Molecular Frame Reconstruction Using Time-Domain Photoionization Interferometry

Photoionization of molecular species is, essentially, a multipath interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (${\mathrm{N}}_2$) is used to provide a time-domain route to “complete” photoionization experiments, in which the rotational wave packet controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle, this methodology provides a time-domain route to complete photoionization experiments and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.

Figure 1

VMI photoelectron images from (a) isotropic (no alignment pulses), (b) aligned, and (c) antialigned nitrogen molecules. The polarization of both alignment pulses and the XUV pulse are linear as indicated in (a). (d) The electron yields; labels provide cationic state assignments for the observed features.

Figure 2

Molecular alignment determination. (Top) Experiment (solid lines) and fit results (dashed) to Eq. (3), for $L=0$, 2, 4, 6 (Legendre polynomial expansion). (Bottom) Calculated axis distribution $P(\theta ,t)$ determined from the fit ($I=20\mathrm{TW}/{\mathrm{cm}}^2$, $T_{\text{rot}}=15\mathrm{K}$); the inset shows $⟨{\cos }^2(\theta ,t)⟩$ for this distribution (a commonly used indicator of the degree of alignment achieved [21, 57, 58]). The temporal axis is defined by the second pulse ($t=0$), and shows the $1/2$ and full revivals at the expected delays of 4.2 and 8.4 ps, respectively, as well as numerous higher-order structures indicating the excitation of a broad angular momentum wave packet.

Figure 3

Fitting of the time-series data. Main panels show the calculation results from Eq. (2) for (a) the $X$- and (b) $A$-channel yields, ${\beta }_{00}(t)$, where x marks points included in the fit; full ${\beta }_{L,M}(t)$ plots are presented in the Supplemental Material [34]. Examples of the full angle-resolved interferograms $S(\theta ,t)$, experimental results (including error bars) and calculated, are also shown, and corresponding axis distributions $P(\theta ,t)$ (bottom).

Figure 4

Molecular frame reconstruction as a function of ionizing orbital (a,b) and polarization geometry (rows). “Recon.” indicates MF PADs reconstructed from the experimental analysis; “Calc.”represents those determined from ab initio calculations. Each panel also shows the ionizing orbital, and labels indicate the MF polarization geometry (photon projection $q$) and corresponding symmetries for the ionization continua accessed.