Analysis of thickness-profiled gratings for oblique incidence using approximate modeling by plane gratings with surface resistance

In this paper, we demonstrate that thickness-profiled metallic gratings placed in a conical mounting can be approximated by a plane grating with surface resistance as a function of the position parameter. As for the method of analysis of thickness-profiled metallic gratings, we apply the multilayered step method, in which the grating region is partitioned into a set of stratified layers having rectangular-profiled gratings, and the flux densities expansion approach. As for the method of analysis for plane gratings with a thickness of zero, a spectral Galerkin method based on the mixed form of current expansions in the spectral and spatial domains is applied to the resistive boundary condition. Both methods are formulated for the three-dimensional scattering problem by linearly and circularly polarized incidence. From a comparison of the numerical results of thickness-profiled and plane metallic gratings for oblique incidence, the limit of the thickness is investigated.