Graphene with massless Dirac fermions can have exceptionally strong third-order optical nonlinearities. Yet reported values of nonlinear optical susceptibilities for third-harmonic generation (THG), four-wave mixing (FWM) and self-phase modulation vary over six orders of magnitude. Such variation likely arises from frequency-dependent resonance effects of different processes in graphene under different doping. Here, we report an experimental study of THG and FWM in graphene using gate tuning to adjust the doping level and vary the resonant condition. We find that THG and sum-frequency FWM are strongly enhanced in heavily doped graphene, while the difference-frequency FWM appears just the opposite. Difference-frequency FWM exhibited a novel divergence towards the degenerate case in undoped graphene, leading to a giant enhancement of the nonlinearity. The results are well supported by theory. Our full understanding of the diverse nonlinearity of graphene paves the way towards future design of graphene-based nonlinear optoelectronic devices.

带有无质量狄拉克费米子的石墨烯可以具有异常强的三阶光学非线性。尚未报告的三次谐波产生（THG），四波混频（FWM）和自相位调制的非线性光学磁化率值在六个数量级上变化。这种变化可能是由于不同掺杂条件下石墨烯中不同过程的频率相关共振效应引起的。在这里，我们报告了使用栅极调谐来调整掺杂水平和改变谐振条件的石墨烯中THG和FWM的实验研究。我们发现在重掺杂石墨烯中THG和和频FWM显着增强，而差频FWM恰好相反。在未掺杂的石墨烯中，差频FWM表现出对简并情况的新颖发散，从而大大增强了非线性。该结果得到了理论的充分支持。我们对石墨烯的各种非线性的充分理解为将来基于石墨烯的非线性光电器件的设计铺平了道路。