Agile spatiospectral and spatiotemporal optical vortices and skyrmions\ liquid crystal textures

We demonstrate the single-path generation of spatiotemporal and spatiospectral optical vortices and skyrmionic polarization textures directly from a single dispersive anisotropic element. Experimentally, optically thick liquid-crystal waveplates with engineered spatial inhomogeneity couple space, frequency, and polarization to convert an incident field into a topological wavepacket. Two dual implementations---spatially varying optical axis at fixed thickness, or varying thickness with uniform axis---interchange near- and far-field topology, producing spatiospectral vortices in one plane and spatiotemporal vortices in the other. Moreover, the approach enables dynamic reconfiguration of the topological wavepackets via polarization tuning and electric-field control of liquid crystals, establishing a compact and agile platform for topological wave-packet engineering.