  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 therefore
resilient to complex 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
different 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
optical Skyrmion where their topological nature is exploited explicitly, and,
in particular, provides an underpinning for the use of Skyrmions in optical
communications and photonic computing.
