Integral equations in scattering by metasurface formed by multilayer graphene grating inside a grounded dielectric slab

The H-polarized waves scattering and absorption by the metasurface, which consists of multilayer grating of finite number of graphene strips inside a grounded dielectric slab is considered. The problem is formulated in the domain of Fourier transform (spectral domain). The solution is obtained in two steps. At first, the scattering operators of a single graphene grating inside the infinite dielectric medium are obtained from the singular integral equations. At the second stage, the integral equations in the operator form relatively unknown Fourier amplitudes are presented for the whole structure. The kernel-functions of these equations contain singularities at the points, which correspond to the propagation constants of the natural waves of the dielectric waveguide with perfectly electric conducting wall. To eliminate the singularities and to convert the kernel-functions to the regular ones, the regularization procedure is proposed. The approach is meshless, full-wave and convergence is guaranteed by the theorems. The numerical results for the plane wave and natural wave of corresponding dielectric waveguide with perfectly electric conducting wall incidence are presented. Special attention is paid to the excitation of the plasmon and grating-mode resonances. By taking layers with different period and chemical potential, one can control the elevation angle of the main lobe and excitation frequency of the natural waves of dielectric waveguide.