Modeling Graphene-Based THz Devices With an Improved Surface Boundary Condition in Leapfrog FDTD Scheme

Finite-difference time-domain (FDTD) method is an efficient full-wave numerical method for simulating graphene-based optoelectronic devices. The previous investigation on modeling graphene in leapfrog FDTD methods shows that dispersive errors increase with tuning up the chemical potential of graphene. In this article, a new implementation of graphene's surface boundary condition (SBC) is proposed to reduce the dispersive errors in the leapfrog FDTD update scheme. To achieve lower dispersive errors, the graphene layer is positioned exactly on the grid lattice of transverse magnetic fields, and each of the transverse magnetic fields is split into two fields on the two sides of graphene. The split magnetic fields are updated using forward and backward differences in the electric fields on the normal direction of graphene plane. Numerical analysis shows that the maximum dispersive error of the proposed graphene model is reduced to only 37.5% of the other publicly reported graphene models in the leapfrog FDTD update scheme. However, the CPU time cost keeps almost the same as the other graphene models. The proposed implementation of the graphene SBC model also shows less CPU time consumption compared with the graphene SBC model which requires to solve a linear system and breaks the leapfrog FDTD update scheme, while the maximum numerical error is the same. The proposed graphene model is applied to simulate graphene terahertz (THz) surface plasmon resonances and modulators to demonstrate the applications in accurately modeling and analyzing graphene-based THz devices.