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The performances of a parallel plate waveguide (PPWG) supported by perfect electric conductor (PEC)-graphene and graphene-graphene plates are evaluated. The graphene plate behavior is modeled as an anisotropic medium with both diagonal and Hall conductivities derived from Kubo formula. The PPWG modes supported by PEC-graphene and graphene-graphene plates are studied. Maxwell’s equations are solved for these two waveguides, while the graphene layers are biased\udwith an electric field only and with both electric and magnetic fields. It is shown that when both electric and magnetic biases are applied to the graphene, a hybrid mode (simultaneous transverse\udelectric (TE) and transverse magnetic (TM) modes) will propagate inside the waveguide. The intensity of each TE and TM modes can be adjusted with the applied external bias fields. Study of\uddifferent waveguides demonstrates that by decreasing the plate separation (d), the wave confinement improves. However, it increases the waveguide attenuation. A dielectric layer inserted between the plates can also be used to improve the wave confinement. The presented analytical procedure is applicable to other guiding structures having walls with isotropic or anisotropic conductivities

Parallel plate waveguide with anisotropic graphene plates: Effect of electric and magnetic biases