Topological Approach of Characterizing Optical Skyrmions and Multi-Skyrmions

Abstract

The skyrmion number of paraxial optical skyrmions can be defined solely via their polarization singularities and associated winding numbers, using a mathematical derivation that exploits Stokes's theorem. It is demonstrated that this definition provides a robust way to extract the skyrmion number from experimental data, as illustrated for a variety of optical (Néel-type) skyrmions and bimerons and multi-skyrmions. This method generates not only an increase in accuracy, but also provides an intuitive geometrical approach to understanding the topology of such quasi-particles of light and their robustness against smooth transformations.