Probing Molecular Frame Photoionization via Laser Generated High-Order Harmonics from Aligned Molecules

Present experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) for ionization from the outermost valence orbitals of molecules. We show that the details of MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.

Figure 1

${\mathrm{CO}}_2$ differential photoionization cross section (a) and phase of the transition dipole (b). The photon energies are expressed in units of harmonic orders for an 800-nm laser. (c) HHG yield as a function of the angle between pump and probe laser polarization directions. The laser intensity and duration are $0.55I_0$ ($I_0={10}^{14}\mathrm{W}/{\mathrm{cm}}^2$), and 120 fs for the pump pulse, and $2.5I_0$ and 25 fs for the probe pulse. Rotational temperature is taken to be 105 K. (d) Harmonic phase (relative to the phase from Kr) for parallel aligned and perpendicular aligned ensembles, under two sets of parameters (solid and dashed lines) that lead to two alignment distributions. Experimental data from Boutu el al. [14] are shown as symbols. Calculations are carried out with the same probe laser parameters as in the experiments.

Figure 2

Normalized HHG yield (vs isotropically distributed molecules) from ${\mathrm{CO}}_2$ for different harmonics as a function of pump-probe delay time near the $3/4$ revival. Laser parameters are the same as in Fig. 1c. The experimental data are taken from Zhou et al [13]. The alignment parameter $⟨{cos}^2\theta ⟩$ is plotted for reference (a).

Figure 3

Alignment parameter $⟨{cos}^2\theta ⟩$ (a), phase (b), and magnitude (c) of the 31th order harmonic from ${\mathrm{CO}}_2$, as functions of pump-probe delay time near the half-revival. The experimental data are taken from Wagner et al [11]. The laser intensity and duration are $0.38\times I_0$ and 140 fs for the pump, and $2.5\times I_0$ and 30 fs for the probe. The rotational temperature is taken to be 70 K.

Figure 4

(a) Same as in Fig. 1a, but for ${\mathrm{N}}_2$. (b),(c): Alignment parameter $⟨{cos}^2\theta ⟩$ and harmonic yields H21–H25 and H35–H37 from ${\mathrm{N}}_2$. The experimental data and laser parameters are taken from Itatani et al [8].