Analysis of Graphene-Based Multilayered Three-Dimensional Structures by the Extended Method of Lines

In this paper, the method of lines is extended to analyze graphene-based multilayered 3-D structures. The graphene plates with tensor conductivity may cover partially or totally the interfaces between two consecutive layers. The impedance and admittance transformation formulas are then derived at the interfaces. Hence, the impedance and admittance at all the planes of the multilayered structure are obtained. Consequently, the scattering parameters are derived too. To verify the presented technique, as an example of a multilayered structure, graphene plates are placed within a rectangular waveguide. Then, for different numbers of plates and also for different states of the graphene plates which may cover the cross section of the waveguide totally or partially along the x- or y-directions, the scattering parameters of the structure are calculated. The obtained results are compared with those of the CST simulation software, which are in good agreement.