Skyrmionic textures within SU(6) structured light

Skyrmions are topological quasi-particles with local spin textures, which are considered to be robust against structural deformation. Néel and Bloch states are famous examples of skyrmions, which exhibit radical and chiral spin profiles, respectively. Here, we show a skyrmion can be continuously transformed to an antiskyrmion or various other states with unique spin textures through the underlying symmetry of the special unitary group of degree six, SU(6), for photons with spin and orbital angular momentum. We employ a Lie group theory for coherent photons to describe the SU(6) transformation and establish a relationship between the generator of rotation and its expectation values on a hypersphere of S³⁵ S 35 . We propose a simple experimental setup to control the SU(6) states in combinations with wave-plates and vortex lenses to realise the generalised Euler’s formula physically in a Mach-Zehnder interferometer. We show that skyrmionic states are described on higher-order Poincaré spheres together with a recently proposed skyrmionic torus.