Rigorous coupled-wave analysis of planar-grating diffraction

TLDR

Grating fringes can be oriented slanted or unslanted relative to the grating surfaces. A rigorous coupled‑wave method based on a state‑variable representation yields a matrix formulation that unifies planar‑grating diffraction analysis and is benchmarked against modal and approximate theories, emphasizing the necessity of higher‑order waves and boundary diffraction for accurate predictions. The method delivers accurate diffraction characteristics for general slanted gratings and quantifies the errors introduced by approximate theories.

Abstract

A rigorous coupled-wave approach is used to analyze diffraction by general planar gratings bounded by two different media. The grating fringes may have any orientation (slanted or unslanted) with respect to the grating surfaces. The analysis is based on a state-variables representation and results in a unifying, easily computer-implementable matrix formulation of the general planar-grating diffraction problem. Accurate diffraction characteristics are presented for the first time to the authors' knowledge for general slanted gratings. This present rigorous formulation is compared with rigorous modal theory, approximate two-wave modal theory, approximate multiwave coupled-wave theory, and approximate two-wave coupled-wave theory. Typical errors in the diffraction characteristics introduced by these various approximate theories are evaluated for transmission, slanted, and reflection gratings. Inclusion of higher-order waves in a theory is important for obtaining accurate predictions when forward-diffracted orders are dominant (transmission-grating behavior). Conversely, when backward-diffracted orders dominate (reflection-grating behavior), second derivatives of the field amplitudes and boundary diffraction need to be included to produce accurate results.