Mode Propagation Analysis of Magnetically Biased Graphene Microstrips via an Efficient Finite-Difference Scheme

A full-vectorial finite-difference (FD) scheme is proposed in this work to accurately extract the propagating modes on a magnetically biased graphene microstrip. Initially, the anisotropic surface conductivity of graphene is introduced, and the appropriate eigenvalue problem is formulated starting from Maxwell's equations. In particular, an FD approximation is utilized, while the discretization of the computation domain is based on the popular Yee cell. Then, the relationship between tangential, to the propagation direction, electromagnetic components is derived, leading to a linear eigenvalue problem. The numerical results highlight the expected difference between the propagation properties of the edge modes, thus validating the successful implementation of the featured modal solver. Moreover, it is shown that the number of unknown components is efficiently reduced due to the proper elimination of the longitudinal fields and the linearity of Maxwell's equations.