Design of a compact device to generate and test beams with orbital angular momentum in the EUV.

We present a compact design to generate and test optical-vortex beams with possible applications in the extreme ultraviolet (EUV) region of the electromagnetic spectrum. The device consists of a diffractive mask where both the beam with orbital angular momentum and the reference wavefront to test its phase are generated. In order to show that the proposal would work in the EUV, simulations and proof-of-principle experiments were performed, using typical parameters for EUV holography scaled to visible wavelengths. As the simplest case, we consider the well-known Laguerre-Gaussian (LG)-like beams, which have a single vortex in the propagation axis. To further test the versatility of the device, we consider Mathieu beams, more complex structured beams that may contain several vortices. In the experiment, a spatial light modulator was used to display the mask. As examples, we show the results for a LG-like beam with topological charge ℓ=1 and Mathieu beams with topological charge ℓ=2 and ellipticity q=2. These results show the potential of the device to generate a variety of beam shapes at EUV wavelengths.