Separation of target structure and medium propagation effects in HHG

We calculate high-harmonic generation (HHG) by intense infrared lasers in atoms and molecules with the inclusion of macroscopic propagation of the harmonics in the gas medium. We show that the observed experimental spectra can be accurately reproduced theoretically despite the sensitivities of the HHG spectra to the experimental conditions. We further demonstrate that the simulated (or experimental) HHG spectra can be factored out as a product of a ‘macroscopic wave packet’ and the photo-recombination transition dipole moment where the former depends on the laser properties and the experimental conditions, while the latter is the property of the target only. The factorization makes it possible to extract target structure from experimental HHG spectra, and for ultrafast dynamic imaging of transient molecules. (Some figures in this article are in colour only in the electronic version) High-harmonic generation (HHG) has been employed to probe electronic structure of molecules on an ultrafast time scale in recent years [1–3]. When molecules are placed in an intense laser field, electrons that are removed earlier may be driven back to recollide with the parent ion. HHG occurs when the returning electrons recombine with the parent ion with the emission of high-energy photons as in an inverse photoionization (PI) process. Since PI is a sensitive tool for probing electronic structure of molecules, HHG may serve likewise, but with the advantage of ultrafast temporal resolution as well as covering a coherent broad spectral range from XUV to soft x-rays. Experimentally, however, HHG is generated from all the molecules in the interaction region. The radiations from them co-propagate with the fundamental infrared (IR) beam nonlinearly. To extract structure information of individual molecules, e.g., the amplitude and phase of PI transition dipole from the measured HHG, the propagation effect in the medium should be investigated. For molecular targets, this has not been performed so far. Instead, it was often assumed that HHG was measured under the perfect phase-matching conditions and that the observed harmonics were directly proportional to the harmonics from a single molecule. While such assumptions may be adequate for explaining many experimental observations qualitatively, such as the dependence of HHG on molecular alignment and on symmetry of the molecular orbital, the two-centre interference [4, 5], and multiple-orbital contributions to HHG [6], they are inadequate if accurate structure information of individual molecules is to be extracted from the observed HHG spectra. 0953-4075/11/095601+05$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 095601 C Jin et al