Spatio-temporal dependence of high harmonic generation in noble gas

We experimentally study the pressure dependent high harmonic generation (HHG) from Argon in a semi-infinite gas cell. A spatio-temporal model considering the time dependent radial variation of the ionization rate, quantum diffusion, and phase mismatch is proposed. It is used to predict the relationship between the gas pressure and photon flux of high harmonics form Argon in experiments. Good consistence is found between the theoretical prediction and the experimental data over 11 odd order harmonics when the gas pressure varies from 30 mbar to 200 mbar. The comparison between our model and simplified on-axis HHG model proves that the radial and temporal variations of experimental parameters are able to significantly modify the phase-matching condition and the origin of observable HHG. We also find at the optimal gas pressure (e.g. 150 mbar @ 27^th harmonic), most of the observable HHG radiation (∼82%) comes from a condensed capsule-like spatial volume (∼4.17%) within the laser and gas interaction region, where the transient phase-matching condition is satisfied. Therefore, the quick numerical calculation within such small spatio-temporal volume can be used as an efficient guidance to search the optimal gas pressure in experiment. The spatio-temporal dependence of the observable HHG radiation also hints the existence of time dependent spatial chirp among the different attosecond pulses generated by a multi-cycle driving laser.