High-order harmonic generation (HHG) is an instrumental process enabling the transfer of short infrared pulse coherence properties into the Extreme Ultraviolet (EUV) spectral range. This phenomenon has opened the way to ultrafast pump-probe experiments at the nanoscale level. Recently, HHG has provided a straightforward approach to frequency upconvert beams structured in their phase and/or polarization. An emblematic example is the optical vortex beam, which is characterized by an azimuthally twisting wavefront. From a fundamental point of view, such a beam exhibits a phase singularity on the propagation axis and is carrying orbital angular momentum (OAM). Vector beams denote another structured beam family, exhibiting a spatially varying polarization.
In this paper, we will present our recent results on the generation and characterization of EUV vortex beams exhibiting very high topological charges (up to 100). Besides, using a similar HHG up-conversion scheme, we will show the production of so-called EUV vector-vortex beams that present the combined characteristics of the vortex and vector beams. Finally, progress on plasma-based soft x-ray laser amplification of such structured beams will be outlined,
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