# Topological defects, geometric phases, and the angular momentum of light

## TL;DR

This paper explores how geometric phases in optics explain topological defects and polarization patterns in vector vortex beams, linking angular momentum shifts to geometric phase holonomy.

## Contribution

It presents a unified framework connecting geometric phases, topological defects, and angular momentum in light beams, offering new insights into their interrelations.

## Key findings

- Spin redirection phase causes topological phase singularities.
- Angular momentum shift is equivalent to geometric phase holonomy.
- Unified explanation for polarization patterns in vector vortex beams.

## Abstract

Recent reports on the intriguing features of vector vortex bearing beams are analyzed using geometric phases in optics. It is argued that the spin redirection phase induced circular birefringence is the origin of topological phase singularities arising in the inhomogeneous polarization patterns. A unified picture of recent results is presented based on this proposition. Angular momentum shift within the light beam (OAM) has exact equivalence with the angular momentum holonomy associated with the geometric phase consistent with our conjecture.