Coupled wave analysis of obliquely incident waves in thin film gratings

The problem of a guided wave obliquely incident on a grating etched in a thin film guide is considered. Two-dimensional coupled wave equations for the incident and reflected beams are derived for the cases of TE-TE, TE-TM, and TM-TM coupling. Two methods, a ray optic approximation and a coupled beam method, are proposed for the numerical solution of the coupled wave equations. Both methods are illustrated by a number of calculated examples.