Skyrmions based on optical anisotropy for topological encoding

The observation of skyrmions across diverse physical domains suggests that they are universal features of $S^2$ -valued fields, reflecting the ubiquity of topology in the study of the natural world. In this paper, we develop an abstract technique of parameter space dimensionality reduction that extends the skyrmion framework to fields taking values in manifolds of dimension greater than 2, thereby broadening the range of systems that can support skyrmions. To prove that this is more than just a mathematical abstraction, we apply our technique to light-matter interactions, directly encoding skyrmionic structures into the optical anisotropy of spatially varying structured matter by selecting a distinguished axis, an approach fundamentally different from the more commonly known skyrmions formed by director fields in liquid crystals. We experimentally realize such skyrmions using a liquid-crystal-based tunable elliptical retarder array as a proof-of-concept platform and demonstrate complex, reconfigurable skyrmionic states exhibiting topological robustness under artificially introduced stochastic perturbations. Exploiting this robustness, we demonstrate a promising application of skyrmions in topologically protected information storage and provide an easily verifiable rule, which we term the 60° rule, that serves as a practical engineering criterion for guaranteeing robustness against noise and measurement errors.