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.

We customize a transversely structured, tunable light landscape on the basis of orbital angular momentum (OAM)-carrying beams for the purpose of advanced optical manipulation. Combining Laguerre-Gaussian (LG) modes with helical phase fronts of opposite OAM handedness, counter-rotating transfer of OAM is enabled in a concentric intensity structure, creating a dynamic "grinding" scenario on dielectric microparticles. We demonstrate the ability to trap and rotate silica spheres of various sizes and exploit the light fields’ feature to spatially separate trapped objects by their size. We show the adaptability of the light field depending on the chosen LG mode indices, allowing on-demand tuning of the trapping potential and sorting criteria. The versatility of our approach for biomedical application is examined by spatial discriminating yeast cells and silica spheres of distinct diameter.

We extend the established transverse customization of light, in particular, amplitude, phase, and polarization modulation of the light field, and its analysis by the third, longitudinal spatial dimension, enabling the visualization of longitudinal structures in sub-wavelength (nm) range. To achieve this high-precision and three-dimensional beam shaping and detection, we propose an approach based on precise variation of indices in the superposition of higher-order Laguerre-Gaussian beams and cylindrical vector beams in a counter-propagation scheme. The superposition is analyzed experimentally by digital, holographic counter-propagation leading to stable, reversible and precise scanning of the light volume. Our findings show tailored amplitude, phase and polarization structures, adaptable in 3D space by mode indices, including sub-wavelength structural changes upon propagation, which will be of interest for advanced material machining and optical trapping.

We transfer on-demand structuring of three-dimensional scalar amplitude and phase patterns to polarization-structured, vectorial light fields and its singularities. Our approach allows inheriting non-diffracting as well as self-imaging propagation properties to tailored singular ellipse fields, including self-replicating amplitude, polarization, and singularity configurations. It is experimentally realized by amplitude, phase and polarization modulation of the angular spectrum of the light field. We demonstrate the customization of complex singularity formations embedded in three-dimensionally (3d) tailored vectorial field. Our findings show that embedded networks of polarization singularities can be customized to propagate in a robust way along curved trajectories, creating and annihilating during propagation. This 3d structuring of vectorial singular light fields opens new perspectives for in-depth singularity studies and for advancing applications as optical micro-manipulation and material machining.

Due to their topological stability and spatial confinement, particle-like field configurations have gained significant interest in many areas of physics. Only recently, the first skyrmionic hopfion was proposed in light, but its higher-order analog in optics has stayed a theoretical construct so far, and direct experimental observations also prove difficult in non-optical systems. Here we overcome this challenge by the experimental realization and analysis of a second-order skyrmionic hopfion in the polarization and phase texture of a paraxial light field in three-dimensional space. Thereby, we exemplify advanced control of observed parameters in a localized space, pioneering further experimental studies on higher-order hopfions in optics and beyond.