# The Role of Electron Trajectories in XUV-Initiated High-Harmonic Generation
## 2 Experimental Results
### Energy- and Delay-Resolved XUV-Initiated HHG Spectra  
Figure 2a shows experimental HHG spectra without and with helium in the target gas cell. Without helium, only the spectrum of the incident harmonics generated in the xenon gas are visible, mainly H11 to H17, with a weak signal at H19 and H21. Note that the pedestal structures around H11-H17 in the spectrum are lens flare artifacts of the imaging system. In the presence of helium and for full temporal overlap of the XUV and IR fields, XUV-initiated HHG is clearly visible, ranging from H19 to H25. As we scan the delay, each harmonic shows intensity oscillations at a frequency equaling twice the IR frequency. Although only H17 possesses sufficient energy for direct photoionization of the helium atom; H11, H13, and H15 also strongly contribute to the XUV-initiated HHG as they excite the helium atom below the ionization threshold [24]. The cutoff around H25 is compatible with the IR intensity in the gas cell.  
Scanning the XUV-IR delay provides insight into pulse envelope effects in the interplay between the IR pulse and the APT. Figure 3a shows experimental XUV-initiated HHG spectra as a function of the delay, in a logarithmic color plot (negative delay: XUV precedes the IR). The pedestal artifacts of Figure 2a are also visible in these spectra. The experimental results contain several characteristic spectral features that we will use in order to study the electron trajectories in detail. First, we observe a correspondence between the XUV-IR delay and the measured cutoff frequency (indicated by the white  
Figure 2: XUV-initiated HHG spectra in experiments and theory. **(a)** Experimental data. Measured spectrum without (red curve) and with (blue curve) helium in the target gas cell. XUV-initiated HHG is clearly visible up to H25. H11–H15 exhibit pronounced pedestal structures that are due to an experimental artifact. **(b)** Time-dependent Schrödinger equation (TDSE) calculation results. Dipole spectrum without (red curve) and with (blue curve) the IR field.  
line in Figure 3a). Second, we identify spectral components with pronounced positive and negative frequency shifts in the range H17-H23, for negative and positive delays, respectively (marked by \"A\"). The magnitudes of the observed shifts reach 0.9 eV, more than half of the photon energy of the IR pulse. Third, the sub-cycle oscillations of the frequency-shifted spectral components are phase-shifted with respect to those of the unshifted part of the harmonics (marked by \"B\"). Finally, we observe a weak spectral tilt of the odd harmonics as a function of the delay. We note that we do not find any signatures of XUV free induction decay [30] or HHG by frustrated tunneling ionization [31] below the ionization threshold.  
Figure 3: XUV-initiated HHG spectra as a function of the XUV–IR delay. **(a)** Experimental data. The arrows indicate characteristic features in the spectrum: A, strongly frequency-shifted spectral components, with positive (negative) shifts for negative (positive) XUV-IR delays; B, sub-cycle temporal delay of the oscillations of the shifted spectral components with respect to odd harmonic signals. The white dotted curve sketches the cutoff as it follows the envelope of the 25 fs IR pulse. The pedestal artifacts from Figure 2 are also visible in this plot. **(b)** TDSE calculation results. The characteristic features are also found in the single atom response calculation. Some TDSE features are not found in the experiment, for example most of the signal is between the odd harmonics at negative delays. As a guide to the eye we display white-dashed boxes around the A-type features found in the experiments.