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

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