Optical skyrmions, hopfions, and other exotic topologies of light

Optical Skyrmions, much like their counterparts in other areas of physics, have recently drawn the attention of many studies due to their inherent topological robustness to external perturbations. One of such perturbations extensively studied is atmospheric turbulence, as enabling stable data transmission through air would be a significant advance in telecommunication technologies, both in classical and quantum information contexts. This work gives the theoretical basis to understand the concepts behind topological light beams, such as Skyrmions, Bimerons, and Hopfions, while focusing on Skyrmionic fields and developing numerical and experimental tools to simulate and test the conservation of the Skyrme number, the characterizing topological charge, through free-space propagation. The Skyrme number was found to be resilient to very intense simulated turbulence, with Cn2 in the order of 1e-8. During the study, the pivotal role of metalenses is confirmed as an essential step in integrating such complex optical fields in a compact and effective way. The experimental verification of the topological robustness paves the way to further studies that will in the future bridge the gap between optical Skyrmions theoretical foundations and concrete applications in real scenarios.