Multi-layered Parallel Plate Waveguide with Electrically and Magnetically Biased Graphene Walls

The performance of a newly designed multi-layered parallel plate waveguide (PPWG), supported by two, three and four graphene plates, is evaluated here. The graphene layers used for this study were biased with both electric and magnetic fields. The graphene plates behavior was modeled as an anisotropic medium, with both diagonal and Hall conductivities derived from the Kubo formula. Maxwells equations were solved for these waveguides; and it is shown, here, that when both electric and magnetic biases were applied to the graphene, hybrid modes (simultaneous transverse electric (TE) and transverse magnetic (TM) modes) propagated inside the waveguides. The intensity of each TE and TM mode could be adjusted with an applied external field bias. This feature is valuable for various applications, such as converting TE modes to TM modes, and vice versa. In addition, due to the anisotropic properties of graphene walls, PPWGs with graphene walls under magnetic field biases are applicable to the design of non-reciprocal devices, such as isolators, circulators and one-way couplers. This study of wave confinement has shown that, by varying the bias, full control can be exerted over the waves propagation within a waveguide; whereby, increasing the bias causes added phase changes over the propagation length, while increasing the waveguides attenuation. This full control would also be helpful when using the waveguide structure to design numerous devices, such as switches, couplers, attenuators and modulators. It must be emphasized that the presented analytical procedure is also applicable to other guiding structures that have walls with isotropic or anisotropic conductivities.