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Knotted and linked phase singularities in monochromatic waves

Knotted and linked phase singularities in monochromatic waves
Knotted and linked phase singularities in monochromatic waves
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.
phase singularities, dislocations, knots, links, paraxiality
1364-5021
2251-2263
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61

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

Record type: Article

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.

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Published date: 8 September 2001
Keywords: phase singularities, dislocations, knots, links, paraxiality

Identifiers

Local EPrints ID: 29378
URI: http://eprints.soton.ac.uk/id/eprint/29378
ISSN: 1364-5021
PURE UUID: 6de39b72-8f3e-444d-9e06-f9d726ec2687

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Date deposited: 12 May 2006
Last modified: 15 Mar 2024 07:31

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Contributors

Author: M.V. Berry
Author: M.R. Dennis

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