Method of Analytical Regularization Based on the Static Part Inversion in the H-Wave Scattering by a PEC Strip Grating on Top of a Dielectric Substrate

Considered is the plane H-polarized wave scattering from an infinite flat grating of perfect electrically conducting strips, placed on the interface of a dielectric slab. We reduce this problem to a dual series equation for the complex amplitudes of the Floquet spatial harmonics. Then we perform analytical regularization of this equation, based on the inversion of the static part of the problem with the aid of the Riemann-Hilbert Problem. This yields a Fredholm second-kind infinite matrix equation, numerical solution of which has a guaranteed convergence. We perform numerical experiments demonstrating how the rate of convergence depends on the thickness and dielectric permittivity of the slab.