Efficient Dispersive GSTC-FDTD Algorithm Using the Drude Dispersion Model

Metasurfaces are artificial sheets with sub-wavelength thickness and they are two-dimensional equivalents of metamaterials. The generalized sheet transition conditions (GSTCs) have been recently proposed for electromagnetic analysis of the metasurfaces. In GSTCs, the metasurface is generally modeled as a sheet with zero-thickness. However, the conventional finite-difference time-domain (FDTD) method is not straightforwardly applied to analyze electromagnetic wave propagation in the metsurface by harnessing GSTCs because GSTCs exhibit electric and magnetic discontinuities. Alternatively, the GSTC-FDTD formulation is highly suitable for analyzing the electromagnetic properties of metasurfaces by introducing electric and magnetic virtual grids. Meanwhile, metasurfaces can be realized by using 2-D materials such as black phosphorus and thus the dispersion characteristics of metasurfaces should be considered. In this work, we propose an efficient dispersive GSTC-FDTD algorithm by employing the Drude dispersion model. Moreover, for the first time, the numerical surface susceptibility inherent to the dispersive GSTC-FDTD formulation is derived and its numerical accuracy is investigated. Numerical examples illustrate high efficiency of the proposed Drude-dispersive GSTC-FDTD algorithm.