Determination of Floquet's Modes in Graphene-Based Periodic Structures Using Method of Lines

In this work, the Method of Lines (MoL) is proposed for the analysis of anisotropic graphene-based periodic structures for the first time. This method is based on the Floquet's theorem and stable impedance/admittance transformation. Using Floquet's theorem, we equivalent the periodic structure with a transmission line. Due to this equivalence, an eigenvalue problem is developed. Floquet's modes of the periodic structure are the solutions of this eigenvalue problem. To verify the accuracy and efficiency of the proposed method, numerical results for different graphene-based periodic waveguides are presented and compared with those of commercial EM solvers which are in excellent agreement.