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...

Establishing the structure of molecules and solids has always had an essential role in physics, chemistry and biology. The methods of choice are X-ray and electron diffraction, which are routinely used to determine atomic positions with sub-ångström spatial resolution. Although both methods are currently limited to probing dynamics on timescales longer than a picosecond, the recent development of femtosecond sources of X-ray pulses and electron beams suggests that they might soon be capable of taking ultrafast snapshots of biological molecules and condensed-phase systems undergoing structural changes. The past decade has also witnessed the emergence of an alternative imaging approach based on laser-ionized bursts of coherent electron wave packets that self-interrogate the parent molecular structure. Here we show that this phenomenon can indeed be exploited for laser-induced electron diffraction (LIED), to image molecular structures with sub-ångström precision and exposure times of a few femtoseconds. We apply the method to oxygen and nitrogen molecules, which on strong-field ionization at three mid-infrared wavelengths (1.7, 2.0 and 2.3 μm) emit photoelectrons with a momentum distribution from which we extract diffraction patterns. The long wavelength is essential for achieving atomic-scale spatial resolution, and the wavelength variation is equivalent to taking snapshots at different times. We show that the method has the sensitivity to measure a 0.1 Å displacement in the oxygen bond length occurring in a time interval of ∼5 fs, which establishes LIED as a promising approach for the imaging of gas-phase molecules with unprecedented spatio-temporal resolution.

Understanding molecular femtosecond dynamics under intense X-ray exposure is critical to progress in biomolecular imaging and matter under extreme conditions. Imaging viruses and proteins at an atomic spatial scale and on the time scale of atomic motion requires rigorous, quantitative understanding of dynamical effects of intense X-ray exposure. Here we present an experimental and theoretical study of C 60 molecules interacting with intense X-ray pulses from a free-electron laser, revealing the influence of processes not previously reported. Our work illustrates the successful use of classical mechanics to describe all moving particles in C 60 , an approach that scales well to larger systems, for example, biomolecules. Comparisons of the model with experimental data on C 60 ion fragmentation show excellent agreement under a variety of laser conditions. The results indicate that this modelling is applicable for X-ray interactions with any extended system, even at higher X-ray dose rates expected with future light sources.

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We review the status of strong-field and attosecond processes in bulk transparent solids near the Keldysh tunneling limit. For high enough fields and low-frequency excitations, the optical and electronic properties of dielectrics can be transiently and reversibly modified within the applied pulse. In Ghimire et al (2011 Phys. Rev. Lett. 107 167407) non-parabolic band effects were seen in photon-assisted tunneling experiments in ZnO crystals in a strong mid-infrared field. Using the same ZnO crystals, Ghimire et al (2011 Nat. Phys. 7 138-41) reported the first observation of non-pertubative high harmonics, extending well above the bandgap into the vacuum ultraviolet. Recent experiments by Schubert et al (2014 Nat. Photonics 8 119-23) showed a carrier envelope phase dependence in the harmonic spectrum in strong-field 30 THz driven GaSe crystals which is the most direct evidence yet of the role of sub-cycle electron dynamics in solid-state harmonic generation. The harmonic generation mechanism is different from the gas phase owing to the high density and periodicity of the crystal. For example, this results in a linear dependence of the high-energy cutoff with the applied field in contrast to the quadratic dependence in the gas phase. Sub-100 attosecond pulses could become possible if the harmonic spectrum can be extended into the extreme ultraviolet (XUV). Here we report harmonics generated in bulk MgO crystals, extending to ∼26 eV when driven by ∼35 fs, 800 nm pulses focused to a ∼1 VÅ −1 peak field. The fundamental strong-field and attosecond response also leads to Wannier-Stark localization and reversible semimetallization as seen in the sub-optical cycle behavior of XUV absorption and photocurrent experiments on fused silica by Schiffrin et al (2013 Nature 493 70-4) and Schultze et al (2013 Nature 493 75-8). These studies are advancing our understanding of fundamental strong-field and attosecond physics in solids with potential applications for compact coherent short-wavelength sources and ultra-high speed optoelectronics.

We report time-resolved electroabsorption of a weak probe in a 500 μm thick zinc-oxide crystal in the presence of a strong midinfrared pump in the tunneling limit. We observe a substantial redshift in the absorption edge that scales with the cube root of intensity up to 1 TW/cm(2) (0.38 eV cm(2/3) TW(-1/3)) after which it increases more slowly to 0.4 eV at a maximum applied intensity of 5 TW/cm(2). The maximum shift corresponds to more than 10% of the band gap. The change in scaling occurs in a regime of nonperturbative high-order harmonic generation where electrons undergo periodic Bragg scattering from the Brillouin zone boundaries. It also coincides with the limit where the electric field becomes comparable to the ratio of the band gap to the lattice spacing.

We report the compression of intense, carrier-envelope phase stable mid-IR pulses down to few-cycle duration using an optical filament. A filament in xenon gas is formed by using self-phase stabilized 330 J 55 fs pulses at 2 m produced via difference-frequency generation in a Ti:sapphire-pumped optical parametric amplifier. The ultrabroadband 2 m carrier-wavelength output is self-compressed below 3 optical cycles and has a 270 J pulse energy. The self-locked phase offset of the 2 m difference-frequency field is preserved after filamentation. This is to our knowledge the first experimental realization of pulse compression in optical filaments at mid-IR wavelengths ͑Ͼ0.8 m͒. © 2007 Optical Society of America OCIS codes: 190.5530, 320.5520. Progress in strong-field physics has been accelerated by the development of lasers operating near the 0.8 m wavelength that feature high peak power, few-cycle duration, and reliable control over the carrier-envelope phase 1 (CEP). Furthermore, the fundamental scaling laws 2,3 governing the intense laseratom interaction suggest that the advancement of longer-wavelength mid-IR laser sources capable of similar optical quality will have a major impact in strong-field physics. The most compelling examples include the generation of shorter attosecond x-ray bursts and the rescattering of electrons at kilovolt energies. [3][4][5] A recently demonstrated 80 J, 2 m prototype system 6 based on optical parametric chirped-pulse amplification via difference-frequency generation defines a standard for future development of longwavelength drivers. However, the optical parametric chirped-pulse amplification architecture is faced with important technical challenges, 7 such as the need for specific pump laser design and unwanted generation of parasitic fluorescence underlying the primary pulse for high parametric gain configurations. 6 Currently, femtosecond optical parametric amplifiers (OPAs) pumped by multimillijoule Ti:sapphire chirped-pulse amplification systems can deliver multicycle pulses in the mid-IR with sufficient peak power to investigate the efficacy of the nonlinear pulse compression techniques developed at shorter wavelengths. In particular, optical filaments formed in a noble gas by intense 0.8 m pulses have demonstrated pulse compression down to the few-cycle regime with excellent beam stability and spatial mode quality. 8This Letter demonstrates, for the first time to our knowledge, the self-compression in an optical filament of high-peak-power mid-IR pulses derived by difference-frequency generation in a Ti:sapphire pumped OPA. This efficient scheme produces fluorescence-free, sub-3 optical cycle pulses near the 2 m wavelength with 270 J energy at a 1 kHz repetition rate. The intense 2 m field carries a constant CEP offset, thus making it an attractive longwavelength driver for benchmark strong-field experiments.A schematic of the experimental setup is shown in Fig. 1. High-peak-power multicycle mid-IR pulses are produced in a slightly modified traveling-wave OPA (TOPAS, L...

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