Spatiotemporal Knots and Links of Extended (3+1)‐Dimensional Variable‐Coefficient Lugiato–Lefever Model in WGM Microcavities

ABSTRACT Spatiotemporal optical links (STOLs) and knots (STOKs) are frontier research topics in topological photonics due to their nontrivial topological structures and intrinsic robustness. Existing microcavity dynamics studies mostly employ simplified linear, low‐dimensional, and homogeneous models, which neglect realistic spatiotemporal inhomogeneity and cannot accurately characterize STOL and STOK evolution. To overcome this limitation, this work introduces toroidal vortex dual topological charges, and explores how spatiotemporal modulation coefficients in the (3+1)‐dimensional variable‐coefficient LLE govern the formation, topological robustness, and dynamical evolution of STOLs and STOKs. The results verify that the model can accurately depict the evolution of three‐dimensional spatiotemporal topological optical fields in microcavities and reproduce their dynamical behaviors. Within valid parameter ranges, these coefficients regulate the spatial distribution and evolutionary rhythm of topological optical fields, allowing active manipulation of STOL and STOK configurations. The obtained spatiotemporal topological structures sustain long‐term stable self‐evolution, show strong immunity to environmental disturbances and random noise, and possess excellent structural stability and topological robustness. This work advances the topological theory of high‐dimensional LLE models, reveals the stabilization mechanism of microcavity optical fields, and provides theoretical support for topological photonic devices, optical encoding, and microcavity photonic sources.