Particle-like topologies in light

Abstract

Three-dimensional (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions, that realise integer topological numbers in their configuration via homotopic mappings from real space to the hypersphere (sphere in 4D space) or the 2D sphere. They have received tremendous attention as exotic textures in particle physics, cosmology, superfluids, and many other systems. Here we experimentally create and measure a topological 3D skyrmionic hopfion in fully structured light. By simultaneously tailoring the polarisation and phase profile, our beam establishes the skyrmionic mapping by realising every possible optical state in the propagation volume. The resulting light field’s Stokes parameters and phase are synthesised into a Hopf fibration texture. We perform volumetric full-field reconstruction of the $${{{\Pi }}}_{{{3}}}$$ Π 3 mapping, measuring a quantised topological charge, or Skyrme number, of 0.945. Such topological state control opens avenues for 3D optical data encoding and metrology. The Hopf characterisation of the optical hypersphere endows a fresh perspective to topological optics, offering experimentally-accessible photonic analogues to the gamut of particle-like 3D topological textures, from condensed matter to high-energy physics.

Topological quasiparticles of light: Optical skyrmions and beyond

“…k, Topologically robust skyrmions with customized geometry generated on a structured localized spoof plasmons supported by ultrathin space-coiling meta-structures [45]. l, The 3D polarization texture of the vector beam representing an optical hopfion, where each Hopf fiber is constructed by a trajectory of a certain polarization ellipse (The hue colors depict different ellipse azimuths and dark to bright progression corresponds to the polarisation variation from left-to right-handed circular state) [75].…”

“…A 3D analysis of the Stokes vector field of a paraxial full-Poincaré vector beam can reveal a construction analogue to skyrmion tube [84]. Using a hypersphere as a higher-dimensional generalization of a Poincaré sphere, the unwrapping of the vector field structure results in a skyrmionic texture in 3D which was termed an optical hopfion [75]. In such optical hopfion, each fibre in the Hopf fibration corresponds to the trajectory of a certain polarization ellipse and the hopfionic vector beam is formed [75] (Fig.…”

Nonseparable states of light: From quantum to classical

“…Skyrmions are special states of quasiparticles with a sophisticated space-vector topology, and in recent time, its optical counterparts were introduced from the quantum and material physics into optics, as a powerful tool to shape new topological states of light [121][122][123]. More recently, skyrmion topology also found its efficacy in tailoring reconfigurable patterns in vector beams by fully exploiting the salient particle-like topology of skyrmions [124][125][126]. Thus, more skyrmionic nonseparable states in structured light are expected in the future.…”

Optical magnetism and wavefront control by arrays of strontium atoms

“…9 corresponds to a nontrivial topological winding number W = 1, in which case the Stokes vector profile of the beam cross-section covers the Poincaré sphere exactly once. Baby-Skyrmions, different from the full 3D Skyrmions [79][80][81], can optically appear as a result of different light-matter interfaces [82][83][84][85] and are known in magnetic structures [86] and superfluids [87][88][89].…”