Quantum-mechanical analysis of pulse reconstruction for a narrow bandwidth attosecond x-ray pulse

The photoelectron energy spectra (PESs) excited by narrow bandwidth attosecond x-ray pulses in the presence of a few-cycle laser are quantum-mechanically calculated. Transfer equations are used to reconstruct the detailed temporal structure of an attosecond x-ray pulse directly from a measured PES. Theoretical analysis shows that the temporal uncertainties of the pulse reconstruction depend on the x-ray bandwidth. The procedure of pulse reconstruction is direct and simple without making any previous pulse assumption, data fitting analysis and time-resolved measurement of PESs. The temporal measurement range is half of a laser optical cycle.