Topological charge of soft X-ray vortex beam determined by inline holography

A Laguerre–Gaussian (LG) vortex beam having a spiral wavefront can be characterized by its topological charge (TC). The TC gives the number of times that the beam phase passes through the interval [Formula: see text] following a closed loop surrounding the propagation axis. Here, the TC spectra of soft X-ray vortex beams are acquired using the in-line holography technique, where interference between vortex waves produced from a fork grating and divergent waves from a Fresnel zone plate is observed as a holographic image. The analyses revealed the phase distributions and the TC for the LG vortex waves, which reflects topological number of the fork gratings, as well as for the Hermite–Gaussian (HG) mode waves generated from the other gratings. We also conducted a simulation of the present technique for pair annihilation of topological defects in a magnetic texture. These results may pave the way for development of probes capable of characterizing the topological numbers of magnetic defects.