High-harmonic generation (HHG) traditionally combines ~100 near-infrared laser photons to generate bright, phase-matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here, we show that by guiding a mid-infrared femtosecond laser in a high-pressure gas, ultrahigh harmonics can be generated, up to orders greater than 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to more than 1.6 kilo-electron volts, allowing, in principle, the generation of pulses as short as 2.5 attoseconds. The multiatmosphere gas pressures required for bright, phase-matched emission also support laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density the recolliding electrons responsible for HHG encounter other atoms during the emission process.

An accurate analytic model describing the microscopic mechanism of high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results reveal that (i) the emitted HHG spectra are highly anisotropic and laser-polarization dependent even for cubic crystals; (ii) the harmonic emission is enhanced by the inhomogeneity of the electron-nuclei potential; the yield is increased for heavier atoms; and (iii) the cutoff photon energy is driver-wavelength independent. Moreover, we show that it is possible to predict the laser polarization for optimal HHG in bulk crystals solely from the knowledge of their electronic band structure. Our results pave the way to better control and optimize HHG in solids by engineering their band structure. DOI: 10.1103/PhysRevLett.118.087403 Atoms and molecules interacting with strong laser pulses emit high-order harmonics of the fundamental driving laser field. The high-harmonic generation (HHG) in gases is routinely used nowadays to produce isolated attosecond pulses [1][2][3][4] and coherent radiation ranging from the visible to soft x rays [5]. Because of a higher electronic density, solids are one promising route towards compact, brighter HHG sources. The recent observation of nonperturbative HHG in solids without damage [6][7][8][9][10], extending even beyond the atomic limit [10], has opened the door to the observation and control of attosecond electron dynamics in solids [8,9,11], all-optical band-structure reconstruction [12], and solid-state sources of isolated extreme-ultraviolet pulses [9,11]. However, in contrast to HHG from gases, the microscopic mechanism underlying HHG from solids is still controversially debated in the attoscience community, in some cases casting doubts on the validity of the proposed microscopic model and resulting in confusion about the correct interpretation of experimental data. Various competing simplified models have been proposed but they often are based on strong approximations and a priori assumptions, often stating that there is a strong similarity with the processes underlying atomic-gas HHG emission. However, it is clear that many-body effects due to the crystalline structure of solids and the fermionic nature of interaction electrons play a decisive role that fundamentally distinguishes the solid from the gas case. It is the scope of the present work to unravel within an ab initio approach what the impact is of the underlying electronic band structure of the solids in the observed HHG emission.The process of HHG from gases is by now well understood in terms of the three-step model [13][14][15] in which electrons are first promoted from the ground state of the atom (or molecule) to the continuum, then accelerated by the electric field, and finally recombine with the parent ion. With this simple, intuitive model most of the observed effects are well described, in particular, the dependence of the harmonic cutoff energ...

High-energy isolated attosecond pulses required for the most intriguing nonlinear attosecond experiments as well as for attosecond-pump/attosecond-probe spectroscopy are still lacking at present. Here we propose and demonstrate a robust generation method of intense isolated attosecond pulses, which enable us to perform a nonlinear attosecond optics experiment. By combining a two-colour field synthesis and an energy-scaling method of high-order harmonic generation, the maximum pulse energy of the isolated attosecond pulse reaches as high as 1.3 μJ. The generated pulse with a duration of 500 as, as characterized by a nonlinear autocorrelation measurement, is the shortest and highest-energy pulse ever with the ability to induce nonlinear phenomena. The peak power of our tabletop light source reaches 2.6 GW, which even surpasses that of an extreme-ultraviolet free-electron laser.