Simulation of Multilayer Graphene–Dielectric Metamaterial by Implementing SBC Model of Graphene in the HIE-FDTD Method

An improved FDTD method is introduced to propose a new numerical simulation approach for a multilayer graphene-dielectric metamaterial (MGDM) structure, which is a promising effective medium with tunable constitutive parameters in terahertz photonic devices. We applied the hybrid implicit-explicit FDTD (HIE-FDTD) method, which is a popular method for analyzing dimensionally non-uniform structures with fine features in one or two directions to model the MGDM structure. Considering the ignorable atomic thickness of graphene layers in the structure, we increased the fine dimension of the mesh to the scale of the dielectric layer using the surface boundary condition (SBC) method for modeling the graphene sheets; this means that we integrated the SBC model of graphene in the HIE-FDTD method. Therefore, the thickness limitations of both graphene and dielectric layers can be eliminated in the computational resources. Accordingly, we implemented the introduced method in a proposed tunable graded index (GRIN) lens structure based on the MGDM and achieved valid results.