Observation of optical vortex knots and links associated with topological charge

Knots and links, as three-dimensional topologies, have played a fundamental role in many physical fields. Despite knotted vortex loops having been shown to exist in the light field, the three-dimensional configuration of vortex loop is fixed due to their topological robustness, making the fields with different topologies independent of each other. In this work, we established the mapping between the torus knots/links and the integer topological charge of the optical vortex, and demonstrated the change of the intermediate state with fractional charges. Furthermore, we experimentally observed the transformation process of the three-dimensional topological structure by only changing the topological charge. Remarkably, we revealed two different reconnection mechanisms associated with the odd or even index of the torus topology. We hope these results may provide new insight for the study of singular optics and evolution in other physical fields.