Coherent contribution of consecutive electron rescatterings in the extreme ultraviolet supercontinuum

In this article, coherent contributions of high-order quantum paths are proposed to generate a highly efficient and fine appearance attosecond pulse. We show how the electron dynamics of the high-order harmonics evolves so that harmonics are generated by a helium atom exposed to the two-color waveform composed of sub-one-cycle pulses. The leading and the trailing of the pulse is constructed by the near-infrared driving pulse and a midinfrared control pulse, respectively, thereby tunnel ionization and recombination are effectively manipulated. This waveform not only broadens the bandwidth but also leads to the contribution of high-order rescatterings in the generated supercontinuum and thereby enhances the harmonic yields. Whereas the effective duration of the waveform is lesser than the midinfrared pulse, with prolonging the pulse trailing, the long path of first-order rescattering is completely suppressed and high-order rescatterings of different electron trajectories appear. The most interesting feature is that under optimized conditions, the short paths of consecutive rescatterings coherently contribute in the high-order-harmonic generation process that leads to a fine appearance in the attosecond pulses.

Figure 1

(a) Amplitude of electric fields (vs atomic unit) of the half-cycle 800-nm driving pulse, the half-cycle 2000-nm control pulse, two-color field synthesized by half-cycle 800-nm driving and half-cycle 2000-nm control pulses as a function of time (optical cycle), and the ionization rate in the two-color pulse. (b) Classical sketch of the electron dynamics—ionization and recombination times—in the two-color pulse. The intensities of the driving pulse and the control pulse are 2 × 10${}^{14}$ and 1 × 10${}^{14}$ W/cm${}^2$, respectively. The arrows plot the possible HHG process based on the well-known three-step model.

Figure 2

The harmonic spectrum of a helium atom exposed to the two-color field synthesized by half-cycle 800-nm driving and half-cycle 2000-nm control pulses and the monocycle 800-nm driving pulse alone. The intensities of the driving pulse and the control pulse are 2 × 10${}^{14}$ and 1 × 10${}^{14}$ W/cm${}^2$, respectively. The intensity of the monocycle 800-nm driving pulse is 3 × 10${}^{14}$ W/cm${}^2$.

Figure 3

The quantum wavelet transform of the induced dipole acceleration as a function of the photon burst time and the photon energy performed by the Gabor transform for a two-color synthesized field containing half-cycle 800-nm driving and half-cycle 2000-nm control pulses.

Figure 4

The quantum wavelet transform of the induced dipole acceleration as a function of the photon burst time and the photon energy for the two-color field synthesized by half-cycle 800-nm driving and half-cycle 2300-nm control pulses.

Figure 5

The harmonic spectrum of a helium atom exposed to the two-color field synthesized by half-cycle 800-nm driving and the prolonged control fields described in the the figure key.

Figure 6

Isolated attosecond pulse (solid line) calculated by synthesizing the all continuum and isolated attosecond pulse (dashed line) calculated by synthesizing the 100th–115th harmonics obtained from the harmonics spectra of Fig. 5 for ${\lambda }_c$ = 2600 nm.

Figure 7

The quantum wavelet transform of the induced dipole acceleration as a function of the photon burst time and the photon energy for the two-color field synthesized by the half-cycle 800-nm driving pulse and the (a) half-cycle 2600-nm control pulse and (b) half-cycle 2800-nm control pulse.