Unconditionally Stable One-Step Leapfrog ADI-FDTD for Dispersive Media

A novel unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time domain is developed for modeling dispersive media. In contrast to previous approaches, the proposed method uses a vector fitting technique to incorporate various types of dispersive media through electric polarization terms governed by an auxiliary differential equation (ADE). Moreover, a semi-implicit finite-difference scheme is applied to the ADE to maintain the unconditional stability of the method. The stability is verified analytically by von Neumann analysis with the Jury criterion. Numerical experiments are carried out to illustrate the stability and accuracy. The proposed method is used to investigate surface plasmon polaritons (SPPs) on graphene sheets biased by an electrostatic field.