期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 457, 期 2013, 页码 2251-2263出版社
ROYAL SOC
DOI: 10.1098/rspa.2001.0826
关键词
phase; singularities; dislocations; knots; links; paraxiality
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 (in, it) torus knot if in and n are coprime, and N linked rings or knots if rn 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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