Resolving Multiple Molecular Orbitals Using Two-Dimensional High-Harmonic Spectroscopy

High-harmonic radiation emitted from molecules in a strong laser field contains information on molecular structure and dynamics. When multiple molecular orbitals participate in high-harmonic generation, resolving the contribution of each orbital is crucial for understanding molecular dynamics and for extending high-harmonic spectroscopy to more complicated molecules. We show that two-dimensional high-harmonic spectroscopy can resolve high-harmonic radiation emitted from the two highest-occupied molecular orbitals, HOMO and HOMO-1, of aligned molecules. By the application of an orthogonally polarized two-color laser field that consists of the fundamental and its second-harmonic fields to aligned ${\mathrm{CO}}_2$ molecules, the characteristics attributed to the two orbitals are found to be separately imprinted in odd and even harmonics. Two-dimensional high-harmonic spectroscopy may open a new route to investigate ultrafast molecular dynamics during chemical processes.

Figure 1

Schematic layout for two-dimensional high-harmonic spectroscopy for probing multiple molecular orbitals. (a) Recombination in an orthogonally polarized two-color laser field. Temporal variation of the two-color laser field is depicted as a black dashed line. Emitted odd and even harmonics are polarized to ${\widehat{d}}_x$ and ${\widehat{d}}_y$, respectively. (b) Orbital structures and induced dipole moment of the HOMO and HOMO-1 in ${\mathrm{CO}}_2$. The length of the arrow indicates the relative strength of the oscillating dipole moment due to the structure. (c) The spectral image shows a typical harmonic spectrum from aligned ${\mathrm{CO}}_2$ molecules. The HOMO and HOMO-1 can be separately encoded in the odd and even harmonics by the different strength of dipole moment induced in the two-color laser field on the two orthogonal axes.

Figure 2

Calculated harmonic spectra with the three different orbital configurations for (a) all valence orbitals, (b) HOMO, and (c) HOMO-1. The black and red lines correspond to alignment and antialignment, respectively. [(d)–(f)] The calculated harmonic intensities from the 27th to 30th harmonics, indicated with arrows in (a)–(c). The dashed line shows the degree of alignment. Calculated intensities are normalized against the randomly aligned case.

Figure 3

Harmonic spectra generated by an orthogonally polarized two-color laser field and the change of harmonic intensities with respect to pump-probe time delay: (a) ${\mathrm{N}}_2$, (b) ${\mathrm{CO}}_2$. The time domain is set to $T_{\text{rot}}/2$ ($T_{\text{rot}}$: rotational period, 8.4 ps for ${\mathrm{N}}_2$, 42.5 ps for ${\mathrm{CO}}_2$). Right axis: degree of alignment, ${\cos }^2\theta$ (calculation, dashed black line). Left axis: normalized harmonic intensity (experiment, line plus symbol). (c) Normalized odd (red) and even (blue) harmonic intensities generated from aligned ${\mathrm{CO}}_2$ molecules. Harmonic intensities are normalized against the randomly aligned case.

Figure 4

Harmonic spectra generated from aligned ${\mathrm{CO}}_2$ molecules (a) in the orthogonally polarized two-color laser field and (b) in a single-color laser field.