Using HIE-FDTD method to simulate graphene's interband conductivity

A hybrid implicit-explicit-finite-difference time-domain (HIE-FDTD) method is modified to simulate the graphene. In this method, both the intraband and interband conductivity of grahene are considered. A simple Pade fit method is used to represent the interband conductivity which has complex relation with the angular frequency, and is incorporated into the HIE-FDTD method directly through an auxiliary difference equation. An infinite graphene sheet is simulated using presented technique and the result is compared with that of the conventional FDTD scheme and theoretical value. The results show that the HIE-FDTD method has excellent computational accuracy and considerably higher computational efficiency than FDTD scheme. Besides, the numerical example presents that the interband conductivity of the graphene has important effect on the numerical result at high frequency range, especially when the chemical potential is small.