Boundary Integral Equations Approach for a Scattering Problem of a TE-Wave on a Graphene-Coated Slab

This paper focuses on a transmission problem describing the scattering of a TE-wave on a slab having an absolutely conducting wall at the bottom and covered with graphene at the top, accounting for the optical nonlinearity of graphene. This problem is reduced to a nonlinear hypersingular boundary integral equation defined on R. To find an approximate solution to this equation, we develop a novel mathematical approach that combines the collocation method using Chebyshev series to represent a solution (it allows to calculate hypersingular integrals analytically) with an iterative scheme (it allows to account for the nonlinearity of graphene). Using this approach, we numerically simulate the scattering of TE-wave at 3 THz by a ten-micron graphene-coated slab filled with silica. It is shown that by tuning the chemical potential of graphene, one can modulate both the phase and amplitude of the reflected wave. The presented simulation results also demonstrate the effect of the nonlinearity of graphene on the reflected wave.