Accurate Time-Domain Modeling of Arbitrarily Shaped Graphene Layers Utilizing Unstructured Triangular Grids

Abstract

The accurate modeling of curved graphene layers for time-domain electromagnetic simulations is discussed in the present work. Initially, the advanced properties of graphene are presented, focusing on the propagation of strongly confined surface plasmon polariton waves at the far-infrared regime. Then, the implementation of an unstructured triangular grid was examined, based on the Delaunay triangulation method. The electric-field components were placed at the edges of the triangles, while two different techniques were proposed for the sampling of the magnetic ones. Specifically, the first one suggests that the magnetic component is placed at the triangle’s circumcenter providing more accurate results, although instability may occur for nonacute triangles. On the other hand, the magnetic field was sampled at the triangle’s centroid, considering the second technique, ensuring the algorithm’s stability, but further approximations were required, leading to a slight accuracy reduction. Moreover, the updating equations in the time-domain were extracted via an appropriate approximation of Maxwell equations in their integral form. Finally, graphene was introduced in the computational domain as an equivalent surface current density, whose location matches the corresponding electric components. The validity of our methodology was successfully performed via the comparison of graphene surface wave propagation properties to their theoretical values, whereas the global error determination indicates the minimal triangle dimensions. Additionally, an instructive setup comprising a circular graphene scatterer was analyzed thoroughly, to reveal our technique’s advantages compared to the conventional staircase discretization.

Initial Finite-Difference Time-Domain (FDTD) Modeling of Graphene Based on Intra-band Surface Conductivity

“…The Kubo formula is one widely employed model. The electrical conductivity of materials, including graphene, can be determined using the Kubo formula, an advanced theoretical framework [15]. The Kubo formula considers the interplay between charge carriers' quantum mechanical nature and the crystal lattice.…”