Unfolding unstable skyrmionic polarization textures

TL;DR

This paper investigates the stability of skyrmionic polarization textures in light, revealing how small perturbations can alter their topological charge and implications for localized and aberrated structures.

Contribution

It demonstrates that the topological charge of polarization skyrmions changes under perturbations, challenging previous assumptions about their stability and dependence on vortex charges.

Findings

Skyrmion number depends on the maximum of vortex charges in superposition.

Small perturbations can split phase singularities, altering topological charge.

Results impact understanding of localized polarization structures and aberrations.

Abstract

Polarization of light can form skyrmionic textures, akin to nonlinear solitons in condensed matter, yet their disparate physical context has motivated extensive debate regarding their stability. Here we show that the topological charge of such structures (skyrmion number) changes when an arbitrarily small perturbation splits coalescent phase singularities. In a superposition of two vortex beams, the skyrmion number generally only depends on the higher order topological charge $\lrr{Q_{\rm sk}=\max\lr{\ell_2,\ell_1}}$ rather than the difference of charges of the vortices in superposition $\lrr{Q_{\rm sk}=\ell_2-\ell_1}$, which only holds in the absence of perturbation. These results have significant implications for polarization structures with wavelength-scale localization and those experiencing complex aberrations.