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Plasmons in highly-doped graphene offer the means to dramatically enhance light absorption in the atomically-thin material. Ultimately the absorbed light energy induces an increase in electron temperature, accompanied by large shifts in the chemical potential. This intrinsically incoherent effect leads to strong intensity-dependent modifications of the optical response, complementing the remarkable coherent nonlinearities arising in graphene due to interband transitions and anharmonic intraband electron motion. Here we show that the out-of-equilibrium electronic distribution induced by intense, resonant illumination of plasmons in nanostructured graphene results in a strong transient, incoherent nonlinear optical response that can dominate over the sought-after coherent nonlinear response. Under such conditions, our results indicate that the combined changes in electronic temperature and chemical potential effectively detune the graphene plasmon resonances from their linear-regime values, effectively enabling all-optical modulation. Additionally, a significant saturation of absorption is predicted to occur due to such incoherent processes. The relatively low electronic heat of graphene and the comparatively small number of electrons involved in its plasmons are ultimately responsible for this behavior, which limits the coherent nonlinear manipulation of optical pulses down to very short durations (below 100 fs), but opens new opportunities for transient plasmon-assisted light modulation, with potential uses in nonlinear nanophotonic devices such as optical switches and saturable absorbers. We anticipate that these findings will elucidate the role of coherent and incoherent nonlinearities for future studies and applications of plasmon-assisted nonlinear optics.
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