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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. 18, Iss. 9 — Sep. 1, 2001
  • pp: 2089–2094

Description of phase singularities and their application to focusing design

Gabriel Martínez-Niconoff, Javier Muñoz-Lopez, and Edgar Méndez-Martínez  »View Author Affiliations


JOSA A, Vol. 18, Issue 9, pp. 2089-2094 (2001)
http://dx.doi.org/10.1364/JOSAA.18.002089


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Abstract

We describe the focusing region associated with transmittances, analyzing its associated phase function. We show that generic features can be studied from the differential equation for focusing geometry, which is obtained through angular representation for diffraction fields. With the treatment, we recover the results for circular zone plates, and by introducing a linear transformation into the transmittance function we generate structures that keep the ability to generate focusing. According to the choice of the parameters involved, the diffraction field presents new focusing regions, whose three-dimensional geometry and spatial evolution can be described in a selective fashion with analysis of only the phase singularities associated with the diffraction field and avoidance of the integral representation. The treatment is also applied to a simple lens. We recover the theoretical predictions obtained by Berry and Upstill [M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North–Holland, Amsterdam, 1980), Vol. XVIII, p. 259], and these predictions are corroborated experimentally. The results obtained are shown.

© 2001 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(080.1510) Geometric optics : Propagation methods

Citation
Gabriel Martínez-Niconoff, Javier Muñoz-Lopez, and Edgar Méndez-Martínez, "Description of phase singularities and their application to focusing design," J. Opt. Soc. Am. A 18, 2089-2094 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-9-2089


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References

  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), p. 109.
  2. R. Courant and D. Hillbert, Methods of Mathematical Physics (Interscience, Berlin, 1989), Vol. II, p. 10.
  3. M. V. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” in Progress in Optics, E. Wolf, ed. (North–Holland, Amsterdam, 1980), Vol. XVIII, p. 259.
  4. I. Freund and A. Belenkiy, “Higher-order extrema in two-dimensional wave fields,” J. Opt. Soc. Am. A 17, 434–445 (2000).
  5. N. M. Ceglio and D. W. Sweeney, “Zone plate-coded imaging: theory and applications,” in Progress in Optics XXII, E. Wolf, ed. (North–Holland, Amsterdam, 1982), Chap. IV, pp. 289–353.
  6. A. W. Lohman, Optical Information Processing (University of Erlangen–Nurnberg, Erlangen, Germany, 1978), p. 113.
  7. M. Born, and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), p. 237.

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