Approximate analysis of dielectric gratings with multiple reflection by boundary

Abstract

Approximate two‐wave analysis of planar dielectric gratings with boundary reflection is presented. The analysis is derived from previous rigorous theory [2] by neglecting the higher‐order waves and the second derivatives of the field amplitudes but taking into account the effect of boundary reflection. The pulsation phenomena of the diffraction efficiency due to the multiple reflection usually ignored in most of the approximate analysis can be given clearly by simple 2 × 2 matrix calculations for practical gratings of small index‐modulation type. The analysis can be applied not only to isotropic but also to anisotropic gratings so long as incident waves and only one diffracted wave play a dominant role. Numerical results are given and are compared with rigorous results.