Extracting the phase of high-order harmonic emission from a molecule using transient alignment in mixed samples

We report measurements of both the phase and intensity of high-order harmonic emission from aligned ${\mathrm{CO}}_2$ molecules, using a mixture of a molecular and an atomic gas. The molecules are transiently aligned using an ultrashort pulse, and a subsequent stronger pulse is used to generate high-order harmonics from a mixed $\mathrm{Kr}∕{\mathrm{CO}}_2$ sample. The high-order harmonic emission from the molecules interferes with the reference emission from the atoms. By monitoring the change in harmonic emission as a function of gas mixture and molecular alignment, we can retrieve the orientational dipole that has general features consistent with a two-center emission model.

Figure 1

(Color online) (a) (Upper plot) Calculated alignment parameter $⟨{\cos }^2\theta ⟩$ for a rotational wave packet excited in ${\mathrm{CO}}_2$. (Lower plot) High-order harmonic intensity for the 31st harmonic emission from $\mathrm{Kr}:{\mathrm{CO}}_2$ mixtures as a function of time delay between the alignment and harmonic generation pulses for several mixture ratios. The range of time delays shown corresponds to the quarter and half rotational revivals. (b) A schematic describing the experiment. Harmonic emission from ${\mathrm{CO}}_2$ molecules at different orientations interferes to create the emission from ${\mathrm{CO}}_2$. The resultant emission interferes with the emission from krypton.

Figure 2

(Color online) (a) Intensity of the 31st harmonic order as a function of ${\mathrm{CO}}_2$ fraction at two time delays, 21.72 and $21.25\mathrm{ps}$ (corresponding to the maximum antialignment and alignment during the half revival). (b) The interference third term of Eq. (2) as a function of ${\mathrm{CO}}_2$ fraction, for the same two time delays.

Figure 3

(Color online) (a) The magnitude and phase of the rotationally averaged harmonic emission of ${\mathrm{CO}}_2$, retrieved by fitting the harmonic intensity from several mixtures to Eq. (2). The solid lines show the magnitude and phase retrieved from the first fitting step. The measured phase is relative to the phase of emission from krypton. The dotted lines show the fit from the second fitting procedure. The alignment parameter $⟨{\cos }^2\theta ⟩$ is also plotted for reference.

Figure 4

(Color online) Magnitude (a) and phase (b) of the orientational dipole $B\left(\theta \right)$ retrieved from the second fitting procedure for harmonic orders 21–35. Magnitude (c) and phase (d) of the orientational dipole predicted by the two-center emission model.