Metrology of Time-Domain Soft X-Ray Attosecond Pulses and Reevaluation of Pulse Durations of Three Recent Experiments

Attosecond pulses in the soft x-ray (SXR) to water-window energy region offer the tools for creating and studying target-specific localized inner-shell electrons or holes in materials, enabling monitoring or controlling charge and energy flows in a dynamic system on attosecond timescales. Recently, a number of laboratories have reported generation of continuum harmonics in the hundred-electron-volt to kilovolt region with few-cycle long-wavelength mid-infrared lasers. These harmonics have the bandwidth to support pulses with durations of a few to a few-ten attoseconds. But harmonics generated in a gas medium have attochirps that cannot be fully compensated by materials over a broad spectral range; thus, realistically what are the typical shortest attosecond pulses that one can generate? To answer this question, it is essential that the temporal attosecond pulses be accurately characterized. By reanalyzing the soft x-ray attosecond metrology reported in three recent experiments [Li et al. 53-attosecond x-ray pulses reach the carbon K-edge, Nat. Commun. 8, 186 (2017); Gaumnitz et al. Streaking of 43-attosecond soft x-ray pulses generated by a passively CEP-stable mid-infrared driver, Opt. Exp. 25, 27506 (2017); Cousin et al. Attosecond Streaking in the Water Window: A New Regime of Attosecond Pulse Characterization, Phys. Rev. X 7, 041030 (2017)] using a newly developed broadband phase retrieval algorithm, we demonstrate that the generated attosecond pulses in the first two papers have durations of about 60 as, longer than what they have reported. Similarly, the duration from the third experiment is retrieved to be about half of the 322-as upper limit cited in that work. We also introduce the autocorrelation (AC) of the streaking spectrogram. By comparing the ACs from the experiments and from the retrieved SXR pulses, the accuracy of the retrieved results can be directly visualized. Our retrieval method is fast and accurate, and it shall provide a powerful tool for the metrology of the emerging few-ten-attosecond pulses.