above threshold into the continuum and then, it also stands for Above Threshold Ionization (ATI). It is a typical mechanism underlying PES and PAD measurements in the perturbative regime (see Sec. \[sec:pes\_pad\]), providing mostly structural information. The second mechanism illustrated in the case of atoms is known as Optical Field Ionization (OFI) in which the laser acts as a quasi stationary field. For sufficiently large fields, bound electron can tunnel through the barrier, which means that both barrier height and width (thus tunnel characteristic time) allow ionization. This typically corresponds to moderate values of the Keldysh parameter ($\gamma \lesssim 1$). The limiting case corresponds to full barrier suppression which can be associated to a critical laser intensity in atoms and which reasonably matches ion appearance intensities in atomic gases [@Aug89].

The cases of molecules and clusters mix the above considerations with structural properties of the considered systems. For example, ionization barriers are influenced by neighbouring ions. A typical example is the case of strong field ionization of diatomic molecules [@Sei95; @Zuo95] in which an appropriate internuclear separation leads to lowering or suppression of inner and outer potential barriers, thus leading to enhanced ionization. The effect was also studied in small 