  In this paper, knotted objects (RS vortices) in the theory of topological
phase singularity in electromagnetic field have been investigated in details.
By using the $\phi$-mapping topological current theory proposed by Prof. Duan,
we rewrite the topological current form of RS vortices and use this topological
current we reveal that the Hopf invariant of RS vortices is just the sum of the
linking and self-linking numbers of the knotted RS vortices. Furthermore, the
conservation of the Hopf invariant in the splitting, the mergence and the
intersection processes of knotted RS vortices is also discussed.
