A Unified View of DI- and ETD-FDTD Methods for Drude Media

A unified view of direct-integration (DI) and exponential-time-differencing (ETD) methods to incorporate Drude media, such as isotropic plasma and microwave graphene, into finite-difference time-domain (FDTD) simulators is provided. To this end, the Drude constitutive relation is expressed in integral form and the DI integrators are obtained by applying quadrature rules. Analogously, the ETD integrators are obtained by starting from the variation of constants formula and applying the same quadrature rules as in the DI case. This approach allows one to directly compare the two families of methods. In addition, the accuracy of each integrator is discussed and the stability condition of the resulting FDTD schemes is derived in exact closed form by applying the von Neumann method.