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.

We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphenecovered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n2,gr = −10 −13 m 2 /W. Whereas the sign of n2,gr turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.

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Abstract:Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in understanding the differences between so-called Type I and Type II combs. and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000). 3. T. W. Hänsch, "Nobel Lecture: Passion for precision," Rev. Mod. Phys. 78, 1297-1309(2006. 4. N. R. Newbury, "Searching for applications with a fine-tooth comb," Nature Photon. 5, 186-188 (2011). 5. V. Torres-Company and A. M. Weiner, "Optical frequency comb technology for ultra-broadband radio-frequency photonics," Laser and Photon. Rev. (in press, 2013). DOI 10.1002/lpor201300126. 6. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, "Microresonator-based optical frequency combs," Science 332, 555-559 (2011). 145-152 (2014). 43. F. Leo, S. Coen, P. Kockaert, S. P. Goza, P. Emplit, and M. Haelterman, "Temporal cavity solitons in onedimensional Kerr media as bits in an all-optical buffer," Nat. Photonics 4, 471-476 (2010). 44. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andres, "Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media," Opt. Express 18, 14979-14991 (2010). 45. M. Erkintalo and S. Coen, "Coherence properties of Kerr frequency combs," Opt. Lett. 39, 283-286 (2014). 46. M. Haelterman, S. Trillo, and S. Wabnitz, "Additive-modulation-instability ring laser in the normal dispersion regime of a fiber," Opt. Lett. 17, 745-747 (1992). 47. I. V. Barashenkov and Y. S. Smirnov, "Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons," Phys. Rev. E 54, 5707-5725 (1996)

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.