Abstract
Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb. However, the dynamical origin of in these lower harmonics is less understood and largely unexplored. Here we perform an ab initio quantum study of the near- and below-threshold harmonic generation of caesium (Cs) atoms in an intense 3,600-nm mid-infrared laser field. Combining with a synchrosqueezing transform of the quantum time-frequency spectrum and an extended semiclassical analysis, the roles of multiphoton and multiple rescattering trajectories on the near- and below-threshold harmonic generation processes are clarified. We find that the multiphoton-dominated trajectories only involve the electrons scattered off the higher part of the combined atom-field potential followed by the absorption of many photons in near- and below-threshold regime. Furthermore, only the near-resonant below-threshold harmonic is exclusive to exhibit phase locked features. Our results shed light on the dynamic origin of the near- and below-threshold harmonic generation.
Highlights
Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb
The atomic ionization potential of Cs is equal to 0.143099 a.u. (Supplementary Table 1), which coincides with the 11.3 harmonic order
We find that only the resonant trajectories possess the single phase-component, which implies that the dynamical phases in below-threshold resonance harmonic generation are locked
Summary
Near- and below-threshold harmonic generation provides a potential approach to generate vacuum-ultraviolet frequency comb. The HHG process for the harmonics above the ionization threshold Ip can be well understood by the semiclassical three-step model[9,10] and the strong field approximation[11]. We employ a synchrosqueezing transform (SST)[22,23,24,25] (Supplementary Method) to analyse the timefrequency spectra of the near- and below-threshold HHG of Cs. By comparing the SST time-frequency spectra and the extended semiclassical calculations, we distinguish the contributions of the short trajectories, long trajectories, multi-rescattering trajectories and resonant trajectories in the near- and below-threshold harmonic generation, and demonstrate the features of the spectral dynamical phase. We find that the multiphotondominated processes only occur when the electrons are scattered off the higher part of the combined atom-field barrier potential (HBP) followed by the absorption of many photons in near- and below-threshold harmonic generation. The frequency comb is produced by superposing several belowthreshold harmonics of Cs, and the result is in good agreement with the recent experimental results[12]
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