Solid-state harmonics beyond the atomic limit


Strong-field laser excitation of solids can produce extremely nonlinear electronic and optical behaviour. As recently demonstrated, this includes the generation of high harmonics extending into the vacuum-ultraviolet and extreme-ultraviolet regions of the electromagnetic spectrum1,2,3,4,5,6,7,8. High harmonic generation is shown to occur fundamentally differently in solids and in dilute atomic gases1,2,3,4,5,6,9,10,11,12,13. How the microscopic mechanisms in the solid and the gas differ remains a topic of intense debate1,2,3,4,5,6,7,8,9,10,11,14,15,16,17,18. Here we report a direct comparison of high harmonic generation in the solid and gas phases of argon and krypton. Owing to the weak van der Waals interaction, rare (noble)-gas solids are a near-ideal medium in which to study the role of high density and periodicity in the generation process. We find that the high harmonic generation spectra from the rare-gas solids exhibit multiple plateaus extending well beyond the atomic limit of the corresponding gas-phase harmonics measured under similar conditions. The appearance of multiple plateaus indicates strong interband couplings involving multiple single-particle bands. We also compare the dependence of the solid and gas harmonic yield on laser ellipticity and find that they are similar, suggesting the importance of electron–hole recollision in these solids. This implies that gas-phase methods such as polarization gating for attosecond pulse generation and orbital tomography could be realized in solids.

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Figure 1: Representative spectra of HHG from solid Ar and Kr on a logarithmic scale for the driving wavelength of λ0 = 1,333 nm.
Figure 2: Evolution of the HHG spectrum as a function of the laser intensity.
Figure 3: Comparison of the spectral cutoff of HHG in solid and gas Ar and Kr as a function of the laser intensity.
Figure 4: Comparison of ellipticity dependence of the 25th and 31st harmonics from solid and gas-phase Ar at similar peak fields.


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At Stanford/SLAC, this work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, through the AMOS programme within the Chemical Sciences Division (G.N., D.A.R.) and the Office of Science Early Career Research Program (S.G.). At Louisiana State University this work is supported by the National Science Foundation under grant number PHY-1403236. Solid Ar samples were characterized at Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, the use of which is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract number DE AC02-76SF00515.

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G.N., S.G. and D.A.R. conceived the experiments. G.N. performed the experiment and analysed the data. M.W., K.J.S., and M.B.G. developed the single electron laser excitation theory and performed the calculation. D.A.B. performed the DFT calculations. All authors contributed to the interpretation of the results and writing of the manuscript.

Corresponding authors

Correspondence to Georges Ndabashimiye or David A. Reis.

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The authors declare no competing financial interests.

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Ndabashimiye, G., Ghimire, S., Wu, M. et al. Solid-state harmonics beyond the atomic limit. Nature 534, 520–523 (2016).

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