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

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 1.

    Bonaccorso, F., Sun, Z., Hasan, T. & Ferrari, A. C. Graphene photonics and optoelectronics. Nat. Photon. 4, 611–622 (2010).

    ADS  Article  Google Scholar 

  2. 2.

    Koppens, F. H. L., Chang, D. E. & García de Abajo, F. J. Graphene plasmonics: a platform for strong light-matter interactions. Nano Lett. 11, 3370–3377 (2011).

    ADS  Article  Google Scholar 

  3. 3.

    Nair, R. R. et al. Fine structure constant defines visual transparency of graphene. Science 320, 1308–1308 (2008).

    ADS  Article  Google Scholar 

  4. 4.

    Mak, K. F. et al. Measurement of the optical conductivity of graphene. Phys. Rev. Lett. 101, 196405 (2008).

    ADS  Article  Google Scholar 

  5. 5.

    Koppens, F. H. L. et al. Photodetectors based on graphene, other two-dimensional materials and hybrid systems. Nat. Nanotech. 9, 780–793 (2014).

    ADS  Article  Google Scholar 

  6. 6.

    Sun, Z., Martinez, A. & Wang, F. Optical modulators with 2D layered materials. Nat. Photon. 10, 227–238 (2016).

    ADS  Article  Google Scholar 

  7. 7.

    Wang, F. et al. Gate-variable optical transitions in graphene. Science 320, 206–209 (2008).

    ADS  Article  Google Scholar 

  8. 8.

    Liu, M. et al. A graphene-based broadband optical modulator. Nature 474, 64–67 (2011).

    ADS  Article  Google Scholar 

  9. 9.

    Chen, C. et al. Controlling inelastic light scattering quantum pathways in graphene. Nature 471, 617–620 (2011).

    ADS  Article  Google Scholar 

  10. 10.

    Mikhailov, S. A. Non-linear electromagnetic response of graphene. Europhys. Lett. 79, 27002 (2007).

    ADS  Article  Google Scholar 

  11. 11.

    Glazov, M. M. & Ganichev, S. D. High frequency electric field induced nonlinear effects in graphene. Phys. Rep. 535, 101–138 (2014).

    ADS  MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Kumar, N. et al. Third harmonic generation in graphene and few-layer graphite films. Phys. Rev. B 87, 121406 (2013).

    ADS  Article  Google Scholar 

  13. 13.

    Hong, S. et al. Optical third-harmonic generation in graphene. Phys. Rev. X 3, 021014 (2013).

    Google Scholar 

  14. 14.

    Säynätjoki, A. et al. Rapid large-area multiphoton microscopy for characterization of graphene. ACS Nano 7, 8441–8446 (2013).

    Article  Google Scholar 

  15. 15.

    Woodward, R. I. et al. Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2 using multiphoton microscopy. 2D Mater. 4, 011006 (2017).

    Article  Google Scholar 

  16. 16.

    Hendry, E., Hale, P. J., Moger, J., Savchenko, A. K. & Mikhailov, S. A. Coherent nonlinear optical response of graphene. Phys. Rev. Lett. 105, 097401 (2010).

    ADS  Article  Google Scholar 

  17. 17.

    Ciesielski, R. et al. Graphene near-degenerate four-wave mixing for phase characterization of broadband pulses in ultrafast microscopy. Nano Lett. 15, 4968–4972 (2015).

    ADS  Article  Google Scholar 

  18. 18.

    Zhang, H. et al. Z-scan measurement of the nonlinear refractive index of graphene. Opt. Lett. 37, 1856–1858 (2012).

    ADS  Article  Google Scholar 

  19. 19.

    Yang, H. et al. Giant two-photon absorption in bilayer graphene. Nano Lett. 11, 2622–2627 (2011).

    ADS  Article  Google Scholar 

  20. 20.

    Dremetsika, E. et al. Measuring the nonlinear refractive index of graphene using the optical Kerr effect method. Opt. Lett. 41, 3281–3284 (2016).

    ADS  Article  Google Scholar 

  21. 21.

    Vermeulen, N. et al. Negative Kerr nonlinearity of graphene as seen via chirped-pulse-pumped self-phase modulation. Phys. Rev. Appl. 6, 044006 (2016).

    ADS  Article  Google Scholar 

  22. 22.

    Gu, T. et al. Regenerative oscillation and four-wave mixing in graphene optoelectronics. Nat. Photon. 6, 554–559 (2012).

    ADS  Article  Google Scholar 

  23. 23.

    Wu, R. et al. Purely coherent nonlinear optical response in solution dispersions of graphene sheets. Nano Lett. 11, 5159–5164 (2011).

    ADS  Article  Google Scholar 

  24. 24.

    Sun, D. et al. Coherent control of ballistic photocurrents in multilayer epitaxial graphene using quantum interference. Nano Lett. 10, 1293–1296 (2010).

    ADS  Article  Google Scholar 

  25. 25.

    Yoshikawa, N., Tamaya, T. & Tanaka, K. High-harmonic generation in graphene enhanced by elliptically polarized light excitation. Science 356, 736–738 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  26. 26.

    Giorgianni, F. et al. Strong nonlinear terahertz response induced by Dirac surface states in Bi2Se3 topological insulator. Nat. Commun. 7, 11421 (2016).

    ADS  Article  Google Scholar 

  27. 27.

    Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2016).

    Article  Google Scholar 

  28. 28.

    Cheng, J. L., Vermeulen, N. & Sipe, J. E. Third order optical nonlinearity of graphene. New J. Phys. 16, 53014 (2014).

    Article  Google Scholar 

  29. 29.

    Cheng, J. L., Vermeulen, N. & Sipe, J. E. Third-order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature. Phys. Rev. B 91, 235320 (2015).

    ADS  Article  Google Scholar 

  30. 30.

    Margulis, V. A., Muryumin, E. E. & Gaiduk, E. A. Frequency dependence of optical third-harmonic generation from doped graphene. Phys. Lett. A 380, 304–310 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    Mikhailov, S. A. Quantum theory of the third-order nonlinear electrodynamic effects of graphene. Phys. Rev. B 93, 085403 (2016).

    ADS  Article  Google Scholar 

  32. 32.

    Rostami, H. & Polini, M. Theory of third-harmonic generation in graphene: a diagrammatic approach. Phys. Rev. B 93, 161411 (2016).

    ADS  Article  Google Scholar 

  33. 33.

    Alexander, K., Savostianova, N. A., Mikhailov, S. A., Kuyken, B. & Van Thourhout, D. Electrically tunable optical nonlinearities in graphene-covered SiN waveguides characterized by four-wave mixing. ACS Photon. 4, 3039–3044 (2017).

    Article  Google Scholar 

  34. 34.

    Das, A. et al. Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor. Nat. Nanotech. 3, 210–215 (2008).

    Article  Google Scholar 

  35. 35.

    Ye, J. T. et al. Liquid-gated interface superconductivity on an atomically flat film. Nat. Mater. 9, 125–128 (2009).

    ADS  Article  Google Scholar 

  36. 36.

    Li, Z. Q. et al. Dirac charge dynamics in graphene by infrared spectroscopy. Nat. Phys. 4, 532–535 (2008).

    Article  Google Scholar 

  37. 37.

    Liu, W. T. et al. Nonlinear broadband photoluminescence of graphene induced by femtosecond laser irradiation. Phys. Rev. B 82, 081408 (2010).

    ADS  Article  Google Scholar 

  38. 38.

    Shen, Y. R. The Principles of Nonlinear Optics (Wiley-Interscience, New York, NY, 1984).

    Google Scholar 

  39. 39.

    Boyd, R. W. Nonlinear Optics (Academic Press, New York, NY, 2008).

    Google Scholar 

  40. 40.

    Sarma, S. D., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011).

    ADS  Article  Google Scholar 

  41. 41.

    Lui, C. H., Mak, K. F., Shan, J. & Heinz, T. F. Ultrafast photoluminescence from graphene. Phys. Rev. Lett. 105, 127404 (2010).

    ADS  Article  Google Scholar 

  42. 42.

    Shi, S.-F. et al. Controlling graphene ultrafast hot carrier response from metal-like to semiconductor-like by electrostatic gating. Nano Lett. 14, 1578–1582 (2014).

    ADS  Article  Google Scholar 

  43. 43.

    Constant, T. J., Hornett, S. M., Chang, D. E. & Hendry, E. All-optical generation of surface plasmons in graphene. Nat. Phys. 12, 124–127 (2015).

    Article  Google Scholar 

  44. 44.

    Cheng, J. L., Vermeulen, N. & Sipe, J. E. Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects. Sci. Rep. 7, 43843 (2017).

    ADS  Article  Google Scholar 

  45. 45.

    Wang, Y., Tokman, M. & Belyanin, A. Second-order nonlinear optical response of graphene. Phys. Rev. B 94, 195442 (2016).

    ADS  Article  Google Scholar 

  46. 46.

    Xu, X. Z. et al. Ultrafast growth of single-crystal graphene assisted by a continuous oxygen supply. Nat. Nanotech. 11, 930–935 (2016).

    ADS  Article  Google Scholar 

  47. 47.

    Xu, X. Z. et al. Ultrafast epitaxial growth of metre-sized single-crystal graphene on industrial Cu foil. Sci. Bull. 62, 1074–1080 (2017).

    Article  Google Scholar 

  48. 48.

    Li, X. et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324, 1312–1314 (2009).

    ADS  Article  Google Scholar 

Download references

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).

Author information

Affiliations

Authors

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.

Corresponding authors

Correspondence to Wei-Tao Liu or Shiwei Wu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing