Focusing ability of electrically large graphene-dielectric-graphene reflector at microwaves analysed using method of analytical regularization.

The studied geometry is a two-dimensional thin dielectric parabolic reflector, sandwiched between graphene. It is illuminated by an E-polarized electromagnetic plane wave. The goal is to determine the focusing ability, scattering and absorption characteristics of such a composite reflector depending on the problem parameters. Two-sided generalized boundary conditions are imposed to the solution of the presented composite reflector. The scattering is formulated as an electromagnetic boundary-value problem; it is reduced to two sets of coupled singular integral equations. The first one is regularized by Fourier inversion procedure and second one is subjected to analytical regularization based on the known Riemann-Hilbert problem technique. The resultant matrix is in a block form and it is of a Fredholm second-kind nature that guarantees convergence and accuracy. The numerical results are computed by using this formulation and the physics of the problem is studied in terms of problem parameters. When the relative dielectric constant and thickness of the composite reflector are chosen as small as possible, in microwaves, the scattering pattern of reflector and the field level at geometrical focus can be controlled in a wide range by adjusting the chemical potential of graphene. This means that the field level increases from small value to a level of near PEC reflector case. In this case it is seen that the results are obtained in the presence of a dielectric layer opposite to the single graphene reflector without dielectric. The details will be discussed in the numerical results. Highly accurate data is obtained from the method and the full wave formulation of the problem supports our findings.This article is part of the theme issue 'Analytically grounded full-wave methods for advances in computational electromagnetics'.