Faraday rotation in a disordered medium

The Faraday rotation angle $\ensuremath{\Theta}$ is calculated in a diffusive regime on a three-dimensional disordered slab. It is shown that $\mathrm{tan}\phantom{\rule{0.16em}{0ex}}\ensuremath{\Theta}$ is (i) an oscillating function of the magnetic field or the medium's internal properties, and (ii) proportional to the ratio of the inelastic mean-free path ${l}_{\mathrm{in}}$ to the mean-free path $l$, that is, to the average number of photon scatterings. The maximum rotation is achieved at frequencies when the photon's elastic mean-free path is minimal. We have obtained the rotation angle of backscattered light taking into account the maximally crossed diagrams. The latter leads to an ellipticity in the backscattered wave that can serve as a precursor of weak localization. The critical strength of the magnetic field is ${B}_{c}\ensuremath{\sim}{g}_{c}\ensuremath{\sim}\ensuremath{\lambda}/l$ beyond which rotation in the backscattered wave disappears. The traversal time of an electromagnetic wave through the slab is estimated in a diffusive regime. The disorder enhanced the traversal time by an additional factor ${l}_{\mathrm{in}}/l$ in comparison with a free light propagation time. Comparison with the experimental data is carried out.