Modeling of Magnetized Graphene From Microwave to THz Range by DGTD With a Scalar RBC and an ADE

Abstract

This paper presents a discontinuous Galerkin time-domain (DGTD) method for the transient analysis of magnetized graphene from the microwave to terahertz (THz) frequencies. By considering the atom thick graphene layer as an infinitely thin conductive sheet with finite surface conductivity, a frequency-dependent anisotropic resistive boundary condition (RBC) is obtained. Based on this RBC, the direct volumetric discretization of graphene layer is avoided. Instead of directly deriving the numerical flux for DGTD considering the presence of this anisotropic and dispersive RBC, an auxiliary surface polarization current governed by a first-order time-dependent partial differential equation (PDE) is introduced over the graphene with the purpose to obtain an isotropic and simultaneously nondispersive RBC. In this way, the new formulated numerical flux expression derived from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Rankine–Hugoniot jump relations</i> is isotropic, and no time-domain convolution is involved in the finalized matrix equations. To verify the applicability and accuracy of the proposed algorithm, the Faraday rotation and the surface plasmon resonance of a plane wave through magnetically biased graphene are investigated. For open-region scattering problems, a hybrid DGTD and time-domain boundary integral (TDBI) method is applied to rigorously truncate the computational domain.