Molecular Recollision Interferometry in High Harmonic Generation

We use extreme-ultraviolet interferometry to measure the phase of high-order harmonic generation from transiently aligned ${\mathrm{CO}}_2$ molecules. We unambiguously observe a reversal in phase of the high-order harmonic emission for higher harmonic orders with a sufficient degree of alignment. This results from molecular-scale quantum interferences between the molecular electronic wave function and the recolliding electron as it recombines with the molecule, and is consistent with a two-center model. Furthermore, using the combined harmonic intensity and phase information, we extract accurate information on the dispersion relation of the returning electron wave packet as a function of harmonic order. This analysis shows evidence of the effect of the molecular potential on the recolliding electron wave.

Figure 1

Schematic setup for directly measuring the intensity and phase of high harmonic emission from molecules. HHG from aligned and randomly oriented molecules from two different regions interfere in the far field.

Figure 2

(a) Experimentally measured intensity (from the aligned molecular sample only) for harmonic orders 21–47 as a function of time-delay between the aligning laser pulse and harmonic-generating pulse within the $3/4$ revival. Time zero is shifted to the center of this revival for convenience. (b) Predicted $⟨{cos}^2\theta ⟩$ alignment assuming a rotational temperature of 105 K. The inset plots the angular distribution at three selected times within the revival, color coded to indicate the corresponding time on the $⟨{cos}^2\theta ⟩$ graph. Here, 0° corresponds to alignment along the laser polarization, while 90° corresponds to “antialignment” (i.e., perpendicular to the laser polarization). The critical angle of 34° for harmonic order 33 is also labeled. (c)–(e) Lineout of harmonic orders 23, 27, 33, 37, 39, and 41 that exhibit different substructure in the harmonic emission at optimal alignment. The dashed line shows a least-square fit to Eq. (1) for harmonic orders 23, 33, and 39.

Figure 3

(a),(c) Interference pattern as a function of time within the $3/4$ revival for harmonic orders 27 (a) and 33 (c). (b) Intensity-scaled integrated fringes for the 27th harmonic in the $-100\mathrm{fs}$ to 100 fs interval (red squares), along with least-square fit (red solid line). Integrated fringes outside this temporal window are also shown (black circles) as well as a least-square fit (black solid line). (d) Same as (b), but for the 33rd harmonic.

Figure 4

Extracted value of $R/\lambda$ versus harmonic order from the fits shown in Figs. 2c, 2d, 2e (blue squares with error bar). The calculated value of $R/\lambda$ is also shown for two different dispersion relationships and internuclear separations: $E_k=nh\omega -I_p$ and $R=2.32\AA$ (black solid line), $R=2.45\AA$ (black dashed line); $E_k=nh\omega$ and $R=2.32\AA$ (red solid line), $R=2.45\AA$ (red dashed line).