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.

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The work at Fudan University was supported by the National Basic Research Program of China (grant no. 2014CB921601), National Key Research and Development Program of China (grant nos. 2016YFA0301002, 2016YFA0300900), National Natural Science Foundation of China (grant no. 91421108, 11622429, 11374065), and the Science and Technology Commission of Shanghai Municipality (grant no. 16JC1400401). Part of the sample fabrication was performed at Fudan Nano-fabrication Laboratory. K.L. is supported by the National Natural Science Foundation of China (grant no. 51522201). J.E.S. is supported by the Natural Sciences and Engineering Research Council of Canada. Y.-R.S. acknowledges support from the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, US Department of Energy (contract no. DE-AC03-76SF00098).

Author information

Author notes

  1. These authors contributed equally: Tao Jiang, Di Huang.


  1. State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), Department of Physics, and Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai, China

    • Tao Jiang
    • , Di Huang
    • , Yuwei Shan
    • , Yangfan Yi
    • , Yunyun Dai
    • , Lei Shi
    • , Jian Zi
    • , Yuen-Ron Shen
    • , Wei-Tao Liu
    •  & Shiwei Wu
  2. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin, China

    • Jinluo Cheng
  3. International Center for Quantum Design of Functional Materials, Hefei National Laboratory for Physical Sciences at the Microscale, and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, China

    • Xiaodong Fan
    •  & Changgan Zeng
  4. CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei, China

    • Xiaodong Fan
    •  & Changgan Zeng
  5. State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing, China

    • Zhihong Zhang
    •  & Kaihui Liu
  6. Collaborative Innovation Center of Advanced Microstructures, Nanjing, China

    • Lei Shi
    • , Jian Zi
    • , Wei-Tao Liu
    •  & Shiwei Wu
  7. Department of Physics, University of Toronto, Toronto, Ontario, Canada

    • J. E. Sipe
  8. Physics Department, University of California, Berkeley, CA, USA

    • Yuen-Ron Shen


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S.W. and W.-T.L. conceived and supervised the project. T.J., D.H., Y.S. and Y.Y. prepared the devices and performed the experiments, with assistance from Y.D., L.S. and J.Z. on gate-dependent optical transmittance measurement. X.F., Z.Z., K.L. and C.Z. provided the chemical vapour deposition-grown graphene samples. T.J., D.H., J.C., J.E.S., Y.-R.S., W.-T.L. and S.W. analysed the data. T.J., D.H., J.E.S., Y.-R.S., W.-T.L. and S.W. wrote the paper with contributions from all authors.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Wei-Tao Liu or Shiwei Wu.

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  1. Supplementary Information

    Supplementary Texts 1–5; Supplementary Table 1; Supplementary Figures 1–6.

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