Research into phase singularities and orbital angular momentum states of light now extends across a tremendous spectral reach, from terahertz frequencies to the hard x-ray regime. X-ray experiments on OAM have yielded intriguing results unique to this part of the spectrum. We have generated x-ray vortices with coherent beams using both refractive and diffractive optics and are exploring their application to x-ray magnetic dichroism, phase contrast microscopy, and coherent diffraction. Recently, we found that Laguerre-Gauss modes are present in the harmonics radiated by circularly polarized undulators, opening the door to generation of intense OAM states with free-electron lasers. This talk discusses theoretical and experimental results, including new avenues for exploiting x-ray beams carrying OAM. Article not available.

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