Quantum trajectories for high-order-harmonic generation from multiple rescattering events in the long-wavelength regime

We have performed the quantum trajectory analysis for high-order-harmonic generation (HHG) with different driving laser wavelengths. By defining the ratio of HHG yields of the $N$th and first rescattering events (${Y}_{N}/{Y}_{1}$), we quantitatively evaluate the HHG contributions from multiple rescatterings. The results show that the HHG yield ratio increases gradually with the increase of the laser wavelength, which demonstrates that high-order rescatterings provide ascendent contributions to HHG at longer wavelength. By calculating the classical electron trajectories, we find significant differences exist in the electron behaviors between the first and high-order rescatterings. Further investigations have demonstrated that the increasing HHG yield ratio is mainly attributed to the relatively smaller contributions from the short path of the first electron rescattering at longer laser wavelength.