In this communication, an improved direct-integration auxiliary differential equation (IM-DI-ADE) scheme is introduced for incorporating graphene's Drude dispersion into the finite difference time domain (FDTD) simulations in the GHz and THz frequency ranges. Stability analysis is performed and it is shown that the time-step stability limit of the presented IM-DI-ADE scheme coincides with the conventional non-dispersive FDTD Courant-Friedrichs-Lewy (CFL) limit and removes the additional stability stringent of the classical DI-ADE counterpart. In addition, the presented scheme does not increase the memory storage overhead. Numerical dispersion analysis is also addressed and it is shown that the presented scheme provides high accuracy. The formulation is validated by numerical tests that investigate the tunneling of electromagnetic wave through a graphene sheet and the existence of the surface plasmon polaritons (SPPs) waves created at the interface between the graphene sheet and a dielectric material.

在此通信中，引入了一种改进的直接积分辅助微分方程（IM-DI-ADE）方案，用于将石墨烯的Drude色散合并到GHz和THz频率范围内的时差有限域（FDTD）仿真中。进行了稳定性分析，结果表明，所提出的IM-DI-ADE方案的时间步长稳定性极限与常规的非分散FDTD Courant-Friedrichs-Lewy（CFL）极限一致，并且消除了经典的附加稳定性DI-ADE同行。另外，所提出的方案不增加存储器存储开销。数值色散分析也得到解决，并且表明所提出的方案提供了高精度。