Fourier-matching pseudospectral modal method for diffraction gratings: comment

Abstract

Recently two variants of a pseudospectral modal method were developed for analyzing lamellar diffraction gratings: [J. Lightwave Technol. 27, 5151 (2009)] and [J. Opt. Soc. Am. A 28, 613 (2011)]. Both of them divide the computational domain into nonoverlapping subdomains and replace the spatial derivative in the Helmoltz equation by a differentiation matrix at the Chebyshev collocation points. The authors of the second reference claim that their method is more robust and accurate because they match the Fourier coefficient at the interfaces between the layers and drop some computed eigenmodes. We challenge these two ideas. Instead, we numerically demonstrate that by keeping all computed eigenmodes and by also numerically computing eigenmodes in homogeneous regions, the pseudospectral method performs better.