H-polarized plane-wave scattering by a PEC strip grating on top of a dielectric substrate: analytical regularization based on the Riemann-Hilbert Problem solution

Abstract

ABSTRACTWe consider the H-polarized plane wave scattering from an infinite flat grating of perfectly 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. Numerical results obtained demonstrate how the rate of convergence depends on the geometrical parameters and then concentrate on the resonance effects in the reflection and transmission. We reveal and discuss ultra-high-Q resonances on the lattice modes of such a composite grating, overlooked in earlier studies.