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Properties of Null Knotted Solutions to Maxwell's Equations

Smith, Gregory, Strange, Paul (2017) Properties of Null Knotted Solutions to Maxwell's Equations. In: Andrews, David L. and Galvez, Enrique J. and Glückstad, Jesper, eds. Proceedings of SPIE. Proc. SPIE 10120, Complex Light and Optical Forces XI, 101201C (February 27, 2017). SPIE proceedings , 10120. 101201 1-101201 6. Spie-Int Soc Optical Engineering, San Francisco, USA (doi:10.1117/12.2260484) (KAR id:60761)

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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.

Item Type: Conference or workshop item (Proceeding)
DOI/Identification number: 10.1117/12.2260484
Uncontrolled keywords: Physics of Quantum Materials
Subjects: Q Science > QC Physics
Divisions: Faculties > Sciences > School of Physical Sciences
Depositing User: Paul Strange
Date Deposited: 07 Mar 2017 17:53 UTC
Last Modified: 17 Jul 2019 11:01 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/60761 (The current URI for this page, for reference purposes)
Strange, Paul: https://orcid.org/0000-0001-5818-8032
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