Time-space transformation of femtosecond free-electron laser pulses by periodical multilayers

A scattering scheme to probe the time evolution of femtosecond pulses of a soft X-ray free-electron laser (FEL) in a multilayer structure is presented. The response of periodic multilayers (MLs) with low and high absorption and various numbers of bi-layers to a pulse train of Gaussian-shaped sub-pulses is calculated. During the passage of the incident pulse the interaction length increases and the scattering profile changes as a function of the spatial position of the pulse within the sample. Owing to stretching of the reflected pulse compared with the incident pulse, the time-dependent scattering evolution in the ML can be visualized along a spatial coordinate of a position-sensitive detector. Using a scattering geometry where the mean energy of the incident pulse train is slightly detuned from the energy of maximum reflectivity at the first-order peak, the response of the ML shows an oscillator behaviour along this spatial coordinate at the detector. For a FEL wavelength of 6.4 nm this effect is promising for MLs with low absorption, such as La/C for example. On the other hand, the oscillations will not be present for MLs with high absorption. Therefore a low-absorbing ML is a sensitive tool for studying the possible change of sample absorption caused by femtosecond-pulse interaction with matter.