Interferometry of dipole phase in high harmonics from solids


Understanding the temporal profiles of high harmonics is essential for their applications in attosecond science1,2. Microscopically, the dipole phase plays an important role in determining the high-harmonic emission phase2,3,4. In gas-phase high-harmonic generation, the tunnel-ionized electron spends much of its travel time in the continuum—far from the parent ion, where it accumulates the dipole phase5,6. Therefore, the atomic dipole phase is largely independent of the target atom3. In solid-state high-harmonic generation7,8,9,10,11, since the driven electron experiences a periodic potential during the entire travel time, the dipole phase may depend on the electronic structures of source materials9,12,13,14. Here, we employ an interferometric method to characterize high harmonics from magnesium oxide and quartz crystals. We measure material-dependent intensity-induced high-harmonic phase delays that we attribute to the intensity-induced changes in the dipole phase originating from the interband polarization10,15,16. The material-dependent dipole phase can provide a robust platform for high-harmonic spectroscopy of solids.

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Fig. 1: Homodyne high-harmonic interferometry of MgO crystals.
Fig. 2: Intensity-induced relative fringe shifts for the 15th harmonic from MgO pumped by 1,320 nm pulses.
Fig. 3: Intensity-dependent relative phase shifts due to the dipole phase and the propagation effects measured in MgO pumped by 1,320 nm pulses.
Fig. 4: Simulation of the intensity-induced changes of the dipole phase.
Fig. 5: Intensity-induced relative fringe shifts in high harmonics from MgO and SiO2 pumped by 800 nm pulses.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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This work was primarily supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through the Early Career Research Program. D.A.R. acknowledges support from the AMOS Program in the Chemical Sciences, Geosciences, and Biosciences Division. We thank H. Liu, G. Vampa and B. Iwan for many fruitful discussions and for assisting in experiments.

Author information

J.L., E.F.C. and S.G. conceived the experiments. J.L. and E.F.C. conducted the measurements. J.L. analysed the data and performed the simulations. Y.S.Y. assisted in the measurements and simulations. J.L., E.F.C., Y.S.Y., D.A.R. and S.G. contributed to the interpretation of the results and preparation of the manuscript.

Correspondence to Jian Lu or Shambhu Ghimire.

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Lu, J., Cunningham, E.F., You, Y.S. et al. Interferometry of dipole phase in high harmonics from solids. Nature Photon 13, 96–100 (2019).

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