Plane wave scattering and absorption by flat gratings of impedance strips

The problem of the plane wave scattering by a flat impedance-strip grating located in free space is considered. The formulation involves a set of generalized boundary conditions relating limiting values of the fields to effective electric and magnetic currents. We develop an accurate numerical solution to this problem using the dual series equations and the method of analytical regularization (MAR) based on the main part inversion. This guarantees a fast convergence and controlled accuracy of computations. Reflected, transmitted, and absorbed power fractions as a function of the frequency and the grating parameters are analyzed. Sharp resonances are revealed in the H-polarized scattering near to the grazing of the higher-order modes; these resonances are absent for the perfect electrically conducting strip grating. Low-frequency asymptotics for the reflectance and transmittance in the single-mode regime are presented and compared with numerical solutions.