Optical toroidal vortices under topological perspective

Toroidal vortices are propagating ring-shaped structures that exist widely in fluids and gases that are closely related to the knot theory in topology. In recent years, with the development of modern beam shaping techniques, spatiotemporal light field with entangled spatial and temporal dimensions provides a unique platform for the study of optical topological structures. In this article, a series of recent studies on optical toroidal vortices are reviewed, and the physical mechanisms of generating the optical toroidal vortices are introduced. Optical phase topologies further extended from optical toroidal vortices, including scalar optical hopfions and optical phase Möbius strips, are discussed in details from the perspectives of topology and structured light respectively.