The dating game at dimension zero: Creation and annihilation of phase singularities in random waves

Phase singularities are locations in which the phase of a complex field is undefined. In two dimensions these deep-subwavelength (size zero) optical entities are points in the plane where light is twisted like a corkscrew, with positive or negative topological charge, depending on the twisting direction [1]. In a monochromatic field of random waves phase singularities are frozen in time, with a spatial distribution reminiscent of that of particles in a simple liquid, and strictly related to the wavelength of the field [2]. Only when this wavelength is finely tuned singularities start to move, exhibiting the Brownian statistics of a random walk [3].