What can we learn from high harmonic generation about molecular electronic structure and dynamics? On our way to answering this question we explored new paths in attosecond research. Most important was our dicovery, that many electronic states, analogous to the ionization of multiple orbitals, participate in high harmonic generation. This notion is now generally accepted and can be used for attosecond preparation of molecular electronic wavepackets. Our recent results on water show that lower lying orbitals leave dynamic traces in the harmonic spectra of different isotopes. We have also shed new light on phase matching effects shaping harmonic spectra. Our studies show that absolute harmonic are influenced by the macroscopic propagation. We are further exploring electronic structures on asymmetric top molecules like SO2 and H2O. Our recent results indicate that high harmonic spectra are especially sensitive to subtle alignment changes and pave the way for future studies of excited state non-Born Oppenheimer dynamics on those systems.
a) HOMO and lower bound HOMO-1 of water. b) The corresponding ionic states are bound (and very similar to the neutral ground state) for the HOMO ionization, and strongly repulsive for the HOMO-1 ionization. c) The harmonic yield of heavy water dominates of the yield from water, showing that the slower moving nuclear wavepacket in heavy water is launched via ionizing the HOMO-1.
The high harmonics of water can be used to track sub-femtosecond nuclear motion launched via ionization of the inner valence 3a1 orbital. This introduces a new method to find multi-orbital contributions to high harmonics. We observed nuclear and electronic motion of the water molecule on the attosecond time scale by comparing high harmonic spectra of water (H2O) and heavy water (D2O) (see c in Figure). Both the highest energy occupied orbital (HOMO) and also lower orbitals can participate in HHG, as we showed on the example of the nitrogen molecule in 2008. In water, the more deeply bound HOMO-1 ionization launches a wave packet that straightens the bend angle (a and b in Figure). The ionization from the lone pair HOMO orbital does not launch a motion in the molecule. The efficiency of HHG emission from HOMO-1 is then governed by the spatial overlap of the ionic state nuclear wave packet and the neutral vibrational ground state following recombination. This decreases as the bent molecule straightens out. The loss of overlap is less pronounced for the slower moving heavier isotope, so the harmonic ratio of H2O and D2O maps the bond motion. This observation shows how HHG can record rapid motion, and also reinforces growing evidence that HHG from multiple orbitals is not unusual. Additionally, the method of isotope marking allowed us to infer the multi-orbital character of strong field ionization without using any rotational or vibrational laser preexcitation. Our initial report on lower orbital harmonics in nitrogen have triggered many reports on multi orbital harmonics. Adding the case of water, we now believe that the harmonics from lower orbitals are the rule.
Strong field ionization to multiple ionic states of water
J. P. Farrell, S. Petretti, J. Foerster, B. K. McFarland, L. S. Spector, Y. V. Vanne, P. Decleva, P. H. Bucksbaum, A. Saenz, and M. Gühr
Phys. Rev. Lett., 107, 083001 (2011)
Further reading on multi-orbital ionization in strong fields:
Getting molecular electrons into motion
Science, 335, 1314 (2012)
High Harmonic Generation from Multiple Orbitals in N2
B. K. McFarland, J. P. Farrell, P. H. Bucksbaum and M. Gühr
Science, 322, 1232 (2008)
High harmonic bragg gratings
Bragg grating scheme: Two counterpropagating grating beams create a standing wave with a half wavelength period. A probe pulse is focused in the grating and harmonics of order n in the extreme ultraviolet are produced. Since we are operating in the thick grating or Bragg regime, a strong diffraction of the harmonics is only observed at their Bragg angle.
Transient gratings are generally applied in the IR to UV range to overcome the reduced sensitivity problem on excited states. Two excitation pulses, intersecting under a small angle, create an excitation grating in the sample while a third (probe) pulse is diffracted from the grating. The diffracted signal has high sensitivity to excited state dynamics. We implemented the grating scheme for HHG where the harmonics are not only deflected into a sideband, but also dispersed in angle within a diffraction order, to enable HHS analysis (see figure above). This is achieved by enlarging the angle to 180 deg., resulting in a shorter grating period d, which disperses the harmonics to distinguishable angles without an additional grating element. Thereby we achieve a Bragg grating that is highly selective in its wavelength acceptance resulting in the dispersed and distinguishable harmonics.
Strongly Dispersive Transient Bragg Grating for High Harmonics
J. P. Farrell, L. S. Spector, M. B. Gaarde, B. K. McFarland, P. H. Bucksbaum and M. Gühr
Optics Letters, 35, 2028 (2010)
Harmmonics from aligned asymmetric tops
Sulfur dioxide (SO2) is an asymmetric top molecule. We succeeded in recording the high harmonic yield at different molecular orientations. The image shows idealized sample distributions at different revival times after the alignment laser pulse. The laser polarization is given as the black arrow.
The ability to directly image the structure of the outermost electrons in molecules, and thereby view chemical reactions as they occur, is an important goal in molecular physics and chemistry. We study high-order harmonic generation (HHG) in impulsively aligned quantum asymmetric tops. We quantify the angular contributions of HHG emission, making use of the full rotational revival structure. We find a signal sensitive to all five prolate top revival types and to fractional and multiple revivals, providing a new view of polyatomic rotations. Our results show that not only the HOMO orbital shape, but also the orientation dependence of the recombination dipole controls the harmonic efficiency. This has implications for HHG-based tomographic imaging.
Quantified angular contributions for high harmonic emission of molecules in three dimensions
L. S. Spector, M. Artamonov, S. Miyabe, T. Martinez, T. Seideman, M. Guehr, and P. H. Bucksbaum
arXiv, arXiv:1207.2517v1 (2012)
How phase matching alters harmonic spectra – Argon Cooper minimum
a) Harmonic spectra of argon dispersed with respect to wavelength while preserving the divergence of the harmonic beam. The left and right panels are recorded with different positions of the target gas with respect to the laser focus (1.3 and 1.9mm respectively), which changes the phase matching.
The goal of high harmonic spectroscopy is to deduce information about electronic structure of target atoms or molecules from the shape and phase of a harmonic spectrum generated on that particular target. A general problem in this method is that the spectral information is not only containing the response of the single molecule/atom, but also the macroscopic sample response originating from the phase matching of harmonics. While phase matching is necessary to observe the harmonics, its possibly hazardous in the interpretation of harmonic spectra in terms of single molecule/atom response.
We have studied the influence of phase matching on spectral information using the Cooper minimum of argon as a spectral marker. We have developed a new spectrometer in our lab to observe the wavelength content and divergence of a harmonic spectrum (see figure). The positions of the harmonic target with respect to the laser focus (1.3 and 1.9 mm in the two graphs) lead to different phase matching conditions manifested in dramatically different spectral shape and divergence. The Cooper minimum is absent in the left panel, whereas its pronounced at 51 eV in the left panel (harmonic at 51 eV is less intense than the neighboring ones). We have collaborated with M. Gaarde and K. Schafer (both Louisiana State University) to find the origins for that behavior. We found that the interference of s and d channels in the recombination together with phase matching effects lead to different modulation depth and energy location or also the complete absence of the Cooper minimum structural feature. However, the spectral phase of the d-channel, also reflecting the Cooper minimum, is not altered by phase matching effects. The study cautions to interpret harmonic spectra straight forwards in terms of electronic structure. The best protection against artefacts from phase matching seems to compare two spectra with similar phase matching but different excitation conditions or isotope content of the target (as in our N2 or water studies).
Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra
J. P. Farrell, L. S. Spector, B. K. McFarland, P. H. Bucksbaum, M. Gühr, M. Gaarde, K. Schafer
Phys. Rev. A, 83, 023420 (2011)