Particle-like topologies in light

TL;DR

This paper reports the experimental creation and measurement of a 3D skyrmionic hopfion in structured light, demonstrating complex topological mappings with potential applications in optical data encoding and metrology.

Contribution

It introduces the first experimental realization of a topological 3D skyrmionic hopfion in light, combining polarization and phase tailoring to achieve a quantized topological charge.

Findings

Successfully created and measured a topological charge of 0.945.

Demonstrated volumetric reconstruction of the Hopf fibration in light.

Showcased potential for 3D optical data encoding and advanced metrology.

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 polarization 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 $\Pi_3$ mapping, measuring a quantised topological charge, or Skyrme number, of 0.945. Such topological state control opens new avenues for 3D optical data encoding and metrology. The Hopf characterisation of the optical hypersphere endows a new 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.