Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity

TLDR

The paper presents a numerically stable method for analyzing diffraction gratings of arbitrary profile, depth, and conical mounting. The method builds on the classical modal approach, approximating arbitrary profiles with a stack of lamellar gratings and propagating modal fields through layers using an R‑matrix algorithm. The approach eliminates the numerical instability of conventional algorithms, and numerical examples demonstrate accurate diffraction efficiencies for dielectric and metallic gratings across a wide depth range, with reported convergence and computation times.

Abstract

A numerically stable method is presented for the analysis of diffraction gratings of arbitrary profile, depth, and in conical mountings. It is based on the classical modal method and uses a stack of lamellar gratpermittivity to approximate an arbitrary profile. A numerical procedure known as the R-matrix propagation aling layers gorithm is used to propagate the modal fields through the layers. This procedure renders the implementation of this new method completely immune to the numerical instability that is associated with the conventional algorithm. Numerical examples including diffraction efficiencies of both dielectric and metallic propagation gratings of depths that range from subwavelength to hundreds of wavelengths are presented. Information about the convergence and the computation time of the method is also included.