Time-domain Integral Equation Method For Graphene And Substrate Scattering Properties In Terahertz Frequencies

Due to its unique thermal,mechanical,optical and electrical properties,graphene,as a new type of nanomaterial,with enormous value in electromagnetic and terahertz communications,has quickly become a forerunner in the research.Based on the urgent application and numerical simulation requirements of graphene terahertz devices,a time-domain method to analyze the electromagnetic properties of graphene and substrate in terahertz band is developed.Graphene is a type of dispersion material,and its dispersion characteristic needs to be accurately modeled.According to Kubo's formula,the frequency-domain surface conductivity model of graphene can be obtained.In this thesis,the vector fitting is adopted to approximate the frequency-domain surface conductivity and resistivety in the form of rational fraction sum by using a series of real or complex conjugate pole-residue pairs,aiming at simplifying the derivation of subsequent formulas and the complexity of coding.The time-domain integral equation is the theoretical foundation of this thesis.For the graphene and substrate,resistive boundary condition is imposed on the surface of graphene to obtain the time-domain integral equations,the convolution of graphene's time-domain resistivity and electric current as well as time-domain conductivity and magnetic current are added to reflect the dispersion,using Laguerre polynomial's properties to derive the analytic formula of the convolution.Meanwhile,based on the equivalent principle,the PMCHW formulation are established on the surface of the substrate,and couples these equations to solve the scattering problem.The weighted Laguerre polynomial is adopted as the global temporal basis function,and the main formulas of establishing the integral equation,the testing process,and the matrix equation formation are derived in detail.Numerical results show that the time-domain electric and magnetic current is unconditionally stable in late time.In addition,comparing simulation results of thesis with commercial software,it's shown that the numerical procedure for the analysis of graphene and substrate is correct.