Coupling of guided modes in thin films with surface corrugation

Abstract

Two guided modes in a grounded, thin, dielectric film waveguide having a periodic corrugation of the interface between the film and the cover can interact selectively in the neighborhood of a particular frequency. Five different theories exist for the investigation of this interaction. The first three are small amplitude theories which assume that the amplitude of the corrugation relative to the thickness of the film is small and the third and the fourth theories are large amplitude theories which do not make such an assumption. In the small amplitude theories, solutions are sought as a perturbation of ideal normal modes and boundary conditions are applied on the average flat surface. The first small amplitude theory makes use of quasioptical considerations and the other two small amplitude theories employ wave-theoretical techniques. All three theories lead to identical coupled mode equations governing the interaction. The first large amplitude theory is based on an expansion in terms of local normal modes and is applicable for a grating with a smooth profile. The second large amplitude theory is applicable for a lamellar grating and it makes use of a model of a repetitively mismatched transmission line. The various intrinsic dephasing mechanisms are explained. The large amplitude theories are able to account for the dephasing effects due to the finite (nonvanishing) depth and the finite (noninfinite) length of the corrugations. Some aspects of passive devices and some theoretical considerations of active devices using corrugated waveguides are reviewed. The transmission line model is able to take into account the end effects. For the mode of operation considered, there are no end effects and the overall contribution of the vertical discontinuities vanish for the lamellar grating.