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

Phase singularities can be created and annihilated, but always in pairs. With optical near-field measurements, we track singularities in random waves as a function of wavelength, and discover correlations between creation and annihilation events. OCIS codes: (180.4243) Near-field microscopy; (260.6042) Singular optics; (000.5490) Probability theory, stochastic processes and statistics. Phase singularities are locations in which the phase of a complex field is undefined. In two dimensions these deepsubwavelength (size zero) optical entities are points in the plane around which light’s phase swirls, with positive or negative topological charge, depending on the swirling 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, 3]. Only when this wavelength is finely tuned singularities start to move, exhibiting the Brownian statistics of a random walk [4]. Unlike particles in a simple liquid, their size zero enables phase singularities to be at the same location, fact which can indeed be inferred for singularities in a random wave field [2, 3]. In this relevant case, when two singularities share the same location they always have opposite topological charge, resulting in their mutual annihilation. New pairs can be created as well. With near-field experiments we track phase singularities at varying the wavelength of optical random waves. Figure 1 presents an overview of such near-field measurements, highlighting the creation and