Intensity dependence of multiple orbital contributions and shape resonance in high-order harmonic generation of aligned N${}_2$ molecules

We report measurements and theoretical simulations of high-order harmonic generation (HHG) in aligned N${}_2$ molecules using a 1200-nm intense laser field when the generating pulse is perpendicular to the aligning one. With increasing laser intensity, the minimum in the HHG spectra first shifts its position and then disappears. Theoretical simulations including the macroscopic propagation effects in the medium reproduce these observations and the disappearance of the minimum is attributed to the additional contribution of HHG from inner orbitals. We also predict that the well-known shape resonance in the photoionization spectra of N${}_2$ should exist in the HHG spectra. It is most clearly seen when the generating laser is parallel to the aligning one and disappears gradually as the angle between the two lasers increases. No clear evidence of this shape resonance has been reported so far when using lasers with different wavelengths. Further experimentation is needed to draw conclusions.

Figure 1

Comparison of experimental [red (dark gray) lines] and theoretical [green (light gray) lines] HHG spectra of aligned N${}_2$ in a 1200-nm generating laser where the pump-probe angle $\alpha ={90}^{\circ }$. Laser intensities in the simulations are indicated where $I_0={10}^{14}$ W/cm${}^2$. Degree of alignment is $\langle {\cos }^2\theta \rangle =0.60$ by the aligning laser. See text for additional laser parameters. Only the $\sigma$ orbital is included in the simulations in panels (a) and (b), and both $\sigma$ and $\pi$ orbitals are included in the simulation in panel (c). Arrows indicate the positions of minima.

Figure 2

(a) Calculated macroscopic HHG spectra (envelope only) corresponding to Fig. 1c. Total (HOMO and HOMO-1 together) spectra and individual HOMO and HOMO-1 spectra. (b) Averaged photorecombination transition dipoles (parallel component, the square of the magnitude multiplied by ${\omega }^2$) of the HOMO and HOMO-1 corresponding to panel (a). Laser intensity is $1.1\times {10}^{14}$ W/cm${}^2$. Degree of alignment is $\langle {\cos }^2\theta \rangle =0.60$ by the aligning laser. The pump-probe angle $\alpha ={90}^{\circ }$.

Figure 3

Calculated differential photoionization cross sections [(a) and (c)] and phases [(b) and (d)] of the HOMO and HOMO-1 for N${}_2$ in terms of the alignment angles, respectively. The shape resonance in the HOMO shows up around 30 eV for small alignment angles only. Only the parallel component to the polarization direction of the laser is shown.

Figure 4

Calculated macroscopic HHG spectra (envelope only) of unaligned N${}_2$ and the normalized HHG yields of aligned N${}_2$ with respect to the unaligned ones as a function of the photon energy at the selected pump-probe angle $\alpha$. Laser intensities are indicated where $I_0={10}^{14}$ W/cm${}^2$. Degree of alignment is $\langle {\cos }^2\theta \rangle =0.60$.