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

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.

💡 Research Summary

The paper investigates a novel route to extend the high‑order harmonic generation (HHG) cutoff beyond the conventional limit by employing a combined extreme‑ultraviolet (XUV) and infrared (IR) field configuration. The central idea is that an XUV pulse resonantly excites an inner‑shell electron, creating a transient core‑hole, while the IR field ionizes a valence electron, accelerates it, and drives it back to recombine into the core‑hole. This recombination releases an additional photon energy equal to the core‑valence orbital energy difference (ΔE), thereby shifting the harmonic cutoff by ΔE.

To model this process, the authors use the time‑dependent configuration‑interaction singles (TDCIS) framework, which incorporates a Hartree‑Fock reference state together with single particle‑hole excitations. The Hamiltonian includes the one‑electron part (H₀), the electron‑electron interaction beyond mean‑field (H₁), and the interaction with the external fields (H_L). The electric fields are described as Gaussian envelopes with carrier frequencies ω₀ (IR) and ω_XUV, and a relative delay τ. Both coherent and partially coherent XUV pulses are considered; the latter are modeled using a partial‑coherence method that introduces random spectral phases and defines a coherence time τ_c.

Numerical simulations are performed for krypton (18 active electrons, 3d→4p transition) and argon (8 active electrons, 3s→3p transition). In krypton, the regular IR‑only cutoff lies at ~99 eV; adding a resonant XUV pulse (ω_XUV ≈ 89.8 eV) lifts the cutoff to ~189 eV, exactly the sum of the IR cutoff and the 4p‑3d orbital energy difference. In argon, the IR‑only cutoff is ~60 eV, and the XUV‑assisted process raises it to ~78.9 eV, matching the 3p‑3s energy gap of 18.7 eV. The simulations confirm that the cutoff extension survives the inclusion of electron‑electron correlation and inter‑channel coupling at the single‑excitation level, indicating that the mechanism is robust against many‑body effects.

A key finding is the linear dependence of the microscopic dipole phase on the XUV‑IR delay τ. The phase slope is proportional to ΔE, so a change of τ by a fraction of the IR optical cycle produces a measurable phase shift of the extended harmonics. This sensitivity has macroscopic consequences: if the relative delay varies along the propagation direction (e.g., due to different refractive indices n_XUV ≠ n_IR), the dipole phases become mismatched, leading to destructive interference and a strong suppression of the macroscopic HHG signal. The authors quantify this effect by showing that a delay spread of ~10 fs can cause a phase spread exceeding 2π, effectively erasing the enhanced harmonic yield.

Temporal coherence of the XUV pulse is another critical parameter. When the XUV pulse is partially coherent with an average coherence time ⟨τ_c⟩ ≈ 1 fs, the statistical averaging of random spectral phases reduces the extended harmonic intensity by roughly a factor of five. This result explains why earlier experiments using SASE free‑electron laser (FEL) pulses, which have limited temporal coherence, failed to observe a clear cutoff extension.

The paper also examines the role of inter‑channel coupling by switching it on and off in the TDCIS calculations. The enhancement of the extended plateau remains essentially unchanged, confirming that the dominant physics is the XUV‑driven core‑hole creation and subsequent IR‑driven recombination, rather than many‑body correlation effects.

In the macroscopic propagation analysis, the authors assume plane‑wave fields and neglect Gouy phase, focusing on the phase matching condition. They derive that the dipole emission from atoms at different positions z_i and z_j differs by a factor exp