Method of lines for analysis of plane wave scattering by periodic arrays of magnetically-biased graphene strips

In this paper, efficient analysis of the plane wave scattering by periodic arrays of magnetically-biased graphene strips (PAMGS) is performed using the semi-numerical, semi-analytical method of lines (MoL). In MoL, all but one independent variable is discretized to reduce a system of partial differential equations to a system of ordinary differential equations. Since the solution in one coordinate direction is obtained analytically, this method is time effective with a fast convergence rate. In the case of a multi-layered PAMGS, the governing equations of the problem are discretized concerning periodic boundary conditions (PBCs) in the transverse direction. The reflection coefficient transformation approach is then used to obtain an analytical solution in the longitudinal direction. Here, magnetically-biased graphene strips are modeled as conductive strips with a tensor surface conductivity which is electromagnetically characterized with tensor graphene boundary condition (TGBC). The reflectance and transmittance of different multi-layered PAMGS are carefully obtained and compared with those of other methods reported in the literature. Very good accordance between the results is observed which confirms the accuracy and efficiency of the proposed method.