Abstract

This chapter presents a numerical method for simulating the electromagnetic field interaction with single-layer graphene. The numerical approach is the finite-difference time-domain (FDTD) method. The linear electric material response of graphene is dispersive and demands special care for implementation using a time-domain method. Graphene’s electric conductivity arises from two physical mechanisms: (1) intraband electronic transitions and (2) interband electronic transitions. The intraband electronic transitions are well described by a Drude-type frequency model that is straightforward to implement in FDTD using the auxiliary differential equation (ADE) method. The second (interband) contribution does not have a form directly amenable to the ADE technique. This chapter presents a fitting approach based on Padé interpolation that facilitates incorporation of the interband conductivity term into the FDTD method using ADE. The method is used to model the surface plasmon polariton modes of finite-width graphene waveguides. Highly doped graphene is modeled, so that the surface plasmon modes propagate at near-infrared wavelengths. Both the propagation loss and waveguide dispersion are provided.