Topologically structured singularity networks of light in three dimensions

In the past years, enhanced techniques to tailor amplitude, polarization and phase have established the generation of singularities in all degrees of freedom, as phase or polarization vortex structures and caustics [1] . Structured polarization and phase singularities can have an integer, quantized nature which connects structured light to quantum physics and is likely to improve security in data communication [2] . In optical micromanipulation, the spin and orbital angular momentum of light, defined by its polarization and phase structure, enable the transfer of torque to optically trapped particles [3] , providing additional degrees of freedom to advance optical tweezers [4] .