Optical M\"{o}bius Singularities

TL;DR

This paper explores the geometry and topology of Möbius singularities in three-dimensional elliptically polarized light, detailing their structures, winding numbers, and occurrence probabilities.

Contribution

It introduces a comprehensive analysis of Möbius singularities in nonparaxial light, including their classification, topological features, and statistical likelihoods.

Findings

Möbius singularities are common in 3D elliptically polarized light.

Multiple winding numbers characterize these singularities.

Probabilities for different Möbius configurations are quantified.

Abstract

M\"{o}bius strips with one, two, three, and four, half-twists are shown to be generic features of three-dimensional (nonparaxial) elliptically polarized light. The geometry and topology of these unusual singularities is described and the multitude of winding numbers that characterize their structures is enumerated; probabilities for the appearance of different configurations are presented.