High-order harmonics in the extreme-ultraviolet regime can be produced and a stable waveform-locked attosecond pulse can be formed when quartz is excited by a strong short-pulsed laser, providing a robust path towards attosecond photonics.
The ability to produce and manipulate electrical waveforms is one of the most important ingredients of modern technology. Faster and reproducible waveforms are highly desired for future electronics and signal processing applications. Laser pulses provide ultrafast waveforms, but producing identical waveforms on subsequent pulses is a difficult task. This gets more complicated when the laser’s wavelength gets shorter, such as in the extreme-ultraviolet (EUV) and X-ray wavelength ranges.
Coherent EUV pulses are typically produced through the process of high-order harmonic generation (HHG) by focusing strong near-infrared (NIR) laser pulses in atomic gases. The waveform of EUV pulses depends sensitively on the laser parameters such as peak intensity and carrier-envelope phase (CEP; the offset between the carrier and the envelope of the laser pulse) — both are difficult parameters to control in experiments. The waveform sensitivity is intrinsic to the underlying microscopic dynamics of HHG that occur at the single-atom level, it is therefore difficult to solve the stability issues to produce identical waveforms on subsequent pulses.
There is an ongoing effort in evaluating an entirely different HHG approach, that is, using a solid medium instead; the first demonstration of solid-phase HHG was in zinc oxide crystals1. Writing in Nature Photonics, Manish Garg and colleagues from the Max Planck Institute, Germany, now report high-harmonic generation from quartz crystals, including a careful characterization of the corresponding EUV pulse waveform in the time domain2. Their results show that these waveforms are locked to the pump laser field, and are reproducible at every laser shot despite the fluctuations in the amplitude of the laser field.
Garg and colleagues have possibly overcome the fundamental limitations of gas-phase HHG in terms of the synchronization of the EUV pulse’s waveform. The microscopic process of HHG in atomic gases has been understood using a three-step process: tunnel ionization, free acceleration, and recombination to the parent ion3. This leads to the fact that different harmonic orders have corresponding and unique electron trajectories, whose excursion amplitude depends on the peak intensity and the moment at which they are emitted from the laser field. This is the origin of the high sensitivity of the gas-phase EUV pulse waveform to the intensity and CEP of the NIR laser pulse. Also, because the individual electron trajectories meet the parent ions at slightly different times, there is a delay between different harmonic orders, so-called atto-chirp, which is a disadvantage of attosecond pulse generation, although it can be compensated post-generation by inserting thin metal foils.
The solid-state HHG process is fundamentally different as it involves novel strong-field processes attributed to the high density of the source material. In wide-bandgap semiconductors and insulators, valance bands are filled and conduction bands are empty. In the presence of a strong laser pulse, a small fraction of electrons from the valance band get excited to the lowest conduction band, much like tunnelling from atomic orbitals to vacuum in a gas medium. In particular, interband electron motion in solids is similar to the three-step recollision model of gas-phase HHG4. However, electrons in the conduction band do not move as free particles, and their dynamics are governed by the band structure. At strong fields, Bloch oscillations of electrons within the conduction band could also produce high-order harmonics, which would be markedly different from the gas-phase HHG1. The relative role of inter- and intraband dynamics depends on many things: the shape of the valence and conduction bands, the transition dipole matrix elements between the valence and conduction bands, the bandgap and photon energy, for example. Therefore, the dominant microscopic mechanism could easily depend on the material.
Why quartz? A quartz crystal was used to produce the optical second harmonic of a ruby laser 57 years ago, which marked the birth of nonlinear optics5. In that experiment, the strength of the applied field was about 105 V cm–1, which is a small perturbation to the field-free Hamiltonian. With the advent of ultrafast laser technology, it is now possible to apply ~1,000 times stronger pulses to quartz crystals without causing permanent damage. As a result, high-order harmonics are produced, whose spectra extend to the EUV range6,7,8,9. A typical experimental set-up is shown schematically in Fig. 1. In Garg and colleagues’ work, because of the high applied field, the interaction term of the Hamiltonian is comparable to the field-free Hamiltonian; therefore, the usual perturbation theory of nonlinear optics breaks down5. Clearly, the underlying electron dynamics involve attosecond timescales, but the outstanding question was just how the EUV waveforms are synchronized with the electric field of the driving laser pulse. Does that synchronization depend on the laser parameters, as in the gas phase?
To shed light onto the problem, Garg and colleagues consider an interferometry method, which has been successful in similar gas-phase experiments. In their work, photoelectron interferometry is employed to measure the waveform of the EUV pulse produced by solid-state HHG. The EUV beam produced via high-harmonic generation from a thin quartz crystal is focused together with a reference NIR laser beam onto an argon gas target. EUV photons produce photoelectrons from the atoms via photoionization processes. The reference laser’s photon energy is too small for direct photoionization but its peak intensity is strong enough to produce electrons via the nonlinear absorption process above-threshold ionization (ATI). The ATI electron spectrum extends to the energy range of the EUV photoelectrons. Then, the ATI and EUV processes interfere, producing fringes that are observed in the electron detector.
The important finding of Garg and colleagues’ work is that these fringe positions do not depend on the peak intensity of the pump laser. The fringe positions also remained effectively fixed to the variation in the CEP. Additionally, the entire comb of measured high harmonics from quartz does not show any measurable delay among harmonics, which means there is no intrinsic atto-chirp2. These remarkable experimental observations are in contrast to the gas-phase HHG, but are exactly what the Bloch oscillation model has predicted1,10. The implications of solid-state HHG are in materials science, in attosecond pulse generation in a compact set-up8,11 and in high-harmonic spectroscopy6.
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