A topological approach for characterising optical skyrmions

Skyrmions are topologically protected field configurations characterised by a topological index, the skyrmion number. Optical skyrmions are ideally suited to investigate topological structures due to the ease of generating arbitrary light fields, and the freedom from energy constraints encountered by, for example, magnetic skyrmions. Building on our previous work of a topologically defined skyrmion number,1 here we demonstrate the conservation of the skyrmion number of hedgehog skyrmions and bimerons under propagation. We furthermore generate tunable multi-skyrmions from superpositions of oppositely polarised Gaussian and split-vortex beams of different waists, and find that the skyrmion number is conserved as a function of waist scaling. For both cases, the topological definition of the skyrmion number forms an intuitive geometric approach to understanding the underlying topology and to identifying the individual skyrmion structures.