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

Abstract

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 TE_m → TE_m′, TE_m → TM_m′, TM_m → TM_m′, and TM_m → TE_m′. Comparison with normal-mode analyses for the backscattering problem show agreement for TE_m → TE_m for both the local- and ideal-mode approximations. However, for TM_m → TM_m the results differ when ideal modes are used to describe the incident fields.