Photonic spin skyrmions and hopfions

Topological textures and defects are of great theoretical and practical interest and have been extensively studied in condensed matter systems. In electronic spin systems, two- and three-dimensional topological textures, known as skyrmions and hopfions, have been realized experimentally. Here, we show that the photonic spin density of monochromatic light in real space can form skyrmion and hopfion textures, forming direct photonic analogies to the corresponding electronic spin textures. Such photonic spin textures are created by engineering the spatial profiles for two orthogonal polarization components of the beam. We verify the topological properties of such textures by numerically calculating the skyrmion number or the hopfion number, which evaluates to nonzero integers. We also demonstrate the topological defects corresponding to the skyrmion and the hopfion textures, which are monopole-like points and monopole loops, respectively. We envision such photonic spin textures to find applications in controlling the orientation and rotation of nanoparticles, optical sensing, and transferring the topological textures from light to matter.