SPICE Workshop on Spin textures: Magnetism meets Plasmonics, July 23rd - 25th 2024
Mark Dennis
Three-dimensional (3D) particle-like topological excitations, such as skyrmions and hopfions, were originally proposed as topological models of fundamental particles and nuclei, and since have received much attention in high-energy and condensed matter systems. The field values wrap around a 2-dimensional or 3D sphere target space within a plane or volume, realising a topological mapping of nontrivial degree, the Skyrme number. The full state of light, including polarisation and phase, determines a point on 3-sphere we call the optical hypersphere. Decomposing via the Hopf fibration, the phase varies around Hopf loops, and the base space is the Poincaré sphere parametrising polarisation. We design, experimentally generate and measure an optical beam configuration which realises all polarisations and phases together in a propagation volume, realising a 3D optical skyrmionic hopfion [1]. For sufficiently high topological degree, the 3D polarisation structures are linked and knotted [2]. I will indicate the potential of other complex 3D textures within structured light beams.
[1] Sugic D., Droop R., Otte E., Ehrmanntraut D., Nori F., Ruostekoski J., Denz C., & Dennis M.R. 2021 Particle-like topologies in light, Nature Comm. 12 6785 [2] Parmee C.D., Dennis M.R., & Ruostekoski J. 2022 Optical excitations of Skyrmions, knotted solitons, and defects in atoms, Communications Phys. 5, 54.