Role of laser-driven electron-multirescattering in resonance-enhanced below-threshold harmonic generation in He atoms

We present an ab initio investigation of the below-threshold harmonic generation of helium (He) atoms in few-cycle infrared laser fields by accurately solving the time-dependent Schrödinger equation and Maxwell's equation simultaneously. We find that the enhancement of the below-threshold harmonic generation only occurs to near the resonance structure of He, for which this mechanism is in agreement with the recent experimental study [M. Chini et al., Nat. Photonics 8, 437 (2014)]. Moreover, we perform the quantum and semiclassical trajectories analysis, including both the atomic potential and the laser field, as well as the synchrosqueezed transform of the harmonic spectra. Our results reveal that several multirescattering trajectories contribute to the resonance-enhanced below-threshold harmonic generation.

Figure 1

Spectra density of the below-threshold harmonic as a function of the laser intensity for the on-resonant H13 (red line) and the nonresonant H15 (blue line) of He driven by a few-cycle 760-nm laser pulse in the single-atom response. The $\gamma$ is the Keldysh parameter. Note that the multiphoton ionization is typically classified by $\gamma >1$, while tunneling ionization is classified by $\gamma <1$. Both dashed lines indicate the harmonics yields as a function of the laser peak intensity $I$.

Figure 2

(a) Spatial distribution (upper panel) and the total intensity (lower panel) of He in the below-threshold regions. The laser peak intensity in the center of the gas jet is $I=9.0\times {10}^{13}$ ${\mathrm{W}/\mathrm{cm}}^2$. The red solid line indicates the ionization potential $I_p$. The other parameters used are the same as those in Fig. 1. (b) Macroscopic HHG spectra in below-threshold and above-threshold regions.

Figure 3

(a) Classical returning energy as a function of the ionization time (black line) and return time (green line), assuming initially the electrons with a small initial velocity are released at the core. (b) Position vs time in near- and below-threshold regions. Several typical rescatterings are marked by $1^{\prime }$ (short) and 1 (long), and multirescattering trajectories are marked by 2 (second return) and 3 (third return). The green solid line indicates the corresponding laser fields, and the laser parameters used are the same as those in Fig. 2.

Figure 4

Semicalssical returning energy map. Note that the probability of the electrons with the corresponding return time and return energy is calculated by using an extended semiclassical method introduced in Ref. [24]. The black solid line indicates the ionization potential $I_p$.

Figure 5

(a) Gabor time-frequency analysis of the harmonic spectra of He. (b) SST time-frequency analysis of the harmonic spectra of He. The laser parameters used are the same as those in Fig. 2. The green dashed line indicates the corresponding semiclassical result shown in Fig. 3 and the yellow solid line indicates the ionization potential $I_p$.