Abstract

Perturbative optical nonlinearities induced by static electric fields1 have proven useful in visualizing dynamical function in systems including operating circuits2,3, electric and magnetic domain walls4, and biological matter5, and in controlling light for applications in silicon photonics6. Here, we extend field-induced second-harmonic generation to the non-perturbative regime. We demonstrate that static or transient fields up to terahertz (THz) frequencies applied to silicon and ZnO crystals generate even-order high harmonics. Images of the even harmonics confirm that static fields delivered with conventional electronics control the spatial properties of the high-harmonic emission. Extending our methodology to higher-harmonic photon energies7,8 paves the way for realizing active optics in the extreme ultraviolet and will allow imaging of operating electronic circuits9, of Si-photonic devices10 and of other functional materials11,12, with higher spatio-temporal resolution than perturbative methods. For THz spectroscopy, our method has the bandwidth to allow measurement of attosecond transients imprinted on THz waveforms.

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Acknowledgements

We thank A. Laramée and C. A. Couture (Advanced Laser Light Source), D. Crane and B. Avery (NRC Canada) for technical support, and G. Lopinski (NRC Canada) for discussions and for lending electrical equipment. This material is based on work supported by the US Air Force Office of Scientific Research under award numbers FA9550-16-1-0109 and FA9550-15-1-0037; and by Canada’s National Research Council (NRC), the Natural Sciences and Engineering Research Council (NSERC), Canada Foundation for Innovation (CFI) and the Ontario Research Fund (ORF).

Author information

Affiliations

  1. Department of Physics, University of Ottawa, Ottawa, Ontario, Canada

    • G. Vampa
    • , T. J. Hammond
    • , M. Taucer
    • , Xiaoyan Ding
    •  & P. B. Corkum
  2. Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    • G. Vampa
  3. INRS-EMT, Varennes, Quebec, Canada

    • X. Ropagnol
    • , T. Ozaki
    • , S. Delprat
    • , M. Chaker
    • , N. Thiré
    •  & F. Légaré
  4. few-cycle Inc., Montreal, Quebec, Canada

    • B. E. Schmidt
  5. National Research Council of Canada, Ottawa, Ontario, Canada

    • D. D. Klug
    • , A. Yu. Naumov
    • , D. M. Villeneuve
    • , A. Staudte
    •  & P. B. Corkum

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Contributions

G.V. and P.B.C. conceived the experiment. G.V., T.J.H., M.T., X.D. and N.T. performed the measurements with static fields. G.V. and X.R. performed the THz experiment. S.D. fabricated the electrodes. N.T., B.E.S. and A.S. maintained the laser sources. D.D.K. provided theoretical support. T.O., M.C., A.Yu.N., D.M.V., A.S., F.L. and P.B.C. supervised the experiments. All authors contributed to the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to G. Vampa.

Supplementary information

  1. Supplementary Information

    Supplementary notes and figures.

  2. Supplementary Video 1

    Electric field build up.

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DOI

https://doi.org/10.1038/s41566-018-0193-5

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