Extended Method of Lines to Model Cylindrical Graphene-Based Multilayer Structures

In this article, the method of lines (MoL) is extended to analyze 2-D multilayer structures loaded with graphene plates in cylindrical coordinates. Accordingly, the admittance transformation matrices through a 2-D interface are derived taking into account the tensor-form conductivity of the magnetized graphene plate. The transformations determine the admittance matrices on all the planes of the multilayer structure. Furthermore, a technique to obtain the characteristic equation and hence the propagation constant of the structure is proposed by matching the fields at the interfaces loaded with graphene. As a result, the proposed method is able to analyze a generic graphene-loaded multilayer structure in cylindrical coordinates. As a proof of concept, the MoL is exploited to analyze 2-D cylindrical graphene microstrip and stripline transmission lines. The proposed method is validated by comparing the results with COMSOL simulations exhibiting a good agreement. Tuning the chemical potential of the graphene plate has potential applications in tunable microwave attenuators and phase shifters.