Screening and fluctuation of the topological charge in random wave fields

Vortices, phase singularities, and topological defects of any kind often reflect information that is crucial for understanding physical systems in which such entities arise. With near-field experiments supported by numerical calculations, we determine the fluctuations of the topological charge for phase singularities in isotropic random waves as a function of the size 푅 of the observation window. We demonstrate that for two-dimensional fields such fluctuations increase with a superlinear scaling law, consistent with a 푅 log 푅 behavior. Additionally, we show that such scaling remains valid in the presence of anisotropy.