Wavelength and intensity dependence of recollision-enhanced multielectron effects in high-order harmonic generation

Using a model molecular system ($A_2$) with two active electrons restricted to one dimension, we examine high-order harmonic generation (HHG) enhanced by rescattering. Our results show that even at intensities well below the single ionization saturation, harmonics generated from the cation ($A_2{}^{+}$) can be significantly enhanced due to the rescattering of the electron that is initially ionized. This two-electron effect is manifested by the appearance of a secondary plateau and cutoff in the HHG spectrum, extending beyond the predicted cutoff in the single active electron approximation. We use our molecular model to investigate the wavelength dependence of rescattering enhanced HHG, which was first reported in a model atomic system [I. Tikhomirov, T. Sato, and K. L. Ishikawa, Phys. Rev. Lett. 118, 203202 (2017)]. We demonstrate that the HHG yield in the secondary cutoff is highly sensitive to the available electron rescattering energies as indicated by a dramatic scaling with respect to driving wavelength.

Figure 1

HHG spectra generated from the $A_2$ TAE (solid red) and SAE (dashed blue) molecule and from its corresponding cation $A_2{}^{+}$ (dotted green). Here the driving laser field has a peak intensity of $5\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$ and a wavelength of 1400 nm. For each system the simulation is initialized from its ground state. The vertical dashed lines correspond to the first and second cutoffs.

Figure 2

Gabor analysis of the HHG from $A_2$ molecule with the same laser parameters as in Fig. 1. The time-frequency profiles are obtained from (a) TAE and (b) SAE simulations. The horizontal dashed lines correspond to the first and second cutoffs (same as previous figure). Only the first cutoff is indicated in (b).

Figure 3

Gabor analysis of the HHG from $A_2$ molecule with the same laser peak intensity as in Fig. 2 but with a different wavelength, 2750 nm. The horizontal dashed lines for the first and second cutoffs are shown, similar to Fig. 2. The white arrows indicate emission at the second cutoff present in (a) TAE simulation but not in (b) SAE simulation.

Figure 4

Time profiles of the first (solid blue) and second (dotted red) cutoffs from TAE calculations. As a reference, the time profiles of the first cutoff (dashed cyan) from SAE calculations are also shown. The upper and lower panels correspond to driving field wavelengths of 1400 and 2750 nm, respectively, from the previous figures. The vertical gray lines indicate emission times predicted by the semiclassical model.

Figure 5

Wavelength dependence of the yields at the first and second cutoffs obtained from TAE calculations, indicated by diamonds ($Y_{\text{C1}}$) and circles ($Y_{\text{C2}}$). The fitted trends (dashed curves) are also shown with ${\lambda }^{-1}$ and ${\lambda }^{-6}$ dependence for $Y_{\text{C1}}$ and $Y_{\text{C2}}$, respectively. The peak intensity is fixed at $5\times {10}^{13}$ ${\mathrm{W}/\mathrm{cm}}^2$. The scale for corresponding maximal return energies, $3.2U_p$, is included.

Figure 6

Intensity dependence of the yields at the first and second cutoffs obtained from TAE calculations, indicated by diamonds ($Y_{\text{C1}}$) and circles ($Y_{\text{C2}}$). The driving wavelength is fixed at 900 nm. As in Fig. 5, the scale for corresponding maximal return energies is included.