Knotted and linked phase singularities in monochromatic waves


Berry, M.V. and Dennis, M.R. (2001) Knotted and linked phase singularities in monochromatic waves. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 457, (2013), 2251-2263. (doi:10.1098/rspa.2001.0826).

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Original Publication URL: http://dx.doi.org/10.1098/rspa.2001.0826

Description/Abstract

Exact solutions of the Helmholtz equation are constructed, possessing wavefront dislocation lines (phase singularities) in the form of knots or links where the wave function vanishes ('knotted nothings'). The construction proceeds by making a nongeneric structure with a strength n dislocation loop threaded by a strength m dislocation line, and then perturbing this. In the resulting unfolded (stable) structure, the dislocation loop becomes an (m, n) torus knot if m and n are coprime, and N linked rings or knots if m and n have a common factor N; the loop or rings are threaded by an m-stranded helix. In our explicit implementation, the wave is a superposition of Bessel beams, accessible to experiment. Paraxially, the construction fails.

Item Type: Article
ISSNs: 1364-5021 (print)
Related URLs:
Keywords: phase singularities, dislocations, knots, links, paraxiality
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 29378
Date Deposited: 12 May 2006
Last Modified: 27 Mar 2014 18:17
URI: http://eprints.soton.ac.uk/id/eprint/29378

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