In this paper, the waveform control of high-order harmonic generation and attosecond pulse generation from a different initial state of He atom has been investigated. The results show that (i) by properly controlling the carrier-envelope phases, the time delays and the laser intensities of a 3-color laser pulse, the best waveforms for the harmonic cut-off extension can be found. Although the harmonic cut-offs from the ground initial state and the superposition initial state are almost the same, the harmonic intensities from the superposition initial state are 4 to 5 orders of magnitudes higher than those from the ground initial state. (ii) With the introduction of the inhomogeneous effect, the harmonic cut-offs can be further extended. However, the harmonic intensities from the superposition initial state are remarkably decreased compared with those from the homogeneous pulses, which is unbeneficial to generate the intense attosecond pulses. (iii) When the ground state is chosen to be the initial and with the assistance of the 4th UV pulse, not only the larger harmonic cut-offs can be obtained, but also the stronger harmonic plateaus can be found, which is favorable for producing the intense attosecond pulses. Thus, at the end of this paper, by superposing the harmonics from the best harmonic spectra, the single attosecond pulses with the duration of 36 as can be obtained.
Bayesian optimal control of the ultrashort circularly polarized attosecond pulse generation by two-color polarization gating
