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Proceedings Paper

Properties of null knotted solutions to Maxwell's equations
Author(s): Gregory Smith; Paul Strange
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Paper Abstract

We discuss null knotted solutions to Maxwell's equations, their creation through Bateman's construction, and their relation to the Hopf-fibration. These solutions have well-known, conserved properties, related to their winding numbers. For example: energy; momentum; angular momentum; and helicity. The current research has focused on Lipkin's zilches, a set of little-known, conserved quantities within electromagnetic theory that has been explored mathematically, but over which there is still considerable debate regarding physical interpretation. The aim of this work is to contribute to the discussion of these knotted solutions of Maxwell's equations by examining the relation between the knots, the zilches, and their symmetries through Noether's theorem. We show that the zilches demonstrate either linear or more complicated relations to the p-q winding numbers of torus knots, and can be written in terms of the total energy of the electromagnetic field. As part of this work, a systematic multipole expansion of the vector potential of the knotted solutions is being carried out.

Paper Details

Date Published: 27 February 2017
PDF: 6 pages
Proc. SPIE 10120, Complex Light and Optical Forces XI, 101201C (27 February 2017); doi: 10.1117/12.2260484
Show Author Affiliations
Gregory Smith, Univ. of Kent (United Kingdom)
Paul Strange, Univ. of Kent (United Kingdom)

Published in SPIE Proceedings Vol. 10120:
Complex Light and Optical Forces XI
David L. Andrews; Enrique J. Galvez; Jesper Glückstad, Editor(s)

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