Spectral properties of high-order harmonic radiation enhanced by XUV-driven electron-hole dynamics

TL;DR

This work tackles the problem of extending high-order harmonic generation beyond the standard cutoff by exploiting XUV-driven inner-shell dynamics that refill transient core holes during recombination. It employs Time-Dependent Configuration-Interaction Singles to model multi-electron and interchannel effects, revealing that the microscopic dipole phase at extended harmonics is linearly sensitive to the XUV-IR delay with slope $\Delta E/\hbar$, and that XUV chirp and partial coherence can strongly modulate the extended spectrum. The study provides Krypton and Argon case analyses to quantify how hole dynamics and core-valence energy differences set the extended cutoff and phase behavior, then assesses macroscopic propagation effects via a one-dimensional Maxwell framework, showing XUV absorption and IR-XUV dispersion can suppress the extended yield, especially under higher pressure or longer propagation distances. The results underscore that both temporal coherence of the XUV pulse and propagation effects are essential to understanding and reproducing experimentally observed extended HHG signals, motivating a full 3D propagation treatment for complete agreement with experiments such as Tross2022.

Abstract

We analyze the spectral properties of high-order harmonic radiation with photon energies extending beyond the regular cutoff energy in standard high-order harmonic generation. The extension of the regular harmonic cutoff results from infrared (IR)-driven recombination of valence photoelectrons into a cationic core hole created by extreme-ultraviolet (XUV) excitation of inner-shell electrons into the transient valence hole in a combined XUV+IR configuration [Buth et al., Opt. Lett. 36, 3530 (2011)]. We show that the microscopic dipole phase at the extended harmonic frequencies is sensitive to the relative IR-XUV delay and IR intensity, whereas the corresponding signal intensity drops significantly for chirped XUV pulses with poor temporal coherence. We discuss the impact of such sensitivity on the macroscopic harmonic radiation, whereby decoherence among the dipole emitters may lead to further signal suppression.

Figures (11)

• Figure 1: (a) Dipole spectrum in krypton in the presence (blue lines) and absence (red lines) of the resonant XUV field. The XUV pulse has a duration of $1$ fs (FWHM), peak intensity of $2\times 10^{12}\mathrm{Wcm}^{-2}$ and central frequency $\omega_{\mathrm{XUV}}=89.78$ eV, corresponding to Hartree-Fock $4p$ and $3d$ orbital energy difference in neutral krypton. The IR field has a duration of $8$ fs, central frequency of $1.0332$ eV (1.2 $\mu m$) and peak intensity of $2\times 10^{14}\mathrm{Wcm}^{-2}$. (b) Schematic of the XUV-driven charge dynamics resulting in the emission of high-order harmonics lying beyond the regular harmonic cutoff region, see text.
• Figure 2: (a) Dipole spectrum in argon in the presence (blue lines) and absence (red lines) of the resonant XUV field. The XUV pulse has a duration of $2$ fs (FWHM), peak intensity of $2\times 10^{12}\mathrm{Wcm}^{-2}$ and central frequency $\omega_{\mathrm{XUV}}=18.67$ eV, corresponding to Hartree-Fock $3p$ and $3s$ orbital energy difference in neutral argon. The IR field has a duration of $22$ fs, central frequency of $1.44$ eV (861 nm) and peak intensity of $2\times 10^{14}\mathrm{Wcm}^{-2}$. (b) Schematic of the hole dynamics resulting in the extended harmonic region, see text.
• Figure 3: (a) Phase and (b) intensity of harmonics $\mathrm{H}_{2j+1}$ vs. delay. (c) Spectral phase difference $\Phi_{2j+1}-\Phi_{2j-1}$ vs. harmonic order for XUV+IR (blue). IR-only (yellow): $\mathrm{H}_{2j+1}$ are defined by the harmonics in the XUV+IR case from which we have subtracted $13\,\omega_0$ and corresponds to the plateau harmonics of IR-only. (d) IR and XUV field configuration for delays $\tau_1=(17^\circ / 360^\circ) T_0$ and $\tau_2=\tau_1-T_0/2$ indicated by the orange ($\tau_1$) and gray ($\tau_2$) vertical lines in (b) and (d). IR parameters: 6fs (FWHM), $2\times 10^{14}\,\mathrm{Wcm}^{-2}$ and $\omega_0\!=\!1.436~$eV. XUV parameters: $0.5~$fs (FWHM), $2\times 10^{13}\,\mathrm{Wcm}^{-2}$ and $\omega_{\mathrm{XUV}}=13\,\omega_0$.
• Figure 4: (a-c) Same as Figs. \ref{['fig:figure2']}(a-c) but for 2 fs XUV pulse. (d) $3s$ and $3p_0$ hole populations at the end of the pulses vs. XUV-IR delay. The intensity profiles of H55 (red) and H61 (black) in (b) are also shown in (d) (not in scale).
• Figure 5: (a) Spectral phase of harmonics H55 - H61 vs IR intensity. (b) Spectral phase vs XUV CEP phase. Same pulse parameters as in Fig. \ref{['fig:figure2']}