Transient Electromagnetic Analysis of Multilayer Graphene with Dielectric Substrate Using Marching-on-in-Degree Method

Abstract

The marching-on-in-degree (MOD) method is applied in this paper to analyze the transient electromagnetic scattering of multilayer graphene and a dielectric substrate. The time domain resistive boundary condition (TD-RBC) integral equation and time domain Poggio–Miller–Chang–Harrington–Wu (PMCHW) integral equation of electric and magnetic currents are employed to model graphene and the dielectric substrate, respectively. These two sets of equations are coupled and solved with the MOD method. The dispersion of multilayer graphene’s surface conductivity/resistivity in the frequency domain is taken into account in the analytical convolution of temporal surface conductivity/resistivity and magnetic/electric current densities. The Rao-Wilton-Glisson (RWG) basis function over triangle patches and weighted Laguerre polynomial (WLP) are used as the spatial and temporal basis/testing functions, respectively. The orthogonal WLPs are defined from zero to +∞ and are convergent to zero with time passing. These advantages ensure late time stability of the transient solution. A stable electric/magnetic current is achieved. A radar cross section and extinction cross section in the frequency domain are also obtained and compared with commercial software results to verify the proposed method.