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.

Method of lines for the analysis of tunable plasmonic devices composed of graphene-dielectric stack arrays.

Due to the increasing interest in emerging applications of graphene or other 2D material-based devices in photonics, a powerful, fast and accurate tool for the analysis of such structures is really in need. In this paper, the semi-analytical method of lines (MoL) is generalized for the diffraction analysis of tunable graphene-based plasmonic devices possessing three dimensional periodicity. We employ Floquet's theorem to handle analytically propagation of waves in the periodicity of the graphene-dielectric arrays in the direction of the layers stacking. This makes the method very effective in terms of computational time and memory consumption. To validate its efficiency and accuracy, the method is applied to plasmonic devices formed by alternating patterned graphene sheets and dielectric layers. Direct comparison with results available in literature and those obtained by a commercial software exhibits their full consistency.