Unravelling the nonlinear generation of designer vortices with dielectric metasurfaces.

Vortex beams are currently drawing a great deal of interest, from fundamental research to several promising applications. While their generation in bulky optical devices limits their use in integrated complex systems, metasurfaces have recently proven successful in creating optical vortices, especially in the linear regime. In the nonlinear domain, of strategic importance for the future of classical and quantum information, to date orbital angular momentum has only been created in qualitative ways, without discussing discrepancies between design and experimental results. Here, we demonstrate and analyze the generation of high-purity second harmonic (SH) optical vortices via dielectric meta-holograms. Through full-wave simulations and a proper fabrication protocol, we achieve efficient frequency doubling of an unstructured pump beam into SH vortices with topological charges from 1 to 10. Interferometric and modal-purity measurements confirm the generation of high-quality SH vortices with minimal deviations from the intended design thanks to a quasi-local control over the SH phase. Through systematic comparisons between experimental data and semi-analytical calculations, we also provide a clear insight into the occurrence of ghost vortices in the metasurface-generated harmonic beams, highlighting the importance of simple designs that can be readily transposed into fabricated devices with high fidelity. Our findings underscore the potential of nonlinear dielectric metasurfaces for versatile structured-light generation and manipulation, paving the way for future developments in integrated photonic systems.