Decoupling of topology and texture in optical skyrmions under turbulence

Abstract: Topological structure is widely invoked as a route to disorder-resilient photonic states, yet whether it protects locally resolved field structure under realistic disorder has not been established. Optical skyrmions, vectorial light fields characterized by a global skyrmion number $N_{sk}$, provide a stringent test of this question under turbulence. Although $N_{sk}$ is expected to be robust, conservation of a global invariant does not guarantee preservation of the underlying polarization texture. Here we reconstruct the full Stokes field of optical skyrmions transmitted through controlled turbulent channels, combining experiment, phase screen simulations, and analytical modelling to independently track global and local observables. We demonstrate a broad disorder regime in which $N_{sk}$ remains conserved while fine polarization structure rapidly degrades. This pronounced decoupling, strengthened for higher-order skyrmions, exposes a hierarchy of robustness between topological invariants and texture-resolved information, defining intrinsic limits of topological protection in disordered wave systems.