Signatures of Electronic Structure in Bicircular High-Harmonic Spectroscopy

High-harmonic spectroscopy driven by circularly polarized laser pulses and their counterrotating second harmonic is a new branch of attosecond science which currently lacks quantitative interpretations. We extend this technique to the midinfrared regime and record detailed high-harmonic spectra of several rare-gas atoms. These results are compared with the solution of the Schrödinger 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 corotating or counterrotating with the laser fields. These results provide the foundation for a quantitative understanding of bicircular high-harmonic spectroscopy.

Figure 1

Experimental high-harmonic spectra generated with counterrotating circularly polarized femtosecond laser pulses in rare-gas atoms. (a) High-harmonic spectrum of neon obtained with $800/400\mathrm{nm}$ pulses with intensities $3.0/1.8\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. (b) High-harmonic spectrum of argon obtained with $1404/702\mathrm{nm}$ pulses with peak intensities of $7.2/6.0\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

Ratios of integrated intensities of neighboring high-harmonic orders as indicated on the vertical axis, as a function of the integer $q$ for Ne, $800/400\mathrm{nm}$ (a) and Ar, $1404/702\mathrm{nm}$ (b). The symbols represent the experimental data. The lines correspond to different theoretical models discussed in the text using the intensities given in the caption of Fig. 1. The theoretical results have been shifted by $+6.2\mathrm{eV}$ in the case of Ar (see text for discussion).

Figure 3

(a) Amplitudes of the matrix elements for ionization of $p_{+}$ and $p_{-}$ orbitals by bicircular laser fields. The wavelengths and intensities are the same as those used in Fig. 2 and are given in the caption of Fig. 1. (b) Amplitudes of the photorecombination matrix elements. (c) Amplitudes of the total induced dipole moments responsible for the emission of the symmetry-allowed harmonics $3q+1$ (magenta) and $3q+2$ (blue). (d) Relative phases of the contributions from $p_{+}$ and $p_{-}$ orbitals to the results of panels (c).