## 4 Applications
### High-Order Harmonic Generation Spectroscopy
In particular, collective electron dynamics involving inner shell electrons have been observed in atoms by recording IR-driven high-order harmonics spectra extending beyond 100 eV. An enhancement in the high energy part of the spectrum (between 70 eV and 100 eV) was recently observed in xenon by using few-cycle pulses at 1.8 \(\upmu\)m and 1.5 \(\upmu\)m [70; 71]. This spectral feature is attributed to a multi-electron effect known as giant resonance [72]. The role of ionization from multiple molecular orbitals has been studied in \(CO_{2}\) and \(N_{2}\) by performing HHG measurements at different pulse intensities and IR wavelengths [73; 74]. Here, intensity-dependent spectral features are attributed to the increasing contribution of deeper orbitals, and wavelength-dependent spectral features are recognized as due to the interference among different ionization-recombination channels involving multiple orbitals. A comprehensive overview on the IR-driven HHG spectroscopy of atoms and molecules is provided in [11]. Efforts are currently devoted to the extension of HHG to the study of condensed-matter systems. Up to date achievements are briefly described below, and the main focus is placed on long-wavelength-driven HHG experiments in bulk crystals. HHG in condensed matter systems is basically different from HHG in gas-phase samples. This is mainly because atoms are highly packed, and in the case of crystals, they are arranged to form a periodic lattice. Charges in crystals are delocalized over the entire lattice structure. As opposed to the atomic/molecular case, the HHG process cannot be described in terms of single electron trajectories, but in terms of charge oscillations. These collective charge motions are called dynamical Bloch oscillations. The electronic properties of bulk materials derive from their band structure. In particular, the valence and the conduction bands are mainly responsible for the behavior of solids interacting with visible and IR radiation. In solid-state systems of technological interest, like semiconductors and insulators, the energy gap ranges from 0.1 eV to 10 eV, thus covering from the mid-IR up to the EUV spectrum. The high harmonics emission in bulk material involves electrons and holes located respectively in the conduction and in the valence bands. In particular, this electron-hole population undergoes intraband acceleration by interaction with the external radiation. The resulting charge currents depends on the energy dispersion profile of the conduction and valence bands. Thus, the emitted HHG spectrum encodes information on the band structure from which it arises. The generation of a high-order harmonics spectrum from solids is challenging because of a number of fundamental limitations. A first limitation is related to material ablation. When a driving radiation with an intensity above the material damage threshold is used, ablation takes place. Ablation leads to changes in the structural properties of the sample, thus preventing the observation of the effects correlated to the periodic arrangement of atoms. Since ablation is mainly induced by multi-photon absorption, the use of the IR long-wavelength is beneficial. Indeed, the lower is the driving photon energy, the lower is the probability of interband transition. A second limitation consists of the strong absorption of photons with energy higher than the band-gap. Due to the high density of the media, absorption of EUV photons becomes more critical than in gas samples, and it is responsible for a significant suppression of the harmonics signal. Sources with a high repetition rate are thus required for HHG experiments in condensed matter systems. The first observation of a broad HHG spectrum from a solid target, extending well beyond the band-gap energy, was reported in 2010 by [PERSON] et al. [75]. A few-cycle mid-IR parametric source was used to drive harmonics generation in a ZnO crystal (bandgap \(\sim\)3.2 eV).