Constrained least squares Fourier modal method for computing scattering from metallic binary gratings

Abstract

In a recent article [J. Opt. Soc. Am. A27, 1694 (2010)], we proposed a rectangular truncation method to mitigate the convergence problems arising from the boundary matching conditions of a binary metallic grating. The proposed method may underestimate the total power in the scattered field for certain grating parameters. In this article, we extend this method to preserve the total power by introducing appropriate constraints and solving the resulting problem as a constrained least squares minimization problem. We provide examples to show that the new method provides a convergent solution for both lossy and lossless binary metallic gratings while preserving the total power.