Ensemble effects on the reconstruction of attosecond pulses and photoemission time delays

A crucial prerequisite for a detailed interpretation of the experimental results obtained with the most common attosecond spectroscopic techniques is a careful characterization of the attosecond extreme-ultraviolet (XUV) and femtosecond infrared (IR) pulses used in the measurements. A commonly adopted approach is based on the measurement of the spectra of the photoelectrons produced by the interaction of the attosecond pulses with a noble gas in the presence of a delayed IR pulse. Feeding the resulting spectrogram to reconstruction algorithms, it is then possible to retrieve the temporal properties of the XUV and IR pulses. To date, all reconstruction techniques are based on the assumption that the spectrogram is produced by the interaction of a single atom with a two-color (XUV-IR) field. In this work, we numerically investigate the effect of the actual XUV and IR beam spatial distributions, and we analyze their impact on the retrieval of the temporal characteristics of the XUV and IR pulses and on the determination of the photoemission time delays. We show that the impact of the ensemble effects can be severe, leading to notable variation of the photoelectron spectrograms, depending on the ratio between the XUV and IR beam spot sizes and on the IR peak intensity. We demonstrate that the photoemission time delay can be retrieved with great accuracy even in the presence of large deformations of the photoelectron spectrograms by employing suitable reconstruction procedures.