Nondiffracting skyrmion topology stairs of arbitrary trajectories

Skyrmions, topological particle-like spin textures, have drawn significant interest in optics for their potential applications in robust information encoding and photonic manipulation. However, conventional skyrmionic beams suffer from spontaneous topological textures evolution during free-space propagation due to the Gouy phase effect, consequently limiting their stability and controllability. Here, we experimentally demonstrate customizable non-diffracting skyrmionic beams (NDSBs) with unprecedented control over topologies (skyrmion number and texture helicity) and propagation trajectory. Utilizing a Fourier-space angular spectrum framework, we achieve arbitrary modulation of amplitude, phase, topological charge, polarization and propagation trajectory during beam propagation. Our approach enables not only the stable preservation of skyrmion textures over long distances but also real-time customized transformations between distinct skyrmion types—anti-skyrmions, bimerons, and higher-order skyrmions—without relying on physical polarization elements. Additionally, we realize the first experimental generation of skyrmions along self-accelerating arbitrary trajectories, such as parabolic and spiral paths. This work establishes a robust and reconfigurable platform for the manipulation of topological light fields, with implications for high-capacity optical communications, encryption, and precision particle manipulation.