In two-dimensional random waves, phase singularities are point-like dislocations with a behavior reminiscent of interacting particles. This - qualitative - consideration stems from the spatial arrangement of these entities, which finds its hallmark in a pair correlation reminiscent of a liquid-like system. Starting from their pair correlation function, we derive an effective pair-interaction for phase singularities in random waves by using a reverseMonte Carlo method. This study initiates a new, to the best of our knowledge, approach for the treatment of singularities in random waves and can be generalized to topological defects in any system.

In order to utilize the full potential of tailored flows of electromagnetic energy at the nanoscale, we need to understand its general behavior given by its generic representation of interfering random waves. For applications in on-chip photonics as well as particle trapping, it is important to discern between the topological features in the flow-field of the commonly investigated cases of fully vectorial light fields and their 2D equivalents. We demonstrate the distinct difference between these cases in both the allowed topology of the flow-field and the spatial distribution of its singularities, given by their pair correlation function g(r). Specifically, we show that a random field confined to a 2D plane has a divergence-free flow-field and exhibits a liquid-like correlation, whereas its freely propagating counterpart has no clear correlation and features a transverse flow-field with the full range of possible 2D topologies around its singularities.