Optical harmonic generation occurs when high intensity light (>10¹⁰ W m^–2) interacts with a nonlinear material. Electrical control of the nonlinear optical response enables applications such as gate-tunable switches and frequency converters. Graphene displays exceptionally strong light–matter interaction and electrically and broadband tunable third-order nonlinear susceptibility. Here, we show that the third-harmonic generation efficiency in graphene can be increased by almost two orders of magnitude by controlling the Fermi energy and the incident photon energy. This enhancement is due to logarithmic resonances in the imaginary part of the nonlinear conductivity arising from resonant multiphoton transitions. Thanks to the linear dispersion of the massless Dirac fermions, gate controllable third-harmonic enhancement can be achieved over an ultrabroad bandwidth, paving the way for electrically tunable broadband frequency converters for applications in optical communications and signal processing.

当高强度光（> 10 ¹⁰  W m ^{– 2}）与非线性材料相互作用。非线性光学响应的​​电气控制实现了诸如门可调开关和变频器之类的应用。石墨烯显示出异常强大的光-物质相互作用以及电学和宽带可调的三阶非线性磁化率。在这里，我们表明，通过控制费米能量和入射光子能量，可以将石墨烯中的三次谐波产生效率提高近两个数量级。这种增强是由于共振多光子跃迁引起的非线性电导率的虚部中的对数共振。由于无质量狄拉克费米子的线性分散，可以在超宽带宽上实现门可控的三次谐波增强，