Extreme-ultraviolet vortices may be exploited to steer the magnetic properties of nanoparticles, increase the resolution in microscopy, and gain insight into local symmetry and chirality of a material; they might even be used to increase the bandwidth in long-distance space communications. However, in contrast to the generation of vortex beams in the infrared and visible spectral regions, production of intense, extreme-ultraviolet and x-ray optical vortices still remains a challenge. Here, we present an in-situ and an ex-situ technique for generating intense, femtosecond, coherent optical vortices at a free-electron laser in the extreme ultraviolet. The first method takes advantage of nonlinear harmonic generation in a helical undulator, producing vortex beams at the second harmonic without the need for additional optical elements, while the latter one relies on the use of a spiral zone plate to generate a focused, micron-size optical vortex with a peak intensity approaching ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, paving the way to nonlinear optical experiments with vortex beams at short wavelengths.

The recent development of ultrafast extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter. Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution. However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within an XUV pulse sequence opens exciting possibilities for coherent control and multidimensional spectroscopy, but has not been accomplished. Here, we overcome these constraints in a highly time-stabilized and phase-modulated XUV-pump, XUV-probe experiment, which directly probes the evolution and dephasing of an inner subshell electronic coherence. This approach, avoiding any XUV optics for direct pulse manipulation, opens up extensive applications of advanced nonlinear optics and spectroscopy at XUV wavelengths.

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.

We report on the experimental evidence of magnetic helicoidal dichroism, observed in the interaction of an extreme ultraviolet vortex beam carrying orbital angular momentum with a magnetic vortex. Numerical simulations based on classical electromagnetic theory show that this dichroism is based on the interference of light modes with different orbital angular momenta, which are populated after the interaction between light and the magnetic topology. This observation gives insight into the interplay between orbital angular momentum and magnetism and sets the framework for the development of new analytical tools to investigate ultrafast magnetization dynamics.