Detailed stability analysis of the Z-transform FDTD implementation of electrically thin Drude-like graphene layer

Abstract

Recently, the Z-transform theory has been incorporated into the finite difference time domain (FDTD) algorithm to model electrically thin Drude-like graphene layer. In this approach, the Graphene dispersion was written in the discrete time domain by discretizing the electric flux D-E constitutive relation. Although this implementation retains the natural zero pole of Drude model, it is found in this paper that its stability is a function of the Graphene parameters which introduces additional stability stringent criterion other than the standard Courant Friedrichs Lewy (CFL) constraint. Alternative implementation that employs the bilinear transformation (237) technique is also introduced in this paper to retain the CFL stability limit. The validity of the obtained stability constraints is shown numerically by studying electromagnetic wave propagation through an infinite thin Graphene sheet. Finally, the accuracy of the stability improved BT-FDTD implementation is studied by investigating the transmission coefficient for normally incident plane wave through an infinite Graphene layer.