Fermionic out-of-plane structure of polarization singularities

TL;DR

This paper introduces a new three-dimensional classification scheme for polarization singularities, expanding the understanding of C points by considering out-of-plane polarization ellipse variations and relating it to the M"obius index.

Contribution

It proposes a novel 3D classification of polarization C points based on out-of-plane ellipse axis variation, extending the traditional in-plane types and linking to the M"obius index.

Findings

New geometric classification scheme for polarization C points.

Derived minimal parameters for the out-of-plane classification.

Connected the classification to the M"obius index of singularities.

Abstract

A new classification of circular polarization C points in three-dimensional polarization ellipse fields is proposed. The classification type depends on the out-of-plane variation of the polarization ellipse axis, in particular, whether the ellipse axes are in the plane of circular polarization one or three times. A minimal set of parameters for this classification are derived, and discussed in the context of the familiar in-plane C point classification into lemon, star, and monstar types. This new geometric classification is related to the M\"obius index of polarization singularities recently introduced by Freund.