Full-Wave Analysis of the Shielding Effectiveness of Thin Graphene Sheets with the 3D Unidirectionally Collocated HIE-FDTD Method

Graphene-based electrical components are inherently multiscale, which poses a real challenge for finite-difference time-domain (FDTD) solvers due to the stringent time step upper bound. Here, a unidirectionally collocated hybrid implicit-explicit (UCHIE) FDTD method is put forward that exploits the planar structure of graphene to increase the time step by implicitizing the critical dimension. The method replaces the traditional Yee discretization by a partially collocated scheme that allows a more accurate numerical description of the material boundaries. Moreover, the UCHIE-FDTD method preserves second-order accuracy even for nonuniform discretization in the direction of collocation. The auxiliary differential equation (ADE) approach is used to implement the graphene sheet as a dispersive Drude medium. The finite grid is terminated by a uniaxial perfectly matched layer (UPML) to permit open-space simulations. Special care is taken to elaborate on the efficient implementation of the implicit update equations. The UCHIE-FDTD method is validated by computing the shielding effectiveness of a typical graphene sheet.