Graphene optical nonlinearity: From the third-order to the non-perturbative electrodynamic regime

A non-perturbative model for graphene optical nonlinearity is developed for the study of ultrafast pulse propagation along a monolayer, as in the case of graphene-comprising nanophotonic integrated waveguides. This graphene `hot electron' model (GHEM) builds upon earlier work, based on the Fermi-Dirac framework for 2D semiconductors, which was aimed mainly at steady-state absorptive response of a monolayer under free-space laser-beam illumination. Our extension adapts the GHEM to in-plane light-matter interaction along graphene monolayers under intense ps-pulse excitation that leads to the carrier-density saturation regime. We first provide a quantitative overview of the `classic' perturbative third-order nonlinear response and then study the static and transient response of graphene as a function of the GHEM parameters, with focus on the monolayer quality and voltage-tunability. These results are compared to phenomenological models for saturable absorption and nonlinear refraction, showing good agreement with recent experimental works. In conclusion, the GHEM unifies the experimentally observed absorptive and refractive optical nonlinearities in a single multi-parametric framework therefore enabling the evaluation of the voltage-tunable light-matter interaction in structures such as diffraction-limited nanophotonic waveguides. This formalism can be readily employed to THz frequencies, adapted to multi-channel (e.g. pump-probe) nonlinear effects, or developed to include carrier and lattice-temperature diffusion to extend its validity threshold.