Runge-Kutta HIE-FDTD formulations for analyzing optical transmission through periodic array of magnetically-biased graphene micro-patch structures

Abstract

In this paper, simple and efficient hybrid implicit-explicit finite difference time domain (HIEFDTD) formulations are presented for analyzing optical transmission through periodic array of magnetically-biased graphene structures. In this respect, the Runge-Kutta (RK) time differencing scheme is extended for incorporating the gaphene's anisotropic conductivity into the HIE-FDTD scheme. The temporal discretization of the presented formulations, which are named as RKHIE-FDTD, is not confined by the graphene's nano thickness and this will allow using larger time-step than that of the classical explicit-FDTD counterpart. Compared with the previous magnetized HIE-FDTD approaches, the presented formulations not only involve less memory indexing overhead and fewer arithmetic operations, but also found to be numerically stable at the conventional HIE-FDTD stability limit. The accuracy and stability of the presented RK-HIEFDTD formulations is verified by first investigating the transmission coefficient for a plane-wave normally incident on an infinite magnetized graphene layer and very good agreement with the analytical solution is observed. Furthermore, a numerical test conducted on a periodic array of magnetically-biased graphene micro-patches deposited on top of SiO2 glass substrate shows that the number and the intensity of the generated resonance frequencies are greatly affected by the graphene's chemical potential as well as by the magnetic field bias intensity.