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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. <b>88</b>, 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

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 and M. V. Berry, “Dislocation in wavetrains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
  2. For a review of singular optics see, for example, M. S. Soskin and M. V. Vasnetsov, “Singular optics,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, pp. 219–276.
  3. M. V. Berry and A. N. Wilson, “Black-and-white fringes and the colors of caustics,” Appl. Opt. 33, 4714–4718 (1994).
  4. M. V. Berry and S. Klein, “Colored diffraction catastrophes,” Proc. Natl. Acad. Sci. U.S.A. 93, 2614–2619 (1996).
  5. G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88, 013901 (2002).
  6. G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88, 183902 (2002).
  7. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999).
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  9. V. A. Pas’ko, M. S. Soskin, and M. V. Vasnetsov, “Transversal optical vortex,” Opt. Commun. 198, 49–56 (2001).
  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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