# Split-And-Delay Unit for FEL Interferometry in the XUV Spectral Range
## 5 Conclusions  
In summary, we have described a split-and-delay unit suitable for interferometric XUV pump-XUV probe experiments at coherent FELs. The SDU consists of two interleaved lamellar gratings. The intensity of the zeroth diffraction order monitored as a function of delay is analogous to that in a Michelson interferometer. The signal from individual orders can be selected using spatially-resolved imaging of the ionization volume with a VMI spectrometer or an ion microscope. The time delay produced by the SDU is precisely determined by an in-vacuum white light interferometer. The WLI in \"electronically scanned\" configuration records the topography of the SDU on a single-shot basis. These data are used to determine the pump-probe delay generated by the SDU for each laser shot. The WLI was characterized with an interferometric measurement using a CW laser to have a precision of 1 nm. Figure 7: Standard deviation of the laser intensity data from the fit plotted as a function of optical path difference \(s\). The black scatter represents the data, and the red curves are fits of a form \(\sin 2\frac{2\pi}{\lambda_{L}}s\), where \(\lambda_{L}\) is the laser wavelength. Each data point is the center of a bin, the size of which is indicated in the left top corner of each plot. This allows for interferometric experiments in the XUV spectral range with a delay resolution down to 3 attoseconds at repetition rates up to 60 Hz. Towards short-wavelength FEL applications, the key aspect defining the usability of the described SDU for phase-resolved studies is whether the individual diffraction orders can be resolved under the particular experimental conditions. For a given light wavelength, this depends on the grating surface quality and period, focusing geometry and the charged particle detector, all of which can be improved. High surface quality of the optics becomes an especially important aspect when dealing with short wavelengths. The major challenge here is to structure the gratings with small period maintaining the flatness of the original substrate. Distortions of the substrate induced by the sawing process lead to phase errors in the reflected wavefront, which reduce the interference contrast in the ionization region. This effect becomes more pronounced the shorter the wavelength is. To some extent, the phase errors produced by the surface inhomogeneity can be scaled down by reducing the angle of incidence of the XUV beam on the SDU, which is required anyway for shorter wavelengths to maintain high reflectivity. Another aspect to take into account is the order separation equal to \(\lambda f/d\) in the focal area. For a fixed wavelength, the free parameters are the mirror focal length and the grating period. Manufacturing lamellar gratings with shorter periods and high surface quality is challenging; therefore, extending the focal length is a feasible option. The imaging detector is yet another key element that defines the resolution of the setup. In the experiment with 38 nm wavelength and a focal length of 300 mm, the resolution of the VMI spectrometer operated in the spatial-imaging mode with a moderate magnification of 20 was sufficient to distinguish individual diffraction orders. A spectrometer purposely designed for magnified spatial imaging of charged particles, i.e., an ion microscope, can reach magnification factors up to 100 [36] and significantly improve the resolution of the setup. In conclusion, we are confident that the lamellar-grating concept can be extended to the few nm-wavelength range for advanced applications with soft X-ray FEL pulses. This work was supported by the Deutsche Forschungsgemeinschaft through the excellence cluster \"The Hamburg Centre for Ultrafast Imaging (CUI)--Structure, Dynamics and Control of Matter at the Atomic Scale\" (DFG-EXC1074), the collaborative research center \"Light-induced Dynamics and Control of Correlated Quantum Systems\" (SFB925), the GrK 1355 and by the Federal Ministry of Education and Research of Germany under contract No. 05K16 GU4.