Focusing of X-ray free-electron laser pulses using multilayer Laue lenses

Achieving the highest possible intensities of pulses at X-ray free-electron laser (XFEL) facilities entails focusing the X-ray beam to the smallest possible dimensions. Multilayer Laue lenses are volume diffractive optics that hold promise to achieve high intensities due to their high numerical aperture at hard X-ray wavelengths. These lenses are made by layer deposition and hence have a small aperture that is usually less than 100 μm. Consequently, they must withstand high intensities and heat loads if used to focus pulses of high energies. Here, we demonstrate the focusing of XFEL pulses using lenses made from layers of Mo₂C and SiC, which were chosen for their high efficiency and low beam heating. We show that lens alignment and characterisation can be carried out using attenuated XFEL pulses using the method of ptychographic X-ray speckle tracking, which also provides an approach for high-resolution projection imaging with XFEL pulses. The approach also gives quantitative information about the distribution of intensity in the focal plane, which is analysed here using plots of the encircled energy describing the proportion of the beam energy concentrated into a certain diameter, showing the possibility to reach 1.8 × 10²⁰ W cm^-2 at a photon energy of 16.9 keV. No measurable change in the wavefront aberrations of the lenses could be detected after their use in an experiment for many days with unattenuated XFEL pulses, showing that the materials and mounting scheme presented here make these lenses suitable for sustained use at XFEL facilities.