Spatial bunching of same-charge polarization singularities in two-dimensional random vector waves

TL;DR

This study investigates how the spatial distribution of polarization singularities, specifically C points, changes in truly two-dimensional random light fields, revealing an unexpected increase in same-charge singularity proximity.

Contribution

It demonstrates experimentally and theoretically that in 2D random vector fields, same-charge polarization singularities tend to cluster more closely than previously observed in higher dimensions.

Findings

Enhanced probability of same-charge C points being close in 2D fields

Experimental and theoretical results show strong agreement

Distribution of singularities differs significantly from 3D cases

Abstract

Topological singularities are ubiquitous in many areas of physics. Polarization singularities are locations at which an aspect of the polarization ellipse of light becomes undetermined or degenerate. At C points the orientation of the ellipse becomes degenerate and light's electric field vector describes a perfect circle in time. In 2D slices of 3D random fields the distribution in space of the C points is reminiscent of that of interacting particles. With near-field experiments we show that when light becomes truly 2D, this has severe consequences for the distribution of C points in space. The most notable change is that the probability of finding two C points with the same topological charge at a vanishing distance is enhanced in a 2D field. This is an unusual finding for any system which exhibits topological singularities as same-charge repulsion is typically observed. All our experimental findings are supported with theory and excellent agreement is found between theory and experiment.