Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings

Abstract

A computationally efficient implementation of rigorous coupled-wave analysis is presented. The eigenvalue problem for a one-dimensional grating in a conical mounting is reduced to two eigenvalue problems in the corresponding nonconical mounting. This reduction yields two n × n matrices to solve for eigenvalues and eigenvectors, where n is the number of orders retained in the computation. For a two-dimensional grating, the size of the matrix in the eigenvalue problem is reduced to 2n × 2n. These simplifications reduce the computation time for the eigenvalue problem by 8–32 times compared with the original computation time. In addition, we show that with rigorous coupled-wave analysis one analytically satisfies reciprocity by retaining the appropriate choice of spatial harmonics in the analysis. Numerical examples are given for metallic lamellar gratings, pulse-width-modulated gratings, deep continuous surface-relief gratings, and two-dimensional gratings.