Signatures of electronic structure in bi-circular high-harmonic spectroscopy

High-harmonic spectroscopy driven by circularly-polarized laser pulses and their counter-rotating second harmonic is a new branch of attosecond science which currently lacks quantitative interpretations. We extend this technique to the mid-infrared regime and record detailed high-harmonic spectra of several rare-gas atoms. These results are compared with the solution of the Schrodinger equation in three dimensions and calculations based on the strong-field approximation that incorporate accurate scattering-wave recombination matrix elements. A quantum-orbit analysis of these results provides a transparent interpretation of the measured intensity ratios of symmetry-allowed neighboring harmonics in terms of (i) a set of propensity rules related to the angular momentum of the atomic orbitals, (ii) atom-specific matrix elements related to their electronic structure and (iii) the interference of the emissions associated with electrons in orbitals co- or counter-rotating with the laser fields. These results provide the foundation for a quantitative understanding of bi-circular high-harmonic spectroscopy.