Nonlinear optics of surface plasmon polaritons in subwavelength graphene ribbon resonators

We study the propagation characteristics of surface Plasmon polaritons (SPPs) on a patterned graphene sheet incorporating a subwavelength ribbon resonator and a Kerr nonlinear bounding medium (substrate or top cladding) which provides tunable bandpass filtering in the THz regime. We study theoretically and via modeling the tunability of maxima in the transmission spectrum, corresponding to the resonant frequencies of the ribbon resonator, by tuning the graphene Fermi level (via an applied gate voltage) and by altering the intensity of the incident THz wave. We determine the intensity-dependent increase in the refractive index of a Kerr nonlinear medium bounding graphene, via self-phase modulation and via the more efficient process of cross-phase modulation, revealing a noticeable red-shift in the resonant frequencies of the ribbon resonator. These concepts lead to ultrafast switching of SPP transmission through the ribbon (from a high to a low state). Using Kerr nonlinear media to bound graphene increases the tunability of graphene-based devices, enabling nonlinear plasmonic and ultrafast processing in the THz regime.