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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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.
|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
|Date Deposited:||12 May 2006|
|Last Modified:||28 Jun 2012 10:14|
|Contributors:||Berry, M.V. (Author)
Dennis, M.R. (Author)
|Date:||8 September 2001|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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