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).


PDF - Version of Record
Download (590Kb)
Original Publication URL:


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
Digital Object Identifier (DOI): doi:10.1098/rspa.2001.0826
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
Accepted Date and Publication Date:
8 September 2001Published
Date Deposited: 12 May 2006
Last Modified: 31 Mar 2016 11:54

Actions (login required)

View Item View Item

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics