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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1132–1138

Unfolding of higher-order wave dislocations

J. F. Nye  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1132-1138 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001132


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Abstract

Wave dislocation reactions, for example, one dislocation splitting into three, are organized by dislocations of higher order. A reaction can be regarded as an unfolding of a higher-order dislocation, rather as singularities in catastrophe theory unfold into clusters of lower-order ones. The paper lists the forms of the first few higher-order wave dislocations. It shows how the reaction reported by Karman [Opt. Lett. 22, 1503 (1997)], in which an Airy dark ring surrounding a focus splits into three, followed by the annihilation of an inner fourth ring by the central ring, is part of the unfolding of a fourth-order dislocation.

© 1998 Optical Society of America

OCIS Codes
(080.3630) Geometric optics : Lenses
(220.2560) Optical design and fabrication : Propagating methods
(350.7420) Other areas of optics : Waves

History
Original Manuscript: September 3, 1997
Revised Manuscript: December 15, 1997
Manuscript Accepted: December 23, 1997
Published: May 1, 1998

Citation
J. F. Nye, "Unfolding of higher-order wave dislocations," J. Opt. Soc. Am. A 15, 1132-1138 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1132


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References

  1. G. P. Karman, M. W. Beijersbergen, A. van Duijl, J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997). [CrossRef]
  2. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974). [CrossRef]
  3. J. F. Nye, “The motion and structure of dislocations in wavefronts,” Proc. R. Soc. London, Ser. A 378, 219–239 (1981). [CrossRef]
  4. J. F. Nye, “Polarization effects in the diffraction of electromagnetic waves: the role of disclinations,” Proc. R. Soc. London, Ser. A 387, 105–132 (1983), Sec. 3. [CrossRef]
  5. R. Thom, Structural Stability and Morphogenesis: An Outline of a General Theory of Models (Benjamin, Reading, Mass., 1975).
  6. V. I. Arnold, “Critical points of smooth functions and their normal forms,” Russian Math. Surveys 30, 1–75 (translated from Uspekhi Math. Nauk 30, 3–65 (1975).
  7. J. F. Nye, J. V. Hajnal, J. H. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. London, Ser. A 417, 7–20 (1988). [CrossRef]
  8. M. V. Berry, “Wave dislocation reactions in nonparaxial Gaussian beams,” J. Mod. Opt. (to be published).
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), Fig. 8.46.
  10. J. F. Nye, “Diffraction by a small unstopped lens,” J. Mod. Opt. 38, 743–754 (1991), Sec. 5. [CrossRef]

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