tightly focused polychromatic knots

The use of structured light has allowed the realization of complex structures with rich topological features. In recent years, it has been shown that the field’s dislocations can form closed trajectories as they propagate, tracing knotted curves in a three-dimensional volume. Following these results, we raise a fundamental question: is it possible to knot the curves traced by the electric field as it evolves over time? In contrast to the case of monochromatic light, the vast “zoo” of polarization states of polychromatic fields remains almost unexplored. In this work, we aim to study the behavior of structured polychromatic light when they are tightly focused by high numerical aperture lenses. Here, we follow a heuristic approach to generate regions of knotted polarization curves on the focal plane based on the knowledge of the tight focusing of vector vortex beams. Our results may provide insight into the potential experimental realization of these new exotic and complex polarization states using current techniques developed for nonlinear and nanophotonics. In addition, these locally knotted fields may find applications in the field of light-matter interaction where the nontrivial topological structure could induce local magnetic fields in semiconductors.