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Linking high harmonics from gases and solids

Nature volume 522, pages 462–464 (2015)Cite this article

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A Corrigendum to this article was published on 07 December 2016

This article has been updated

Abstract

When intense light interacts with an atomic gas, recollision between an ionizing electron and its parent ion1 creates high-order harmonics of the fundamental laser frequency2. This sub-cycle effect generates coherent soft X-rays3 and attosecond pulses4, and provides a means to image molecular orbitals5. Recently, high harmonics have been generated from bulk crystals6,7, but what mechanism8,9,10,11,12 dominates the emission remains uncertain. To resolve this issue, we adapt measurement methods from gas-phase research13,14 to solid zinc oxide driven by mid-infrared laser fields of 0.25 volts per ångström. We find that when we alter the generation process with a second-harmonic beam, the modified harmonic spectrum bears the signature of a generalized recollision between an electron and its associated hole11. In addition, we find that solid-state high harmonics are perturbed by fields so weak that they are present in conventional electronic circuits, thus opening a route to integrate electronics with attosecond and high-harmonic technology. Future experiments will permit the band structure of a solid15 to be tomographically reconstructed.

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Figure 1: Realization of the in situ experiment.
Figure 2: Comparison with theory.
Figure 3: From perturbing to controlling harmonic generation.

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Acknowledgements

We thank A. Larameé from the Advanced Laser Light Source for technical support during the experiment and M. Clerici for lending some equipment. We acknowledge financial support from the US AFOSR, NSERC, FRQNT, MDEIE and CFI.

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Authors and Affiliations

  1. Department of Physics, University of Ottawa, Ottawa, K1N 6N5, Ontario, Canada

    G. Vampa, T. J. Hammond, C. R. McDonald, T. Brabec & P. B. Corkum

  2. INRS-EMT, 1650 boulevard Lionel-Boulet, CP 1020, Varennes, J3X 1S2, Québec, Canada

    N. Thiré, B. E. Schmidt & F. Légaré

  3. National Research Council of Canada, Ottawa, K1A 0R6, Ontario, Canada

    P. B. Corkum

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  1. G. Vampa
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Contributions

G.V. and P.B.C. conceived the experiment; G.V., T.J.H. and N.T. performed the experiment; N.T. and B.E.S. developed the laser source; P.B.C. and F.L. supervised the experiment; C.R.M. and T.B. supervised the theoretical calculations; all authors contributed to the manuscript.

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Correspondence to G. Vampa or P. B. Corkum.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Evolution of conduction band population with time as a function of Bloch vector.

Population in the conduction band (colour-coded, key at right) is created at each peak of the laser field and subsequently accelerated to large crystal momenta. The population is resolved along the ΓM direction of the Brillouin zone.

Extended Data Figure 2 High-harmonic emission is timed to the electron–hole recollision.

The spectral content of the intraband (a) and interband (b) mechanisms as a function of time shows that each high harmonic is emitted at a specific moment of the laser cycle. This moment is the time of generalized recollision between the electron and the hole (red line). The intensity (colour-coded) is on a logarithmic scale. The laser parameters are: ω = 0.0121 a.u., F0 = 0.0049 a.u.

Extended Data Figure 3 Predicted in situ spectrograms.

Simulated spectrogram for interband (a) and intraband (b) emission. Intensity is colour-coded on a logarithmic scale. Each harmonic order has been normalized to simplify comparison. The laser parameters are: ω = 0.0121 a.u., F0 = 0.0049 a.u., F2ω = 10−2 F0.

Extended Data Figure 4 Comparison of atomic and solid high-harmonic generation.

The phase of the modulation of the even harmonic intensity is plotted as a function of harmonic order. The green line is obtained for an atom with ionization potential equal to the bandgap of ZnO (3.3 eV, marked by the vertical black dashed line). The blue line and the black circles are the theoretical prediction for the interband source and the experimental data points, respectively. The theoretical prediction is based on classical trajectory calculation.

Extended Data Figure 5 Cut-off scaling of interband emission.

The high-harmonic cut-off of interband emission predicted by the numerical solution of the two-band model is plotted as a function of field strength. The cut-off scales linearly with the field strength up to the maximum bandgap (reached at the edge of the Brillouin zone). The calculated values (red dots) are connected by the dashed dotted line to show the linear scaling.

Extended Data Figure 6 Scaling of high-harmonic emission with the field strength of the fundamental.

The two-band model predicts that interband emission dominates over a wide range of field strengths. The field strength of our experiment is F0 = 0.0049 a.u. (middle panel), while that of ref. 6 corrected for the reflection loss is F0 = 0.008 a.u. (bottom panel). The vertical black dashed line marks the minimum bandgap (at 3.3 eV).

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Vampa, G., Hammond, T., Thiré, N. et al. Linking high harmonics from gases and solids. Nature 522, 462–464 (2015). https://doi.org/10.1038/nature14517

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