Efficient Implementation of Rigorous Couple-Wave Analysis for Surface-ReliefGratings

摘要

A computationally efficient implementation of rigorous coupled wave analysis ispresented. 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 X 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 X 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.