Optical vortex knots and links via holographic metasurfaces

Vortices arise in many natural phenomena as dark points of total destructive interference. Sometimes they form continuous lines and even enclosed loops with knotted or linked topologies in three spatial dimensions. Since the mathematical topology was introduced into physics, from hydrodynamics, condensed matter physics to photonics, and other modern physical fields, scientists have been exploring the related topological essences of vortex knots; hence, the topology is a forefront topic in different physical systems. Owing to the reliability and observability of light in free space, optical vortex knots and links are the most studied physical topologies. Here, we review some of these developments with a focus on optical vortex knots and links. We first introduce the brief historical perspective and structural properties of optical vortices. Then, we trace the progress on the theoretically constructing, experimentally generating, and characterizing methods of topological light fields. Wherein, we review recent developments of holographic metasurfaces and their applications in generating ultrasmall optical vortex knots. At last, we envision the possible challenges and prospects of topological light fields.