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

Abstract

Abstract Graphene is a single two-dimensional layer of carbon atoms arranged in a hexagonal lattice, possesses interesting optical properties, and has potential for applications in optical devices. Graphene exhibits tunable surface conductivity, which arises from its electronic band structure. Graphene surface conductivity is determined by its chemical potential, which can be controlled by bias voltage and/or chemical doping. The tunability of surface conductivity allowed to tailored optical properties of graphene, making it a controllable material for optoelectronic applications. Graphene surface conductivity is applied to update the field values at each time step in the Finite-Difference Time-Domain (FDTD) method, enabling us to visualize electromagnetic (EM) wave propagation in graphene. The current article serves as a starting point for developing the FDTD approach to simulate EM wave interactions with graphene, particularly at low frequencies. In this study, we use the Kubo formula for low EM wave frequency (10-105 GHz) at ambient temperature to calculate the intra-band surface conductivity of graphene. The outcome shows that the imaginer’s intra-band surface conductivity value is relatively considerable compared to the actual value at frequencies between 102 and 104. Moreover, the chemical potential exhibits a positive linear relationship with the imaginer intra-band surface conductivity and the intra-band conductivity falls to zero as the frequency rises to NIR.