Matrix Exponential FDTD Modeling of Magnetized Graphene Sheet

A novel finite-difference time-domain (FDTD) method is developed for modeling two-dimensional graphene sheet biased with a magnetostatic field. With the use of Dirac Delta function, the graphene sheet is modeled as a polarization current source characterized by an auxiliary equation (AE). Laplace transform and matrix exponential (ME) technique are applied to derive the time-domain mathematical formulations. Numerical experiments are carried out to verify the proposed method in comparison with the analytical results.