Microscope for X-ray orbital angular momentum imaging

Orbital angular momentum (OAM) of photons is carried upon the wave front of an optical vortex and is important in physics research due to its fundamental degree of freedom. As for the interaction with materials, the optical OAM was shown to be transferred to the valence electron based on modified selection rules where a single ion is carefully aligned to the center of a vortex [Schmiegelow et al.(2016)]. We here demonstrate an elaborate way of extracting the distributed OAMs in the two-dimensional x-ray wave field at the exit-face of the specimen by a vorticity-sensitive microscopy, which detects vorticity in the reciprocal-space wave field downstream of the optical vortices. This method enables us to measure the distributed topological charges and OAMs by a single image with the wide field of view over 300 $\mu$m. Among various wavelength, the research of x-ray OAM is especially interesting since it could be closely related to the predicted OAM-induced x-ray dichroism [Veenendaal et al.(2007)].