The method of lines extension for the analysis of multilayered graphene-loaded structures in cylindrical coordinates.

In this paper the extended method of lines (E-MoL) is proposed for the analysis of multilayer graphene-loaded three dimensional structures in cylindrical coordinates. Accordingly, the impedance and admittance matrices are defined as the ratios of the electric and magnetic fields at each plane of the stack. The impedance and admittance parameters are transformed from the input to the output of the structure through layers and interfaces, from which, the scattering parameters are extracted. It is assumed that there is an anisotropic graphene layer at the interface of two successive layers. The impedance and admittance transformations at the interfaces are extracted in the cylindrical coordinates. Then the impedance and admittance values at all planes of the stack and consequently, the scattering parameters of the whole structure are derived. To validate the presented method, two validation benchmarks are provided at the microwave frequency band. A circular waveguide and a coaxial cable loaded with graphene plates are analyzed and the results are compared with those of CST simulation software which show good accordance. It is observed that the E-MoL, as a semi-analytical semi-numerical method, is much more time-efficient than the CST software numerical procedure.