Task 1: Nonlinear transfer of orbital angular momentum from the IR to the XUV

Light beams carrying OAM's have been largely studied over the past twenty years in the visible domain, leading to the development of characterization means based either on interference or diffractive approaches. Here, we will transfer these methods to the XUV range. They are two difficulties identified. First, the harmonics are generated all at once. We must therefore derive selection means to spread them out, without distorting their phase profile, and be able to characterize just one of them. Second, in this spectral range, there is almost no transmissive optics, making the use of standard interferometers difficult. This task is thus split in two substasks:

Experimental diffraction patterns of an OAM beams through a triangular aperture. From left to right, 800nm $\ell_{IR}$=1, $\ell_{IR}$=2 and $\ell_{IR}$=3 and 400nm $\ell_{blue}$=3 beams (LIDyl, unpublished).

• Selection of a single harmonic. Here we will either use low dispersion gratings, or combinations of multilayers mirrors and metallic filters.


• Measurement of the OAM of XUV beams. Several alternatives will be tested. Basically, it is all about measuring a spatial phase profile in the XUV. For this, one should either exploit diffraction or interference phenomena. The two approaches are available in the visible range, with for instance, schemes based on cylindrical lenses, diffraction on triangular slits (see figure), point diffraction interferometry, or even Shack Hartman sensors. Here we will theoretically and experimentally investigate several of these approaches.