Valley in the efficiency of the high-order harmonic yield at ultra-high laser intensities.

We study the process of high-order harmonic generation using laser pulses with non-adiabatic turn-on and intensities well above saturation. As a main point, we report the existence of a valley structure in the efficiency of single-atom high-order harmonic generation with increasing laser intensities. Consequently, after an initial decrease, the high-frequency radiation yield is shown to increase for higher intensities, returning to a level similar to the case below saturation. Such behavior contradicts the general belief of a progressive degradation of the harmonic emission at ultrahigh intensities, based on the experience with pulses with smoother turn-on. We shall show that this behavior corresponds to the emergence of a new pathway for high-order harmonic generation, which takes place during the pulse turn-on. Our study combines trajectory analysis, wavelet techniques and the numerical integration of 3-Dimensional Time Dependent Schrödinger Equation. The increase in efficiency raises the possibility of employing ultrahigh intensities to generate high-frequency radiation beyond the water window.