Degenerate optical memory effect in dielectric films with randomly rough surfaces

By means of perturbation theory we calculate the angular intensity correlations of linearly polarized electromagnetic waves scattered from a thin dielectric film deposited on a planar perfectly conducting substrate. The illuminated surface is a one-dimensional, randomly rough surface with a power spectrum given either by a Gaussian, or by a rectangle defined to enhance the coupling into guided waves. The dielectric film supports, at least, two guided waves in the absence of the roughness that have distinct wave numbers at the frequency v of the incident wave. We analyze the angular dependence of the optical memory effect: In addition to its two well known peaks, we demonstrate that, due to degeneracy of the excitation of guided waves, there appear two pairs of peaks symmetrically located about the former absolute maxima at positions related to the difference between the guided wave numbers. This degenerate memory effect is shown to be a multiple scattering effect. @S0163-1829~97!04723-1#