Knotted Topological Phase Singularities of Electromagnetic Field

In this paper, knotted objects (RS vortices) in the theory oftopological phase singularity in electromagnetic field have beeninvestigated in details. By using the Duan's topological current theory,we rewrite the topological current form of RS vortices and use this topologicalcurrent we reveal that the Hopf invariant of RS vortices is just thesum of the linking and self-linking numbers of the knotted RSvortices. Furthermore, the conservation of the Hopf invariant in thesplitting, the mergence and the intersection processes of knotted RSvortices is also discussed.