Controlling the ionization and recombination rates of an electron in preexcited ions to generate an intense isolated sub-4-as pulse in a multicycle regime

We present a numerical study of an isolated attosecond pulse generation in a preexcited medium driven by a moderately intense multicycle laser pulse, which is synthesized by adding a chirp-free laser pulse to a chirped laser pulse. The results show that by preparing the initial state of ${\mathrm{He}}^{+}$ ion as a preexcited state, the electron trajectories significantly can be modulated and the supercontinuous harmonics with higher emission efficiency can be obtained. Optimizing the chirp parameter allows a multicycle field to behave like a few-cycle one due to the control of electron tunneling. Therefore, a wide 1172-eV intense supercontinuum would be achieved on the high-order-harmonic generation spectrum. The classical and time-frequency approaches reveal that the long quantum path is suppressed and only the short quantum path is left. By properly filtering the harmonics from the supercontinuum, a 34-as intense isolated pulse with clean time profile is directly obtained without any phase compensation. Our simulation shows that by superposing the total supercontinuum region with phase compensation, we can obtain the shortest sub-4-as intense isolated pulse.

Figure 1

(a) Harmonic spectra from ${\mathrm{He}}^{+}$ ions initially prepared in the coherent superposition of the ground and excited states irradiated by a synthesized field of a 9-fs, 800-nm ($\beta =0.58$) and a 9-fs, 800-nm laser pulse (solid black curve). The dotted blue and dashed green curves show harmonic spectra from ${\mathrm{He}}^{+}$ ions initially prepared in the ground and excited states, respectively, irradiated by this field. The intensities of the pulses are $4\times {10}^{14}$ and $4\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. The relative phase $\phi$ is set to zero. (b) Population probabilities of the ground (dotted red curve) and excited (solid blue curve) states as a function of time when the initial state is a coherent superposition of the ground and excited states. The upper and lower insets show the long and short classical-path ionization probabilities. The dashed green curve shows the population probability of the ground state from ${\mathrm{He}}^{+}$ ions initially prepared in the ground state.

Figure 2

The population probability of the ground and excited states as a function of time when ${\mathrm{He}}^{+}$ ions are initially prepared in the excited state with the black solid and blue dotted curves, respectively, with the same synthesized laser field (the population probability of the ground state has been enlarged in the inset).

Figure 3

(a) The temporal profiles of the attosecond pulses from ${\mathrm{He}}^{+}$ ions in the ground state: by superposing the harmonics from the 235th to 285th order (dotted red curve), from the 163rd to 180th order (dashed blue curve), and from the 270th to 320th order (solid green curve). The curves have been multiplied by factors of 1 (dashed blue curve), 250 (solid green curve), and 100 (dotted red curve), for the purpose of clarity. (b) Temporal profiles of the attosecond pulses from ${\mathrm{He}}^{+}$ ions in the coherent superposition state by the harmonics with different central frequencies. The laser parameters are the same as in Fig. 1.

Figure 4

(a) The temporal profile of the attosecond pulse from ${\mathrm{He}}^{+}$ ions in the coherent superposition state by superposing the harmonics from the 186th to 239th order. (b) Dependence of harmonic order on the ionization time (blue circles) and the emission time (red plus signs) in the synthesized laser field (solid black curve). The laser parameters are the same as in Fig. 1.

Figure 5

Time-frequency distributions of HHG corresponding to the (a) dotted blue and (b) solid black curves in Fig. 1. Insets: A detailed view of short and long trajectories near the cutoff. The color bar shows the high-harmonic yield in a logarithmic scale.

Figure 6

Photon energies from ${\mathrm{He}}^{+}$ ions in the coherent superposition state when the $\beta$ parameter changes (a) from 0 to 3.6 per 0.6 and (b) from 1.10 to 1.23 in each 0.01.

Figure 7

(a) Harmonic spectra from ${\mathrm{He}}^{+}$ ions initially prepared in the coherent superposition of the ground and excited states, which correspond to three $\beta$ parameters, 1.12 (dashed red curve), 1.14 (solid blue curve), and 1.16 (dot-dashed green curve), and initially prepared in the ground state (dotted black curve). (b) Dependence of harmonic order on the ionization time (blue circles) and the emission time (red plus signs) in the synthesized laser field ($\beta =1.14$, solid black curve), and the corresponding ionization probability (solid magenta curve) for the solid blue curve in (a).

Figure 8

(a) Electric fields of the synthesized pulse with $\beta =0.58$ (dotted orange curve) and $\beta =1.14$ (solid green curve). Insets: The ionization probability (I.P.) when ${\mathrm{He}}^{+}$ ions are initially prepared as a coherent superposition in the time intervals ranging from $-1.775$ to $-1.770$ o.c. (upper inset) and $-3.218$ to $-2.970$ o.c. (lower inset). (b) Time-frequency distribution of HHG corresponding to the solid blue curve in Fig. 7.

Figure 9

The temporal profiles of the attosecond pulse without any phase compensation from ${\mathrm{He}}^{+}$ ions in the coherent superposition state: (a) by superposing the harmonics from the 186th to 239th order and (b) by the harmonics with different central frequencies with a total bandwidth of 82 eV, which corresponds to the solid blue curve in Fig. 7. The inset in (a) shows the temporal profile of the attosecond pulse from ${\mathrm{He}}^{+}$ ions in the ground state by superposing the harmonics from the 186th to 239th order, which corresponds to the dotted black curve in Fig. 7.

Figure 10

The temporal profiles of the attosecond pulse with phase compensation from ${\mathrm{He}}^{+}$ ions in the coherent superposition state: by superposing the total supercontinuum region (solid blue curve) and by the harmonics from the 125th to 650th order (inset). The laser parameters are the same as those in Fig. 7.