Direct Spectro-Temporal Characterization of Femtosecond Extreme-Ultraviolet Pulses

We propose a method for a straightforward characterization of the temporal shape of femtosecond pulses in the extreme-ultraviolet/soft X-ray spectral region. The approach is based on the presence of a significant linear frequency chirp in the pulse. This allows to establish an homothetic relation between the pulse spectrum and its temporal profile. The theoretical approach is reminiscent of the one employed by Fraunhofer for describing far-field diffraction. As an application, we consider the case of a seeded free-electron laser (FEL). Theory is successfully benchmarked with numerical simulations and with experimental data collected on the FERMI@Elettra FEL. The proposed method provides FEL users with an on-line, shot-to-shot spectro-temporal diagnostic for time-resolved experiments.