Scattering and absorption of light by nanothickness negative-dielectric strip gratings

The goal of the present paper is to study the problems of plane wave scattering of light by a thin flat grating made of penetrable negative-dielectric (ND) strips or of impenetrable strips covered with ND from one or both sides. The problem formulation involves a set of generalized boundary conditions, relating tangential fields to effective electric and magnetic currents. Accurate numerical solution is based on the Floquet-Rayleigh field expansions, which lead to a coupled pair of dual-series equations for the series coefficients. To determine the unknown coefficients a/sub n/ and b/sub n/, we use two dual sets of boundary conditions that hold on the complimentary subintervals (the strip and the slot) of the elementary period. Further, we make an extraction and analytical inversion of the static part of the full-wave dual-series equations that needs the combined application of the Riemann-Hilbert problem (RHP) technique and an inverse Fourier transform depending on the equation features.