The longitudinal dynamics evolution of optical skyrmions via meta-optics.

Skyrmions, as topologically structured light fields, have attracted considerable attention due to their unique topological properties and potential applications such as optical communication and advanced sensing technologies. However, their longitudinal evolution, as a dimension ripe for exploitation, typically remains uncontrolled and non-deterministic, hindering its in-depth exploration and application scenarios. Here, this paper presents a novel method using dielectric metasurfaces for precisely modeling the longitudinal dynamics evolution of skyrmions. We introduce a new mechanism that allows for the accurate period modulation of skyrmions stokes properties along the propagation direction by controlling the differences in numerical apertures of a zero-order right-circularly polarized beam and a first-order left-circularly polarized beam. Crucially, the evolution period can be arbitrarily designed, and the propagation distance can be expanded by increasing the waist radius of input beams. To validate this approach, we showcase this paradigm through displacement sensing applications, where single-snapshot polarization measurements directly infer absolute position within a compact metasurface-integrated platform, offering a compact and simple alternative to conventional scanning-based approaches for displacement sensing. Our approach advances the understanding of dynamically controlled topological light fields and enables compact devices for precision metrology and optical information technologies.