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Predicting graphene's nonlinear-optical refractive response for propagating pulses

Nonlinear-optical refraction is typically described by means of perturbation theory near the material's equilibrium state. Graphene, however, can easily move far away from its equilibrium state upon optical pumping, yielding strong nonlinear responses that cannot be modeled as mere perturbations. So far, one is still lacking the required theoretical expressions to make predictions for these complex nonlinear effects and to account for their evolution in time and space. Here, this long-standing issue is solved by the derivation of population-recipe-based expressions for graphene's nonperturbative nonlinearities. The presented framework successfully predicts and explains the various nonlinearity magnitudes and signs observed for graphene over the past decade, while also being compatible with the nonlinear pulse propagation formalism commonly used for waveguides.