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The photoelectron spectra ͑PES͒ excited by narrow bandwidth femtosecond x rays in the presence of a femtosecond laser were investigated. Two transfer equations were found which can be used to precisely reconstruct the detailed x-ray profile from the measured PES. The reconstruction is a direct procedure without any previous pulse-shape assumption. The method has high time resolution and broad temporal measurement range which depend on the laser and x-ray parameters.

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.

We report a discovery that an intense few-cycle laser pulse passing through gas leaves a fingerprint of its field envelope on the photoelectron energy spectrum, which involves continuous X-ray radiations. The spectrum resulting from the photoionization processes includes significant quantum enhancement and interference and exhibits interesting energetic properties. The spectral cut-off energies reflect the strength, time, and interference of the laser field modulation on the photoelectron energy. These energetic properties suggest a new method for precise intense-laser-pulse measurement in situ. The method has the advantages of accuracy, simplicity, speed, and large dynamic ranges (up to many orders of intensity).

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