Transverse Anderson localization of evanescent waves propagating in randomly layered media

We study theoretically the transverse Anderson localization of light in the simplest geometry, where the p-polarized wave propagates along the layers in the randomly stratified dielectric and evanesces exponentially in the direction across the layers. In this case, there exist two reasons for the localization of the wave in the direction transverse to its propagation: the usual evanescent wave confinement and the Anderson mechanism related to the randomness of the spatial distribution of permittivity. We solve the problem using the retarded-Green-function formalism in the Born approximation and show that, for fixed values of the wave frequency omega and wavenumber q, the random inhomogeneity results in the weakening of the wave localization. In the case of the surface plasmon-polaritons (SPPs) propagation, the Anderson mechanism changes the dispersion law for SPPs, moving the dispersion curves away from the light line. Therefore, the localization depth varies in different ways when increasing the disorder, depending on which of the values, wave vector q or frequency omega, is fixed. Namely, the localization depth increases for given q, but it decreases for given omega.