Generation and Applications of Extreme-Ultraviolet Vortices

Vortex light beams are structures of the electromagnetic field with a spiral phase ramp around a point-phase singularity. These vortices have many applications in the optical regime, ranging from optical trapping and quantum information to spectroscopy and microscopy. The extension of vortices into the extreme-ultraviolet (XUV)/X-ray regime constitutes a significant step forward to bring those applications to the nanometer or even atomic scale. The recent development of a new generation of X-ray sources, and the refinement of other techniques, such as harmonic generation, have boosted the interest of producing vortex beams at short wavelengths. In this manuscript, we review the recent studies in the subject, and we collect the major prospects of this emerging field. We also focus on the unique and promising applications of ultrashort XUV/X-ray vortex pulses