Knotted Topological Phase Singularities of Electromagnetic Field

Details Knotted Topological Phase Singularities of Electromagnetic Field Knotted Topological Phase Singularities of Electromagnetic Field

2007-12-27

arxiv.org/abs/0712.4198v2

Commun.Theor.Phys.Vol.50 (2008)1071-1076

Physics

Optics

6 pages, no figures, author's name have been corrected

Scientific paper

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.

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