Skip to main content
Article thumbnail
Location of Repository

Knotted and linked phase singularities in monochromatic waves

By M.V. Berry and M.R. Dennis


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

Topics: QA, QC
Year: 2001
OAI identifier:
Provided by: e-Prints Soton

Suggested articles


  1. (1994). The knot book.
  2. (1981). Singularities in waves and rays.
  3. (1994). Evanescent and real waves in quantum billiards and Gaussian beams.
  4. (1998). Wave dislocations in nonparaxial Gaussian beams.
  5. (2001). Knotted zeros in the quantum states of hydrogen.
  6. (2000). Phase singularities in isotropic random waves.
  7. (1987). Exact solutions for nondiffracting beams. I. The scalar theory.
  8. (1987). Diffraction-free beams.
  9. (1997). Creation and annihilation of phase singularities in a focal field.
  10. (1998). Airy pattern reorganization and sub-wavelength structure in a focus.
  11. A (2001)Knotted and linked phase singularities 2263 Kelvin, Lord 1867 On vortex atoms.
  12. 1869 On vortex motion.
  13. (1969). The degree of knottedness of tangled vortex lines.
  14. (1992). Helicity and the Calugareanu invariant.
  15. (1998). Unfolding of higher-order wave dislocations.
  16. (1999). Natural focusing and fine structure of light: caustics and wave dislocations.
  17. (1974). Dislocations in wave trains.
  18. (1988). Phase saddles and dislocations in two-dimensional waves such as the tides.
  19. (1997). Singular optics.
  20. (1999). Optical vortices.
  21. (1987). When time breaks down.
  22. (1984). Singular filaments organize chemical waves in three dimensions.
  23. (1985). Organizing centers in a cellular excitable medium.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.