Influence of the laser pulse duration in high-order harmonic generation

High-order harmonic generation (HHG) in gases has been studied for almost 40 years in many different conditions, varying the laser wavelength, intensity, focusing geometry, target design, gas species, etc. However, no systematic investigation of the effect of the pulse duration has been performed in spite of its expected impact on phase-matching of the high-order harmonics. Here, we develop a compact post-compression method based on a bulk multi-pass cell enabling tunable Fourier-limited pulse durations. We examine the HHG yield as a function of the pulse duration, ranging from 42 fs to 180 fs, while maintaining identical focusing conditions and generating medium. Our findings reveal that, for a given intensity, there exists an optimum pulse duration - not necessarily the shortest - that maximizes conversion efficiency. This optimum pulse duration increases as the intensity decreases. The experimental results are corroborated by numerical simulations, which show the dependence of HHG yield on the duration and peak intensity of the driving laser and underscore the importance of the interplay between light-matter interaction and phase-matching in the non-linear medium. Our conclusion explains why HHG could be demonstrated in 1988 with pulses as long as 40 ps and intensities of just a few $10^{13}$ W/cm${^2}$.