  Phase singularities are locations where light is twisted like a corkscrew,
with positive or negative topological charge depending on the twisting
direction. Among the multitude of singularities arising in random wave fields,
some can be found at the same location, but only when they exhibit opposite
topological charge, which results in their mutual annihilation. New pairs can
be created as well. With near-field experiments supported by theory and
numerical simulations, we study the persistence and pairing statistics of phase
singularities in random optical fields as a function of the excitation
wavelength. We demonstrate how such entities can encrypt fundamental properties
of the random fields in which they arise.
