Anderson localization of electromagnetic waves in randomly-stratified magnetodielectric media with uniform impedance

The propagation and the Anderson localization of electromagnetic waves in a randomly-stratified slab, where both the dielectric permittivity and the magnetic permeability depend on one spatial coordinate in a random manner, is theoretically studied. The case where the wave impedance is uniform, while the refractive index is random, is considered in detail. The localization length and the disorder-averaged transmittance of s and p waves incident obliquely on the slab are calculated as a function of the incident angle θ and the strength of randomness in a numerically precise manner, using the invariant imbedding method. It is found that the waves incident perpendicularly on the slab are delocalized, while those incident obliquely are localized. As the incident angle increases from zero, the localization length decreases from infinity monotonically to some finite value. The localization length is found to depend on the incident angle as θ^-4 and a simple analytical formula, which works quite well for weak disorder and small incident angles, is derived. The localization length does not depend on the wave polarization, but the disorder-averaged transmittance generally does.