Ultra-deep sub-wavelength mode confinement in nano-scale graphene resonator-coupled waveguides

Graphene is capable of supporting very slow waves due to sustaining surface plasmon polaritons (SPPs) at THz frequencies, whereas the metal counterpart can support such modes only at optical frequencies. In this paper, a graphene-based resonator-coupled waveguide supporting transverse-magnetic-polarized SPP modes is rigorously studied, which is capable of providing ultra-deep sub-wavelength mode confinement at the working frequency of 40 THz. First, graphene is described both electronically and electromagnetically, as in these regards, graphene's quantum capacitance plays an important role, which is calculated via its DC characteristic. Since we aim to excite extremely slow waves in graphene waveguides, namely, SPP modes, it is necessary to contemplate a non-local conductivity model to characterize graphene. Furthermore, SPP modes create strong fields at the vicinity of a graphene strip in addition to high mode confinement, accentuating the importance of including nonlinear phenomena in characterizing the wave vector of SPP (WVP) modes. Furthermore, the WVP associated with a graphene waveguide is perturbed when placing another waveguide next to it. In this work, these phenomena are explored in detail to design a graphene-based resonator-coupled waveguide, which is superior to a single graphene-based waveguide in terms of confining propagating waves. Here, a comprehensive methodology is established for assessing miniaturized graphene devices, in which nonlinear, coupling, and spatial dispersion phenomena significantly affect their characteristics.