Targeting multiple rescatterings through VUV-controlled high-order-harmonic generation

We theoretically investigate the use of an isolated attosecond vacuum ultraviolet (VUV) pulse to control the emergence of multiple wave-packet rescatterings in the process of high-harmonic generation (HHG). Through numerical solution of the time-dependent Schrödinger equation for a He atom driven by $0.8–2.0\text{−}\mu \mathrm{m}$ light, we establish the relationship between evidence of multiple rescatterings in HHG and the time delay between the VUV and infrared pulses. We find features of multiple rescatterings present in both the time and frequency domains of emitted HHG, and demonstrate the use of VUV-induced multiple rescatterings for generating trains of ultrashort light pulses.

Figure 1

(a) Schematic of the VUV-controlled HHG scheme, in which the moment of ionization is induced by transferring population into excited states using a VUV pulse. Mapping classical predictions of the electron ionization time to return times (b) suggests that multiple rescattering trajectories can be selectively produced in this way.

Figure 2

Wavelet analysis of the electron dipole acceleration for application of the VUV pulse at (a) $t_d=-0.065$ and (b) $t_d=0.129$ field cycles (see inset). Superimposed black circles represent the results of a classical simulation which considers ionization times beginning at the peak of the VUV field and ending at the subsequent zero of the driving field. The presence of several rescattering events in (a) as compared to the single event in (b) shows the desired control. Recombination energies in (b) exceeding the classically predicted energy are attributed to ionization preceding the VUV field maximum.

Figure 3

Harmonic spectra for $t_d=-0.065$ (left) and $t_d=0.1$ (right). Dashed lines in (a) mark the classically predicted maximum rescattering energies of the first, second, and third events, between which individual subplateaus appear (depicted on linear scale in subpanels). In contrast, (b) lacks subplateaus due to the dominant contribution of an isolated rescattering event. Subpanels, presented on a linear scale, are given in the same arbitrary units as the main panels and, hence, scaled by ${10}^{-6}$ to match those of panels (a) and (b).

Figure 4

Attosecond pulse formation for $t_d=-0.065$, constructed by transforming energies corresponding to each of the subplateaus distinguished in Fig. 3: in (a) $115–180$ harmonic orders; in (b) $100–115$ harmonic orders; in (c) $75–100$ harmonic orders; and in (d) $75–180$ harmonic orders, comprising the full HHG plateau. The inset figure is reproduced from Fig. 3, with shaded regions corresponding to the energies considered.

Figure 5

Attosecond pulse formation for $t_d=0.1$, with subpanels considering transformations of the same energy values as Fig. 4. Each subpanel reproduces an isolated attosecond pulse corresponding to the single emission event allowed by the placement of the VUV field. The inset figure is reproduced from Fig. 3.

Figure 6

In the first column, the time-frequency analysis of the HHG spectrum driven by the combination of an IR laser pulse (intensity $2.5\times {10}^{14}$ ${\mathrm{W}/\mathrm{cm}}^2$) and a VUV field: in the first row, 0.8 $\mu \mathrm{m}$ (9.6 fs FWHM) IR and six cycles full width (392 as FWHM) VUV; in the second row, 1.2 $\mu \mathrm{m}$ (14.4 fs FWHM) IR and nine cycles (589 as FWHM) VUV; in the third row, 2 $\mu \mathrm{m}$ (24 fs FWHM) IR and 15 cycles (981 as FWHM VUV). In each case, the VUV field is centered at $-0.08$ field cycles. In the second column, the temporal profile of harmonics with energies exceeding 2.2 au is shown for each driving wavelength.

Figure 7

(a) Time evolution of the frequency emission due to the application of two VUV pulses at $t_d=-0.53$ and $t_d=-0.03$ field cycles. Superimposed are classical predictions induced by the first (black circles) and the second (white circles) VUV pulse. The harmonic spectrum (b) is structurally similar to the case of multiple rescatterings shown in Fig. 3, but exhibits additional interference. The intensity profile of the radiation is shown in (c), in which every element of the attosecond pulse train with the exception of the first demonstrates a substructure beating; (d) examines this substructure between 0.5 and 1.0 field cycles.