Time Domain Integral Equation Method For Graphene Dispersion At Terahertz Frequencies

Graphene,a promising nano-carbon-based material,is infinitely thin and dispersive.It can be widely used in the future electromagnetic and wireless communication systems.This dissertation proposes a numerical method for analyzing graphene dispersion at terahertz frequencies as the urgent need for application and numerical analysis of graphene.The research involves the following parts:After accurate modeling of graphene dispersion,the surface conductivity can be expressed by Kubo formula,which is consist of two contributions representing the electronic intraband relaxation and interband transition respectively.The surface conductivity and resistivity of graphene in frequency domain are approximated by a series of partial fractions in terms of real or complex conjugate pole-residue pairs by vector fitting method.The influence of fitting orders is investigated by setting different orders.Then graphene's frequency domain resistivity is fitted with different temperatures and chemical potential.Finally,the vector fitting method is used to fit the frequency domain resistivity of graphene at terahertz frequencies in this dissertation.The simulation results show that it can be achieved accurately with less fitting orders.Based on the research above,the frequency domain resistivity obtained by the vector fitting method,and it can be transformed into the time domain one by inverse fourier transform.The marching-on-in-degree time domain integral equation(MOD-TDIE)of graphene is established according to the surface resistive boundary condition,the convolution of graphene's time domain resistivity and electric current is added to reflect the dispersion.Then laguerre polynomial's properties are used to derive the analytic formula of the convolution.Utilizing weighted laguerre polynomials as temporal basis functions,the main formulas from the establishment of the integral equation to the matrix equation are given after testing with the Galerkin method.The simulation results show that the solution of time domain current is unconditionally stable in late time,and graphene is dispersed in the frequency domain compared to metal plate.In addition,it shows correction of the analysis of gaphene's dispersion based on MOD-TDIE by comparing with the results of frequency domain method.