biostudies-literatureVermeulen NEuropean Commission (EC)European Research CouncilFonds Wetenschappelijk Onderzoek (Research Foundation Flanders)2675https://www.ebi.ac.uk/biostudies/studies/S-EPMC6041291biostudies-literatureUnknown9(1)Graphene is considered a record-performance nonlinear-optical material on the basis of numerous experiments. The observed strong nonlinear response ascribed to the refractive part of graphene's electronic third-order susceptibility χ⁽³⁾ cannot, however, be explained using the relatively modest χ⁽³⁾ value theoretically predicted for the 2D material. Here we solve this long-standing paradox and demonstrate that, rather than χ⁽³⁾-based refraction, a complex phenomenon which we call saturable photoexcited-carrier refraction is at the heart of nonlinear-optical interactions in graphene such as self-phase modulation. Saturable photoexcited-carrier refraction is found to enable self-phase modulation of picosecond optical pulses with exponential-like bandwidth growth along graphene-covered waveguides. Our theory allows explanation of these extraordinary experimental results both qualitatively and quantitatively. It also supports the graphene nonlinearities measured in previous self-phase modulation and self-(de)focusing (Z-scan) experiments. This work signifies a paradigm shift in the understanding of 2D-material nonlinearities and finally enables their full exploitation in next-generation nonlinear-optical devices.Nature communicationsGraphene's nonlinear-optical physics revealed through exponentially growing self-phase modulation.PMC6041291336940604391618086GA00213NG0F6218NCiuk TKrajewska AStrupinski WKhoder MCastello-Lurbe DPasternak IVan Erps JVermeulen NCheng JThienpont HfalseGraphene's nonlinear-optical physics revealed through exponentially growing self-phase modulation.Graphene is considered a record-performance nonlinear-optical material on the basis of numerous experiments. The observed strong nonlinear response ascribed to the refractive part of graphene's electronic third-order susceptibility χ⁽³⁾ cannot, however, be explained using the relatively modest χ⁽³⁾ value theoretically predicted for the 2D material. Here we solve this long-standing paradox and demonstrate that, rather than χ⁽³⁾-based refraction, a complex phenomenon which we call saturable photoexcited-carrier refraction is at the heart of nonlinear-optical interactions in graphene such as self-phase modulation. Saturable photoexcited-carrier refraction is found to enable self-phase modulation of picosecond optical pulses with exponential-like bandwidth growth along graphene-covered waveguides. Our theory allows explanation of these extraordinary experimental results both qualitatively and quantitatively. It also supports the graphene nonlinearities measured in previous self-phase modulation and self-(de)focusing (Z-scan) experiments. This work signifies a paradigm shift in the understanding of 2D-material nonlinearities and finally enables their full exploitation in next-generation nonlinear-optical devices.2018-01-01T00:00:00Z2018 Jul2025-04-04T18:42:11.483Z2019-03-26T23:46:16ZS-EPMC60412912999296710.1038/s41467-018-05081-z