Spatially Dispersive Graphene Single and Parallel Plate Waveguides: Analysis and Circuit Model

The propagation of surface waves along spatially dispersive graphene-based 2-D waveguides is investigated in detail. Graphene is characterized using a full-k_ρ conductivity model under the relaxation-time approximation, which allows to obtain analytical and closed-formed expressions for the wavenumber of plasmons supported by sheets and parallel plate waveguides, respectively. Per unit length equivalent circuits are introduced to accurately characterize the propagation in different waveguides, and analytical relations between the effective TM-mode circuit lumped elements and graphene conductivity are derived. The proposed circuits allow identifying the different mechanisms involved in spatially dispersive plasmon propagation, explaining their connection with the intrinsic properties of graphene. Results demonstrate that spatial dispersion, which significantly decreases the confinement and the losses of slow surface plasmons, must be accurately assessed in the design of graphene-based plasmonic components at millimeter-waves and low terahertz frequencies.