One-Step Leapfrog HIE-FDTD for Drude Media

A one-step leapfrog hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is developed for Drude dispersive media. The Drude media is modeled through a current source characterized by a semi-implicit auxiliary differential equation. The stability condition is the same as that of conventional leapfrog HIE-FDTD and is determined by the grid cell size along only one direction. The proposed method is used to efficiently investigate the properties of surface plasmon polaritons propagating along a one-atom-thick graphene sheet in low terahertz band with a very fine grid.