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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 8 — Aug. 1, 2002
  • pp: 1694–1700

Singular behavior of the spectrum in the neighborhood of focus

Greg Gbur, Taco D. Visser, and Emil Wolf  »View Author Affiliations

JOSA A, Vol. 19, Issue 8, pp. 1694-1700 (2002)

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In a recent paper [Phys. Rev. Lett. 88, 013901 (2002)] it was shown that when a convergent spatially coherent polychromatic wave is diffracted at an aperture, remarkable spectral changes take place on axis in the neighborhood of certain points near the geometrical focus. In particular, it was shown that the spectrum is redshifted at some points, blueshifted at others, and split into two lines elsewhere. In the present paper we extend the analysis and show that similar changes take place in the focal plane, in the neighborhood of the dark rings of the Airy pattern.

© 2002 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(260.1960) Physical optics : Diffraction theory
(300.6170) Spectroscopy : Spectra

Original Manuscript: January 18, 2002
Manuscript Accepted: March 12, 2002
Published: August 1, 2002

Greg Gbur, Taco D. Visser, and Emil Wolf, "Singular behavior of the spectrum in the neighborhood of focus," J. Opt. Soc. Am. A 19, 1694-1700 (2002)

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  1. A pioneering paper on this subject is due to J. F. Nye, M. V. Berry, “Dislocation in wavetrains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974). [CrossRef]
  2. For a review of singular optics see, for example, M. S. Soskin, M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, pp. 219–276.
  3. M. V. Berry, A. N. Wilson, “Black-and-white fringes and the colors of caustics,” Appl. Opt. 33, 4714–4718 (1994). [CrossRef] [PubMed]
  4. M. V. Berry, S. Klein, “Colored diffraction catastrophes,” Proc. Natl. Acad. Sci. U.S.A. 93, 2614–2619 (1996). [CrossRef] [PubMed]
  5. G. Gbur, T. D. Visser, E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002). [CrossRef] [PubMed]
  6. G. Popescu, A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002). [CrossRef] [PubMed]
  7. M. Born, E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999).
  8. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  9. V. A. Pas’ko, M. S. Soskin, M. V. Vasnetsov, “Transversal optical vortex,” Opt. Commun. 198, 49–56 (2001). [CrossRef]
  10. The term “intensity” is used in optics with several different meanings. In this paper we mean by it the frequency-integrated spectrum, as indicated in Eq. (27).

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