Improved convergence in the analysis of thin metallic gratings with thickness profiles

Abstract

.[1] A combination of the Fourier series expansion method and the multilayered step method is applied to analysis of the scattering problem by a thin metallic grating with a thickness profile. The extremely large permittivity profiles of metallic gratings may affect accuracy of calculations adversely. The convergence of the Fourier expansion method is improved using the spatial harmonics of flux densities instead of electromagnetic fields normal to the surface of a metallic grating. In using the multilayered step method, the scheme used to partition the grating region and the distribution function of dielectric constant within each layer are examined.

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

“…In the following calculations of thickness‐profiled gratings, by the convergence of solutions and the computational time, the spatial harmonic expansion terms are truncated to 2 M + 1 = 151 and the number of partitioned layers is chosen as L = 32. In the multilayered step method, the partitioning step size of the grating smaller in lower layers and the step distribution function were chosen from the results of planar mounting analysis [ Wakabayashi et al , 2003].…”

“…To resolve the problem in the TM case, we present a new method involving flux densities expansion. In addition, to improve convergence in the analysis of thin gratings with various thickness profiles, we investigate an effective scheme for partitioning gratings [ Wakabayashi et al , 2003].…”

“…Some of the reasons for this are that conical mounting analyses require complicated formulations and large calculations, and the convergence of the solutions for a thickness‐profiled metallic grating is even slower at a radio wavelength in addition to when it is in a conical mounting. In this paper, our previous formulations using flux densities expansion for a thickness‐profiled grating of two‐dimensional scattering problem [ Wakabayashi et al , 2003] are extended to include a three‐dimensional scattering problem and circular polarization, and we intend to demonstrate that thin metallic gratings with various thickness profiles placed in a conical mounting can be approximated by a plane grating with surface resistance as a function of the position parameter parallel to the boundary. In order to show the limits of the thickness of metallic gratings that can be disregarded during analyses, we consider circular polarized incidence represented as the combination of two linearly polarizations in addition to linear polarized incidence.…”

“…As for the method of analysis for thickness‐profiled gratings, a combination of the multilayered step method, in which the grating region is partitioned into multilayers having rectangular‐profiled gratings, and the flux densities expansion approach based on the matrix eigenvalue calculations are applied to the gratings for oblique incidence. 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 [ Wakabayashi et al , 2003; Sumitani et al , 2003] is applied to the resistive boundary condition for oblique incidence. For clarity, both methods are formulated for the same analytical model on the three‐dimensional scattering problem by linear and circular polarizations, and by using eigenvectors of unified derivations for all regions of uniform and grating regions.…”