## 4 Applications
### Photoelectron Spectroscopy  
As described in the HHG section, strong fields can induce tunnel ionization in matter, leading to the emission of photoelectrons. The energy and momentum distributions of photoelectrons encode structural and dynamical information on the target. Photoelectrons' detection is thus at the base of a number of spectroscopy techniques. For instance, photoelectrons are widely used for probing structural properties of matter at the atomic scale, in diffraction-based imaging methods. The main advantage of using electrons as a probe lies in their high cross-section of interaction with atoms. Indeed, electrons are charged particles, and their interaction with nuclei and electronic distributions is significantly enhanced with respect to photons. As an example, for energy values in the X-ray spectral window, the photoelectron scattering cross-section is more than five orders of magnitude higher than that of photons [94]. In order to attain sub-nanometer resolution, photoelectrons with an energy of the order of a few hundred eV are required. Ponderomotive acceleration of photoelectrons under high energy IR laser pulses provides the possibility to access such an extreme energy regime. Moreover, by using a few cycle pulses, ultrafast dynamics occurring into the sample can be probed with a sub-cycle resolution. In a strong field experiment, photo-emitted electrons are steered by the external driving field. Depending on the initial conditions (namely, instant of emission and initial momentum), photoelectrons can follow a number of different field-induced trajectories. As a first scenario, they may be driven away from the system they were emitted from, contributing to a process named Above Threshold Ionization (ATI). As an opposite scenario, they may be driven back to the parent ion. In this case, different processes may happen upon return. Recollision with the ion can be responsible for photo-recombination, resulting in the emission of high-order harmonic radiation. Photoelectrons may otherwise experience elastic or inelastic scattering, associated with momentum exchange and ion excitation. Photoelectrons undergoing different processes provide a different informational content. The main achievements obtained by studying photoelectrons in an IR-driven strong-field regime are reported below. In the last few years, remarkable results in molecular imaging have been obtained by applying a photoelectron-based diffraction imaging technique, named Laser-Induced Electron Diffraction (LIED) [95]. LIED allows to extract structural features of gas-phase molecules directly from electrons, which are elastically scattered off the target. In particular, high energy electrons (\(>\)100 eV) steered along the laser polarization direction are selected, and their momentum distribution is detected. The structural properties of molecular scatterers can be retrieved by properly processing this momentum map. In 2012, [PERSON] and coworkers exploited high energy few-cycle pulses tunable in the IR for implementing time-resolved LIED in simple molecules. They succeeded in capturing the dynamical evolution of oxygen and nitrogen structures under a vibrational excitation [96]. Recently, advances have been reported in LIED experiments performed with mid-infrared few-cycle high repetition rate  
Figure 11: (**a**) Measured streaking spectrograms; (**b**) retrieved temporal profile of the XUV pulse. Adapted with permission from [84], [PERSON] NPG, 2016.  
parametric sources, providing the extension of this technique to the sub-A imaging of a polyatomic molecule, such as ethylene [97; 98], and to the exploration with a sub-fs resolution of a chemical process, such as bond-breaking in acetylene [99]. In diffraction experiments, the information on the phase of the diffracted beam is lost. A complete amplitude-phase characterization can in principle be obtained by using a strong-field technique inspired by classical holography, namely Strong-Field Photoelectron Holography (SFPH) [100; 101].