Hypersingular integral equations in H-Polarized wave scattering by a multi-layer structure of semi-Infinite zero-thickness impedance strip gratings in free space

This paper provides a rigorous analysis of the H-polarized plane wave diffraction by a multilayer strip grating, where each layer consists of a semi-infinite array of infinitely thin impedance strips. The grating is placed in free space. We use a full-wave meshless method based on hypersingular integral equations and a Nystrom-type algorithm of discretization. The scattered field is represented as a sum of the field of currents on the infinite perfectly periodic grating and a correction field induced with the edge. Both these fields are found from the hypersingular integral equations. We present numerical results for both perfectly electric conducting (PEC) strips and graphene strips, studying their near-field and far-field behaviour. Our analysis of the end-effect reveals clear maxima in the electromagnetic response near natural wave resonances of the multilayer structure, the Rayleigh-Wood (RA) anomaly, and plasmon resonances.