Time-dependent wave front propagation simulation of a hard x-ray split-and-delay unit: Towards a measurement of the temporal coherence properties of x-ray free electron lasers

For the European x-ray free electron laser (XFEL) a split-and-delay unit based on geometrical wavefront beam splitting and multilayer mirrors is built which covers the range of photon energies from 5 keV up to 20 keV. Maximum delays between Δτ=±2.5 ps at hν=20 keV and up to Δτ=±23 ps at hν=5 keV will be possible. Time-dependent wave-optics simulations have been performed by means of Synchrotron Radiation Workshop software for XFEL pulses at hν=5 keV. The XFEL radiation was simulated using results of time-dependent simulations applying the self-amplified spontaneous emission code FAST. Main features of the optical layout, including diffraction on the beam splitter edge and optics imperfections measured with a nanometer optic component measuring machine slope measuring profiler, were taken into account. The impact of these effects on the characterization of the temporal properties of XFEL pulses is analyzed. An approach based on fast Fourier transformation allows for the evaluation of the temporal coherence despite large wavefront distortions caused by the optics imperfections. In this way, the fringes resulting from time-dependent two-beam interference can be filtered and evaluated yielding a coherence time of τ_{c}=0.187 fs (HWHM) for real, nonperfect mirrors, while for ideal mirrors a coherence time of τ_{c}=0.191 fs (HWHM) is expected.