Topological protection of optical skyrmions through complex media

Optical Skyrmions have many important properties that make them ideal units for high-density data applications, including the ability to carry digital information through a discrete topological number and the independence of spatially varying polarization to other dimensions. More importantly, the topological nature of the optical Skyrmion heuristically suggests a strong degree of robustness to perturbations, which is crucial for reliably carrying information in noisy environments. However, the study of the topological robustness of optical Skyrmions is still in its infancy. Here, we quantify this robustness precisely by proving that the topological nature of the Skyrmion arises from its structure on the boundary and, by duality, is resilient to spatially varying perturbations provided they respect the relevant boundary conditions of the unperturbed Skyrmion. We then present experimental evidence validating this robustness in the context of paraxial Skyrmion beams against complex polarization aberrations. Our work provides a framework for handling various perturbations of Skyrmion fields and offers guarantees of robustness in a general sense. This, in turn, has implications for applications of the Skyrmion where their topological nature is exploited explicitly, and, in particular, provides an underpinning for the use of optical Skyrmions in communications and computing.