Abstract

When the positions of two generic singularities of equally signed topological index coincide, a higher-order singularity with twice the index is created. In general, singularities tend to repel each other when sharing the same topological index, preventing the creation of such higher-order singularities in 3D generic electromagnetic fields. Here, we demonstrate that in 2D random vector waves higher-order polarization singularities—known as polarization vortices—can occur, and we present their spatial correlation. These polarization vortices arise from the overlap of two points of circular polarization (C points) with the same topological index. We observe that polarization vortices of positive index occur more frequently than their negative counterparts, which results in an index-symmetry breaking unprecedented in singular optics. To corroborate our findings, we analyze the spatial correlation of C points in relation to their line classification and link the symmetry breaking to the allowed dipolar and quadrupolar moments of the field at a polarization vortex.

Highlights

  • A hurricane generated from storms swirling in the ocean [1] and a peak in the gravitational-wave strain from the merging of two black holes [2] both represent observations of events in nature exhibiting singular parameters in their describing mathematical model

  • We report our observation of polarization vortices in 2D random vector waves

  • In this paper we presented the experimental observation of higher-order singularities of the polarization state of a random light field, known as polarization vortices

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Summary

INTRODUCTION

A hurricane generated from storms swirling in the ocean [1] and a peak in the gravitational-wave strain from the merging of two black holes [2] both represent observations of events in nature exhibiting singular parameters in their describing mathematical model In many cases, these extreme events contain the formation or annihilation of vortices, given by a flow of a physical quantity around a singular point. Higher-order singularities are not to be expected in random ensembles of waves in 3D In these fields, a multitude of lowest-order singularities occurs [20,21,22], but with a spatial repulsion between the ones with the same topological index [23,24,25,26]. We explain this finding by attributing the field distribution around the vortices to the field’s dipolar and quadrupolar moments

EXPERIMENTAL OBSERVATION OF POLARIZATION VORTICES
Pair and Charge Correlation Function and Index-Symmetry Breaking
Index-Symmetry Breaking in the Spatial Distribution of C Points
Topology of the Director Field Around Vortices
LINKING THE INDEX IMBALANCE TO
CONCLUSION
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