Reflection and transmission characteristics of a slab with periodically varying surfaces

Using a plane wave spectral decomposition of the relevant electromagnetic (EM) fields and the T-matrix solution philosophy, a T-matrix is formulated which completely characterizes the EM response of an infinite material plate bounded by two homogeneous half-spaces, the two interfaces being periodically rough. Individual T-matrices for either of the two periodic bimaterial interfaces are used in this derivation. Using the computed results, the anomalies in the scattering response of the rough slab are explained in terms of reflectionless and transmissionless modes, the Brewster angle, and the conditions for propagation or evanescence of a given plane wave mode.