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

Abstract

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 $$[0, 2\pi ]$$ [ 0 , 2 π ] 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.

Generation and applications of x-ray and extreme ultraviolet beams carrying orbital angular momentum

“…X-ray and EUV beams with OAM can also be created using forked gratings [42][43][44][45], another type of diffractive optics. Several examples are shown in figures 2(d)-(f).…”

“…In addition to generation, characterization of OAM beam in the x-ray regime is non-trivial. Novel interferometric techniques such as in-line holography [42,44] and the advanced imaging method of ptychography [40] have been developed to quantify the OAM quantum number.…”

“…This technique is commonly used to study magnetic textures. Studies have shown that inline holography with a forked diffraction grating can be used to measure the spiral phase distribution of an OAM beam [42,44]. The interference pattern shows a distinct forked pattern, where the number of dislocations in the fork corresponds to the topological charge of the OAM beam.…”

Antiferromagnetic real-space configuration probed by dichroism in scattered x-ray beams with orbital angular momentum

“…Beams with OAM have already found many practical uses in the optical wavelength regime, such as in optical tweezers and subwavelength imaging (21)(22)(23)(24)(25)(26)(27), and potential exists for future applications in optical communications and quantum optics (21)(22)(23)(24)28). However, exploitation of OAM in x-ray beams is a relatively novel field (29)(30)(31)(32)(33)(34)(35). The generation of x-ray OAM beams has been investigated (33)(34)(35)(36), but the interaction between x-rays carrying OAM and matter (37) has only recently been studied experimentally (32,38,39).…”

“…The generation of x-ray OAM beams has been investigated (33)(34)(35)(36), but the interaction between x-rays carrying OAM and matter (37) has only recently been studied experimentally (32,38,39). Potential applications include x-ray holography (30,31), ptychography (36), and microscopy (40).…”