We systematically study the influence of phase matching on interference minima in high-harmonic spectra. We concentrate on structures in atoms due to interference of different angular-momentum channels during recombination. For this purpose, we use the Cooper minimum (CM) in argon at ~47 eV as a marker in the harmonic spectrum. We measure two-dimensional harmonic spectra in argon as a function of wavelength and angular divergence. While we identify a clear CM in the spectrum when the target gas jet is placed after the laser focus, we find that the appearance of the CM varies with angular divergence and can even be completely washed out when the gas jet is placed closer to the focus. We also show that the argon CM appears at different wavelengths in harmonic and photoabsorption spectra measured under conditions independent of any wavelength calibration. We model the experiment with a simulation based on coupled solutions of the time-dependent Schrödinger equation and the Maxwell wave equation, thereby including both the single-atom response and macroscopic effects of propagation and phase matching. The single-atom calculations confirm that the ground state of argon can be represented by its field-free p symmetry, despite the strong laser field used in high-harmonic generation. Because of this, the CM structure in the harmonic spectrum can be described as the interference of continuum s and d channels, whose relative phase jumps by π at the CM energy, resulting in a minimum shifted from the photoionization result. We also show that the full calculations reproduce the dependence of the CM on the macroscopic conditions. We calculate simple phase-matching factors as a function of harmonic order and explain our experimental and theoretical observation in terms of the effect of phase matching on the shape of the harmonic spectrum. Our results emphasize that phase matching must be taken into account to fully understand spectral features related to harmonic spectroscopy. Furthermore, we show that in some cases phase matching can be actively used to enhance the visibility of interference minima in high-harmonic spectra. © 2011 American Physical Society.
Publication Source (Journal or Book title)
Physical Review A - Atomic, Molecular, and Optical Physics
Farrell, J., Spector, L., McFarland, B., Bucksbaum, P., Gühr, M., Gaarde, M., & Schafer, K. (2011). Influence of phase matching on the Cooper minimum in Ar high-order harmonic spectra. Physical Review A - Atomic, Molecular, and Optical Physics, 83 (2) https://doi.org/10.1103/PhysRevA.83.023420