Harmonic generation is a general feature of driven nonlinear systems. In particular high-order harmonic generation (HHG) in atomic gases 1 is the basis for producing attosecond pulses 2,3 . In molecules and clusters, the existence of multiple ionization and recombination sites makes for richer dynamics allowing imaging of molecular orbitals 4,5 , higher conversion efficiency 6 and the possibility of extending the high-energy cutoff 7 . In the strong-field limit, HHG in bulk crystals is fundamentally different from that in the atomic case owing to the high density and periodic structure. Here we present the first observation of HHG in a bulk crystalline solid using a long-wavelength few-cycle laser. The harmonics spectra extend well beyond the band edge of the ZnO crystal, show a clear non-perturbative character and exhibit a cutoff that scales linearly with the electric field of the drive laser. Our results have important implications for the understanding of attosecond electron dynamics and other non-equilibrium band-structure-related phenomena in strongly driven bulk solids.The HHG spectrum from a gas typically comprises a region of rapidly decreasing low orders that scale perturbatively followed by a slowly varying succession of higher orders that scale nonperturbatively with the strength of the drive laser 1 . At the tunnelling limit of strong-field ionization 8 , the non-perturbative harmonic generation process has been described semiclassically in a recollision model 9,10 consisting of three steps: tunnel ionization of an electron, its acceleration in the laser field, and its recombination to the parent ion with an energy release in the form of higher-energy photons-a coherent process that occurs on successive half-cycles of the laser pulse, leading to emission of odd harmonics. The single-atom maximum photon energy is 9,11h ω max = I p + 3.2U p , where I p is the ionization potential and U p = e 2 E 2 λ 2 /16π 2 mc 2 is the ponderomotive energy of the electron in the laser field. The amplitude of the maximum excursion of a recolliding electron is r max = eEλ 2 /4π 2 mc 2 . For the conditions of our experiments, E = 0.6 V Å −1 at λ = 3.25 µm, the atomic case would be U p = 5 eV and r max = 32 Å. The latter is many times the lattice constant of a typical crystal. Thus, we expect the possibility of ionization from one site and recombination on another; however, because of the lattice periodicity the process would still be coherent. We note that at this field strength, the potential across a lattice constant is comparable to the bandgap of a typical insulator. Therefore, the field cannot be thought of as a small perturbation to the crystal. The non-perturbative HHG from bulk crystals has been considered theoretically 12-14 but has never been observed experimentally until now.Previously, experimental observation of non-perturbative HHG in solids was only in reflection geometry [15][16][17][18] perturbative harmonics below the band edge up to the seventh order were produced by exciting semiconducting ZnSe with...

An era of exploring the interactions of high-intensity, hard X-rays with matter has begun with the start-up of a hard-X-ray free-electron laser, the Linac Coherent Light Source (LCLS). Understanding how electrons in matter respond to ultra-intense X-ray radiation is essential for all applications. Here we reveal the nature of the electronic response in a free atom to unprecedented high-intensity, short-wavelength, high-fluence radiation (respectively 10(18) W cm(-2), 1.5-0.6 nm, approximately 10(5) X-ray photons per A(2)). At this fluence, the neon target inevitably changes during the course of a single femtosecond-duration X-ray pulse-by sequentially ejecting electrons-to produce fully-stripped neon through absorption of six photons. Rapid photoejection of inner-shell electrons produces 'hollow' atoms and an intensity-induced X-ray transparency. Such transparency, due to the presence of inner-shell vacancies, can be induced in all atomic, molecular and condensed matter systems at high intensity. Quantitative comparison with theory allows us to extract LCLS fluence and pulse duration. Our successful modelling of X-ray/atom interactions using a straightforward rate equation approach augurs favourably for extension to complex systems.

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High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales [1][2][3][4][5][6] . The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands [7][8][9][10][11][12][13][14] . Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process The recent observation of HHG in bulk solids provides a new approach to attosecond photonics and has opened up exciting opportunities for the study of strong-field and ultrafast electron dynamics in the condensed phase [1][2][3][4][5][6]