Optical harmonic generation occurs when high intensity light (>1010 W m2) 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.

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We acknowledge funding from EU Graphene Flagship, ERC Grant Hetero2D, and EPSRC grants EP/K01711X/1, EP/K017144/1, EP/N010345/1 and EP/L016087/1.

Author information


  1. Cambridge Graphene Centre, University of Cambridge, Cambridge, UK

    • Giancarlo Soavi
    • , Gang Wang
    • , David G. Purdie
    • , Domenico De Fazio
    • , Teng Ma
    • , Birong Luo
    • , Junjia Wang
    • , Anna K. Ott
    • , Duhee Yoon
    • , Sean A. Bourelle
    • , Jakob E. Muench
    • , Ilya Goykhman
    •  & Andrea C. Ferrari
  2. Istituto Italiano di Tecnologia, Graphene Labs, Genova, Italy

    • Habib Rostami
    • , Andrea Tomadin
    •  & Marco Polini
  3. IFN-CNR, Milano, Italy

    • Stefano Dal Conte
    •  & Giulio Cerullo
  4. Dipartimento di Fisica, Politecnico di Milano, Milano, Italy

    • Stefano Dal Conte
    • , Michele Celebrano
    •  & Giulio Cerullo


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A.C.F, G.C. and G.S. conceived and designed the experiments. G.S. and G.W. prepared the experimental set-up. G.S., G.W, S.D.C., M.C. and S.A.B. performed the THG experiments. G.S. analysed the THG data. A.K.O. and D.Y. measured the Raman spectra. D.G.P., T.M., B.L., D.D.F., J.W., J.E.M. and I.G. prepared the samples. H.R. and A.T. developed the THG theory and model for Te. G.S., A.C.F., G.C. and M.P. wrote the paper, with input from all authors.

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The authors declare no competing interests.

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Correspondence to Giancarlo Soavi or Andrea C. Ferrari.

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