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Gate-tunable third-order nonlinear optical response of massless Dirac fermions in graphene

Nature Photonics volume 12, pages 430–436 (2018)Cite this article

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Abstract

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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Fig. 1: Tuning of chemical potential in graphene by ion-gel gating.
Fig. 2: Gate-controlled THG from graphene and its polarization patterns.
Fig. 3: FWM in gated graphene.
Fig. 4: Theoretical understanding of μ-dependent χ(3) in THG.
Fig. 5: Theoretical calculations of μ-dependent χ(3) and comparison with experimental data for FWM from graphene.

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Acknowledgements

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).

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Author notes

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

Authors and Affiliations

  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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Contributions

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.

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Correspondence to Wei-Tao Liu or Shiwei Wu.

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

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Jiang, T., Huang, D., Cheng, J. et al. Gate-tunable third-order nonlinear optical response of massless Dirac fermions in graphene. Nature Photon 12, 430–436 (2018). https://doi.org/10.1038/s41566-018-0175-7

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