Current sheets in the Discontinuous Galerkin Time-Domain method: an application to graphene

We describe the treatment of thin conductive sheets within the Discontinuous Galerkin Time-Domain (DGTD) method for solving the Maxwell equations and apply this approach to the efficient computation of the optical properties of graphene-based systems. In particular, we show that a thin conductive sheet can be handled by incorporating the associated jump conditions of the electromagnetic field into the numerical flux of the DGTD approach. This results in a flexible and efficient numerical scheme that can be applied to a number of systems. Specifically, we show how to treat individual graphene sheets on substrates as well as finite stacks of alternating graphene and dielectric layers by modeling the dispersive and dissipative properties of graphene via a two-term critical-point model for its electrostatically doped conductivity.