Matrix Exponential Enhanced Symplectic FDTD method for Simulating Anisotropic Magnetically Biased Graphene Devices

In this article, we propose a symplectic finite-difference time-domain (SFDTD) algorithm to model magnetically biased anisotropic graphene. The Dirac delta function is employed to represent the surface conductivity of the magnetically biased graphene as a polarized current source, which is then integrated into Maxwell’s equations. The frequency-domain form of the anisotropic dispersion is transformed into a differential form using the symplectic matrix exponential (ME) and Taylor series expansion methods. This differential form (noncommutative) represents a split exponential matrix, which can be discretized using high-order symplectic integration for time evolution and fourth-order finite difference methods for spatial discretization, ultimately leading to the derivation of the update equations. Furthermore, the long-term numerical stability of the SFDTD method is confirmed via the von Neumann method. The accuracy of the proposed model is numerically validated through three examples, showing excellent agreement with analytical solutions. These examples further confirm the accuracy and efficiency of the SFDTD method, demonstrating its applicability to radiation, reflection, and propagation problems in graphene-based devices.