Tunable focused vortex beams

In this manuscript a diffraction-based method for generating focused vortex beams with dynamic control over their axial complex field is introduced and experimentally demonstrated. The vortex beams are optically designed through the combination of a freeform diffractive lens and a spiral phase plate. This particular integration of optical elements enables demonstrated on-axis beam shaping capabilities within the depth of focus to be extended to vortex beams. Using the proposed beam generation method, focused vortex beams with user-defined axial optical parameters, e.g., axial amplitude and phase profiles can be generated via coherent light diffraction by a single-phase element. The beam shaping functionality achieved by this method is expected to enhance the applicability of vortex beams in diverse research areas, including optical tweezers, super-resolution microscopy, and quantum cryptography.