Scattering of guided waves by surface periodic gratings for arbitrary angles of incidence: perturbation field theory and implications to normal-mode analysis

A first-order perturbation theory describing the deflection of guided optical waves by sinusoidal surface corrugations on a slab waveguide is presented. The wave equation is satisfied everywhere in space, and the tangential fields are continuous across all interfaces to order δ0k, where k is the optical wave vector and δ0 is the maximum surface displacement. Analytical expressions are derived for synchronously generated normal modes for the geometries TEm → TEm′, TEm → TMm′, TMm → TMm′, and TMm → TEm′. Comparison with normal-mode analyses for the backscattering problem show agreement for TEm → TEm for both the local- and ideal-mode approximations. However, for TMm → TMm the results differ when ideal modes are used to describe the incident fields.