Navigating optical skyrmions—from historical origins to applications:tutorial

Optical skyrmions are topological structures formed by the distribution of light’s vectorial properties, including polarization, spin, and electromagnetic fields. This tutorial provides a comprehensive overview of the theoretical foundations, configurations, generation mechanisms, and applications of optical skyrmions. Beginning with the historical development from Kelvin’s vortex theory to Skyrme’s soliton model, the article establishes the topological framework using homotopy groups to classify vortices, skyrmions, hopfions, and other related topological structures. The distinct types of optical skyrmions—such as Néel-type, Bloch-type, and high-order variants—are characterized using topological invariants like vorticity, polarity, and helicity. Connections between optical skyrmions and other topological entities are explored, showing how structures like hopfions and knots arise from field mappings between compactified manifolds. Experimental realizations through interference of evanescent fields, metasurfaces, spatial light modulators, and spatiotemporal modulation are described, along with methods for dynamic control and topological transitions. Applications in optical information processing, sensing, and quantum technologies are discussed, highlighting the robustness and subwavelength precision enabled by topological protection. Although prior reviews and tutorials exist, this tutorial is necessary because at this pivotal transition from fundamental research to applications, a comprehensive tutorial is significant for navigating new understanding and applications. This tutorial aims to equip readers with both foundational and practical knowledge, positioning optical skyrmions as versatile tools for advancing topological photonics and next-generation photonic technologies.