Harmonic generation beyond the Strong-Field Approximation: the physics behind the short-wave-infrared scaling laws.

The physics of laser-mater interactions beyond the perturbative limit configures the field of extreme non-linear optics. Although most experiments have been done in the near infrared ( lambda <or= 1 microm), the situation is changing nowadays with the development of sources at longer wavelengths (<5 microm), opening new perspectives in the synthesis of shorter XUV attosecond pulses and higher frequencies. The theory of intense-field interactions is based either on the exact numerical integration of the time-dependent Schrödinger equation or in the development of models, mostly based on the strong-field approximation. Recent studies in the short-wave infrared show a divergence between the predictions of these models and the exact results. In this paper we will show that this discrepancy reveals the incompleteness of our present understanding of high-order harmonic generation. We discuss the physical grounds, provide a theoretical framework beyond the standard approximations and develop a compact approach that accounts for the correct scaling of the harmonic yield.