Stability-Improved HIE-FDTD for Magnetized Graphene from Microwave to THz Band

A stability-improved hybrid implicit-explicit finite-difference time-domain method (HIE-FDTD) for magnetized graphene is proposed. The graphene is treated as a current source modeled by an auxiliary differential equation which is divided into two separate equations to describe isotropic and anisotropic properties. The one time-step iteration in the conventional algorithm is decomposed into two sub steps where the conventional HIE-FDTD combined with the isotropic equation is implemented first followed by the Crank-Nicolson (CN) scheme combined with the anisotropic equation to retain the stability. Numerical results show that, differently from other recent extensions, the stability condition of the proposed method preserves the same form as that of the conventional HIE-FDTD. We illustrate the application of the proposed algorithm to accurately compute graphene transmission properties e.g., Faraday and Kerr rotations.