Mid-infrared high-order harmonic yield scaling: Where to look and what to see

From a fundamental viewpoint, the interaction of ultraintense lasers with atoms constitutes a paradigmatic example among non-perturbative phenomena. The convergence of theory and experiments models this field as a privileged test-ground our theoretical understanding of non-perturbative processes. In a simplified view, theory is based either in the ab-initio numerical integration of the relevant equations (for instance Schrodinger´s) or in the development of models. Among the later, S-matrix approaches combined with the strong-field approximation (SFA) are shown to provide an excellent description of the single and multielectron ionization rates, as well as constituting an adequate formalism to study the process of high-order harmonic generation (HOHG). In this later case, a standard approach combines SFA with a saddle point approximation to compute the harmonic spectra. Despite of its achievements, recent studies on the scaling of the harmonic yield with wavelength show a departure between the predictions of this model and the exact TDSE. From a practical side, the correct scaling of the harmonic yield is fundamental for the quantitative description of the HOHG with short- and mid-wave infrared sources, which may be used to generate shorter single attosecond pulses. In this contribution we shall, first, develop a critical perspective to some recent works approaching the issue of the adequate choice of the spectral regions to test SFA theories (we propose to use the end of the plateau). Second, we will show that the physics behind the scaling law may be understood beyond the strong- field approximation as field dressing of the bound states becomes crucial. Finally, we will discuss an S-Matrix formalism that goes beyond the SFA, holds good quantitative agreement with the exact integration of the TDSE and reproduces the correctly the yield scaling.