Phase-dependent interference fringes in the wavelenght scaling of harmonic efficiency

Abstract

We describe phase-dependent wavelength scaling of high-order harmonic generation efficiency driven by ultra-short laser fields in the mid-infrared. We employ both numerical solution of the time-dependent Schr¨odinger equation and the Strong Field Approximation to analyze the fine-scale oscillations in the harmonic yield in the context of channel-closing effects. We show, by varying the carrier-envelope phase, that the amplitude of these oscillations depend strongly on the rescattering electron trajectory counts. Furthermore, the peak positions of the oscillations vary significantly as a function of the carrier-envelope phase. Owing to its significant practical applications, we also investigate the wavelength dependence of harmonic yield in the single-cycle limit, finding that scaling near the cut-off region departs from the commonly observed ? -x behavior. For a fixed spectral range, we identify a surprisingly smooth behavior of x in ? -x as a function of the ionization potential in the single-cycle limit, which shows suppression of the oscillations in the overall wavelength-scaling. Moreover, we observe that the harmonic efficiency scales as ? -x with x = 5.2, independent from the target atom, and in reasonable agreement with the semi-classical x = 5 scaling.