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Extreme ultraviolet high-harmonic spectroscopy of solids


Extreme ultraviolet (EUV) high-harmonic radiation1,2 emerging from laser-driven atoms, molecules or plasmas underlies powerful attosecond spectroscopy techniques3,4,5 and provides insight into fundamental structural and dynamic properties of matter6,7. The advancement of these spectroscopy techniques to study strong-field electron dynamics in condensed matter calls for the generation and manipulation of EUV radiation in bulk solids, but this capability has remained beyond the reach of optical sciences. Recent experiments8,9 and theoretical predictions10,11,12 paved the way to strong-field physics in solids by demonstrating the generation and optical control of deep ultraviolet radiation8 in bulk semiconductors, driven by femtosecond mid-infrared fields or the coherent up-conversion of terahertz fields to multi-octave spectra in the mid-infrared and optical frequencies9. Here we demonstrate that thin films of SiO2 exposed to intense, few-cycle to sub-cycle pulses give rise to wideband coherent EUV radiation extending in energy to about 40 electronvolts. Our study indicates the association of the emitted EUV radiation with intraband currents of multi-petahertz frequency, induced in the lowest conduction band of SiO2. To demonstrate the applicability of high-harmonic spectroscopy to solids, we exploit the EUV spectra to gain access to fine details of the energy dispersion profile of the conduction band that are as yet inaccessible by photoemission spectroscopy in wide-bandgap dielectrics. In addition, we use the EUV spectra to trace the attosecond control of the intraband electron motion induced by synthesized optical transients. Our work advances lightwave electronics5,13,14,15 in condensed matter into the realm of multi-petahertz frequencies and their attosecond control, and marks the advent of solid-state EUV photonics.

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Figure 1: Generation, energy cutoff and intensity scaling of coherent EUV radiation in SiO2 films.
Figure 2: Semiclassical picture of the field-driven electron dynamics in SiO2.
Figure 3: Field control of laser-driven EUV emission in SiO2 (experiment and simulation).
Figure 4: Coherent EUV source characteristics.


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We thank M. Wismer for support in calculations, and A. Jain for help during experiments. This work was supported by a European Research Council grant (Attoelectronics-258501), the Deutsche Forschungsgemeinschaft Cluster of Excellence: Munich Centre for Advanced Photonics (, the Max Planck Society and the European Research Training Network ATTOFEL.

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Authors and Affiliations



T.T.L. and M.G. conducted the experiments; A.M. and M.Th.H. contributed to the development of the source; E.G. conceived the experiments; T.T.L., M.G. and S.Yu.K. conducted the simulations; S.Yu.K. performed the analytical derivations; E.G., T.T.L., M.G. and S.Yu.K. contributed to the preparation of the manuscript.

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Correspondence to E. Goulielmakis.

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The authors declare no competing financial interests.

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Luu, T., Garg, M., Kruchinin, S. et al. Extreme ultraviolet high-harmonic spectroscopy of solids. Nature 521, 498–502 (2015).

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