Topological transformation and free-space transport of photonic hopfions

Structured light fields embody strong spatial variations of polarization, phase, and amplitude. Understanding, characterization, and exploitation of such fields can be achieved through their topological properties. Three-dimensional (3D) topological solitons, such as hopfions, are 3D localized continuous field configurations with nontrivial particle-like structures that exhibit a host of important topologically protected properties. Here, we propose and demonstrate photonic counterparts of hopfions with exact characteristics of Hopf fibration, Hopf index, and Hopf mapping from real-space vector beams to homotopic hyperspheres representing polarization states. We experimentally generate photonic hopfions with on-demand high-order Hopf indices and independently controlled topological textures, including Néel-, Bloch-, and antiskyrmionic types. We also demonstrate a robust free-space transport of photonic hopfions, thus showing the potential of hopfions for developing optical topological informatics and communications.