Topology of Knotted Optical Vortices

TL;DR

This paper explores the topological properties of knotted optical vortices using $$-mapping theory, revealing their internal structure and linking behavior, which enhances understanding of their complex topological nature.

Contribution

It introduces a novel application of $$-mapping topological current theory to analyze the topology and linking of closed, knotted optical vortices.

Findings

Topological inner structure of optical vortices is characterized.

Linking properties of knotted optical vortices are described.

Theoretical framework for understanding optical vortex topology is developed.

Abstract

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the $\phi$-mapping topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.