Integral equations and sophisticated moment method in the scattering of the terahertz plane waves of two polarizations by a grating of graphene strips

The scattering and absorption of the H and E-polarized plane waves by a flat grating of free standing graphene strips is studied in the THz frequency range. We use the Kubo theory to characterize the surface impedance of graphene and reduce the boundary-value problems to the equivalent integral equations, hyper-singular on the H-case and log-singular in the E-case. Then we discretize them using the projection to the set of orthogonal polynomials; in the H-case these polynomials are chosen to perform the analytical regularization. In each case this technique guarantees fast convergence and controlled accuracy of computations. Reflectance, transmittance, and absorbance of graphene-strip gratings are studied as a function of various parameters. In the H-polarization regime, we find the surface-plasmon resonances and small-scale Rayleigh anomalies. In the E-polarization case, there are no plasmons however the Rayleigh anomalies become well observable. These results can be considered as reference ones opening way to the accurate modeling of tunable absorbers and frequency selective surfaces based on the periodically patterned graphene layers.