A weakly conditionally stable-finite difference time-domain (WCS-FDTD) scheme to simulate graphene is developed. The Pade fit method is used to approximate the interband conductivity of graphene and introduced into the WCS-FDTD method directly by using the auxiliary differential equation. The accuracy of the Pade method is verified, and the effect of chemical potential on the accuracy is discussed. The time step size in proposed method is only determined by one spatial cell size, so the computational efficiency of this method is considerably larger than those of the conventional FDTD method and implicit explicit-finite (HIE)-FDTD method. An infinite graphene sheet and a graphene-based metal sheet are simulated by using presented method, and the results are compared with theoretical value and the numerical results of the conventional FDTD method and HIE-FDTD method.Simulated results show that proposed WCS-FDTD method has high accuracy, and compared with the FDTD method and HIE-FDTD method, its computational time is largely shorted. Besides, the numerical example presents that the interband conductivity has important effect on the performance of the graphene at high-frequency range, especially when the chemical potential is small.
| INTRODUCTIONGraphene has brought a lot of attention to scientific and engineering communities because of its unique properties in microwave and terahertz (THz) spectra, 1-6 so there is a rapidly emerging interest to develop accurate and computationally numerical models to simulate graphene. The finite-difference time-domain (FDTD) method, which can compute the graphene accurately in time domain, is a relatively common scheme. 7,8 However, the FDTD method needs very long computational time when it is used to simulate graphene, because its time step size is confined by the fine spatial cell size in the graphene layer, which is only a one-atom thick.To overcome this problem, many new FDTD methods have been presented recently. [9][10][11][12][13] In literature, 9-11 FDTD method based on the surface impedance boundary condition (SIBC) is developed. In this method, the small spatial mesh inside the graphene layer has been avoided. But this method cannot simulate graphene's interior field distribution, because it neglects the thickness of graphene layer. The subcell FDTD method, 12 which treats graphene as a thin volumetric layer, has also been used to simulate graphene. In this method, the graphene layer occupies a fraction of the FDTD cells. The disadvantage of this method is that it requires a special type of perfectly matched layer (PML) to model infinitely thin sheets. 13 Besides, in these methods, only the intraband conductivity of the graphene with the form of Drude model is handled. The interband conductivity of the graphene, which has complex relation with angular frequency, is neglected completely. So these methods only can give accurate results at the far-infrared frequency band where the
