title: Coupled-mode-theory framework for nonlinear resonators comprising graphene.
abstract: A general framework combining perturbation theory and coupled-mode theory is developed for analyzing nonlinear resonant structures comprising dispersive bulk and sheet materials. To allow for conductive sheet materials, a nonlinear current term is introduced in the formulation in addition to the more common nonlinear polarization. The framework is applied to model bistability in a graphene-based traveling-wave resonator system exhibiting third-order nonlinearity. We show that the complex conductivity of graphene disturbs the equality of electric and magnetic energies on resonance (a condition typically taken for granted), due to the reactive power associated with the imaginary part of graphene's surface conductivity. Furthermore, we demonstrate that the dispersive nature of conductive materials must always be taken into account, since it significantly impacts the nonlinear response. This is explained in terms of the energy stored in the surface current, which is zeroed-out when linear dispersion is neglected. The results obtained with the proposed framework are compared with full-wave nonlinear finite-element simulations with excellent agreement. Very low characteristic power for bistability is obtained, indicating the potential of graphene for nonlinear applications.
authors.affiliation: Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki (AUTH), Thessaloniki 54124, Greece.
authors.forename: Thomas
authors.initials: T
authors.lastname: Christopoulos
authors.affiliation: Institute of Electronic Structure and Laser, Foundation for Research and Technology Hellas (FORTH), Heraklion 71110, Crete, Greece.
authors.forename: Odysseas
authors.initials: O
authors.lastname: Tsilipakos
authors.affiliation: Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki (AUTH), Thessaloniki 54124, Greece.
authors.forename: Nikolaos
authors.initials: N
authors.lastname: Grivas
authors.affiliation: Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki (AUTH), Thessaloniki 54124, Greece.
authors.forename: Emmanouil E
authors.initials: EE
authors.lastname: Kriezis