Abstract

We have derived analytical, approximate solutions to the rigorous coupled-wave equations.¹ The expression found for the diffracted wave amplitudes have been applied to unslanted guided-mode resonance grating filters to predict the resonance line shape and location. For a single-mode waveguide grating at normal incidence, both symmetric (±1 diffracted orders) evanescent waves are retained along with the forward- and backward propagating zero orders such that an effective three-wave solution is obtained. For non normal incidence and dominant coupling to the +1 evanescent wave (with the −1 order coupling being negligible), a two-wave solution is found that is similar to the two-wave result of Kong.² Both the three-wave solution and the two-wave solution have been tested against numerical solutions using the full rigorous coupled-wave theory and excellent agreement found. The analytical solutions expedite calculations of the characteristics of waveguide-grating filters and may provide some additional insights into their properties. This work was partly supported by the Texas Advanced Technology Program under grant no. 003656-023 and by the National Science Foundation under grant no. ECS-9120856.

© 1993 Optical Society of America