Wigner mesure to obtain the radiative transfer equationssatisfied by these components when the fluctuations are no longer ignored. Theradiative transfer equations are coupled through their collisional parts, whichaccount for the scattering of waves by the random fluctuations and theirpossible changes in polarization. The collisional kernels describing theseprocesses depend on the power and cross-power spectral densities of thefluctuations at the wavelength scale. The overall derivation is based on theinterpretation of Wigner transforms and Wigner measures in terms ofsemiclassical pseudo-differential operators in their standard quantization.

Wigner measures of electromagnetic waves in heterogeneous bianisotropic media