Finite-Difference Beam Propagation Method for Graphene-Based Devices

We propose a novel finite-difference beam propagation method capable of dealing with the discontinuity of the tangential component of the magnetic field induced by bi-dimensional graphene layers, which can be arbitrarily placed within dielectric media. In stark contrast with conventional numerical solvers, this approach does not require a discretization step as small as a fraction of the atomic thickness of graphene, allowing ultrafast simulation times. The validity of the method is proved by propagating the plasmonic supermodes of two coupled graphene layers, and the evaluated beat length exhibits excellent agreement with respect to analytical results.