Effect of the carrier phase of ultra-short laser pulses on high-order harmonic generation spectra

We numerically calculated the high-order harmonic generation (HHG) power spectra from a one-dimensional model atom irradiated by linearly polarized ultra-short laser pulses whose duration is two optical cycles. It was found that, the cut-off positions of the HHG spectra change when the carrier phases of the ultra-short laser pulses are altered, and the distinct double plateau structure appears in some special carrier phases. The above issues are reasonably explaned by the three-step model. Finally, the wavelet time-frequency analysis verifies that the three-step model can accurately exactly predict the cut-off frequencies of the ultra-short pulse HHG spectra.