Controlling the Focusing Ability of the Parabolic Graphene Reflector in Free Space at Microwave Frequencies

Abstract

The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on the graphene parameters at microwave frequencies, using the resistive boundary condition for very thin sheets. The scattering is formulated as an electromagnetic boundary-value problem; it is transformed to a singular integral equation that is further treated with the method of analytical regularization (MAR) based on the known solution of the Riemann–Hilbert Problem (RHP). The numerical results are computed by using a Fredholm second-kind matrix equation that guarantees convergence and provides easily controlled accuracy. Compared to THz range, 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. Even though here no dielectric substrate supporting the graphene is considered, the practical realization can also be possible as a thin layer graphene material in GHz range. As we demonstrate, the variation of the chemical potential from 0 to 1 eV can improve the focusing ability within the factor of three. The high accuracy of the used method and the full wave formulation of the problem support our findings.