High-order harmonic generation (HHG) has been recently proven to produce harmonic vortices carrying orbital angular momentum (OAM) in the extreme-ultraviolet (XUV) region from the nonlinear up-conversion of infrared vortex beams. In this work we present two methods to control and extend the OAM content of the harmonic vortices. First, we show that when a driver combination of different vortex modes is used, HHG leads to the production of harmonic vortices with a broad OAM content due to its nonperturbative nature. Second, we show that harmonic vortices with two discrete OAM contributions –so called fractional OAM modes– are generated when HHG is driven by conical refraction beams. Our work offers the possibility of generating tunable OAM beams in the XUV regime, potentially extensible to the soft x rays, overcoming the state of the art limitations for the generation of OAM beams far from the visible domain.
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