# Paraxial Skyrmionic beams

## TL;DR

This paper explores the topological properties of vector vortex beams, specifically their Skyrmionic nature, and discusses how the Skyrmion number characterizes their polarization and amplitude variations.

## Contribution

It introduces the concept of Skyrmion number in vector vortex beams and analyzes its physical significance in describing their topological properties.

## Key findings

- Vector vortex beams exhibit Skyrmionic topological properties.
- The Skyrmion number quantifies the beam's polarization and amplitude variations.
- Understanding Skyrmion number aids in characterizing complex light fields.

## Abstract

Vector vortex beams possess a topological property that derives both from the spatially varying amplitude of the field and also from its varying polarization. This property arises as a consequence of the inherent Skyrmionic nature of such beams and is quantified by the associated Skyrmion number, which embodies a topological property of the beam. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the Skyrmion number in this context.