Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media

Abstract

We study theoretically the propagation and the Anderson localization of p-polarized electromagnetic waves incident obliquely on randomly stratified dielectric media with weak uncorrelated Gaussian disorder. Using the invariant imbedding method, we calculate the localization length and the disorder-averaged transmittance in a numerically precise manner. We find that the localization length takes an extremely large maximum value at some critical incident angle, which we call the generalized Brewster angle. The disorder-averaged transmittance also takes a maximum very close to one at the same incident angle. Even in the presence of an arbitrarily weak disorder, the generalized Brewster angle is found to be substantially different from the ordinary Brewster angle in uniform media. It is a rapidly increasing function of the average dielectric permittivity and approaches 90° when the average relative dielectric permittivity is slightly larger than two. We make a remarkable observation that the dependence of the generalized Brewster angle on the average dielectric permittivity is universal in the sense that it is independent of the strength of disorder. We also find, surprisingly, that when the average relative dielectric permittivity is less than one and the incident angle is larger than the generalized Brewster angle, both the localization length and the disorder-averaged transmittance increase substantially as the strength of disorder increases in a wide range of the disorder parameter. In other words, the Anderson localization of incident p waves can be weakened by disorder in a certain parameter regime.