Measuring the angle-dependent photoionization cross section of nitrogen using high-harmonic generation

We exploit the relationship between high harmonic generation (HHG) and the molecular photorecombination dipole to extract the molecular-frame differential photoionization cross section (PICS) in the extreme ultraviolet (XUV) for molecular nitrogen. A shape resonance and a Cooper-type minimum are reflected in the pump-probe time delay measurements of different harmonic orders, where high-order rotational revivals are observed in N${}_2$. We observe the energy- and angle-dependent Cooper minimum and shape resonance directly in the laboratory-frame HHG yield by achieving a high degree of alignment, $\langle {\cos }^2\theta \rangle \ge 0.8$. The interplay between PICS and rotational revivals is confirmed by simulations using the quantitative rescattering theory. Our method of extracting molecular-frame structural information points the way to similar measurements in more complex molecules.

Figure 1

Experimental setup; see text for details.

Figure 2

Experimental revival scans (black dots) are shown for harmonic orders 19, 25, 27, 31, and 37, all normalized to the corresponding isotropic signals. Laser parameters were obtained from the fit and used in the QRS calculations: the first pump is 80 fs FWHM with the peak at 0 ps, 48 TW/cm${}^2$; the second pump is 80 fs, 56 TW/cm${}^2$; separation between pump pulses is 3.94 ps; probe is 30 fs, 250 TW/cm${}^2;$ and the rotational temperature is 30 K.

Figure 3

(a) Measured XUV intensity as a function of pump polarization angle and photon energy. (b) Calculated harmonic yield as a function of angle and photon energy using QRS theory. The calculations include HHG components parallel and perpendicular to the laser polarization vector. All the harmonic data are normalized to the corresponding values from an isotropic gas.

Figure 4

(a) Theoretical molecular-frame differential PICS of the HOMO (the PICS which are responsible for both parallel and perpendicular components of HHG are included); (b) and (c) PICS retrieved from the experimental angle and delay scans, respectively. All results are normalized to peak value for each harmonic order individually. See text for details of retrieval procedures.