Screening and fluctuation of the topological charge in random wave fields

TL;DR

This paper investigates how the topological charge fluctuations of phase singularities in isotropic and anisotropic random wave fields scale with observation window size, revealing a superlinear R log R behavior supported by experiments and simulations.

Contribution

It provides the first detailed analysis of topological charge fluctuations in random wave fields, establishing a superlinear scaling law valid for both isotropic and anisotropic conditions.

Findings

Topological charge fluctuations scale as R log R in 2D random wave fields.

Scaling law remains valid under anisotropic conditions.

Experimental and numerical results confirm the superlinear growth.

Abstract

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 R of the observation window. We demonstrate that for two-dimensional fields such fluctuations increase with a superlinear scaling law, consistent with a R log R behavior. Additionally, we show that such scaling remains valid in the presence of anisotropy.