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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. 16, Iss. 8 — Aug. 1, 1999
  • pp: 1970–1973

Interference between two diffraction fields with a common caustic region

Gabriel Martı́nez-Niconoff, Javier Muñoz-Lopez, and Alejandro Cornejo-Rodriguez  »View Author Affiliations


JOSA A, Vol. 16, Issue 8, pp. 1970-1973 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001970


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Abstract

We describe the interference between two caustics of diffraction fields that are generated in a double-curve-shaped-slit interferometer. One of the slits is obtained from the other through a projective mapping in the normal direction. In this way the diffraction fields present the same caustic region because the slit functions have a common evolute. Catastrophe functions are used for describing the optical path length of the rays involved. We show that the phase difference between the diffracted rays can also be considered a catastrophe function, which permits us to describe the geometry of the interference pattern because its singular points correspond to organized regions of the interference pattern. Experimental results are shown.

© 1999 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(080.1510) Geometric optics : Propagation methods
(260.3160) Physical optics : Interference

History
Original Manuscript: November 2, 1998
Revised Manuscript: January 19, 1999
Manuscript Accepted: January 19, 1999
Published: August 1, 1999

Citation
Gabriel Martı́nez-Niconoff, Javier Muñoz-Lopez, and Alejandro Cornejo-Rodriguez, "Interference between two diffraction fields with a common caustic region," J. Opt. Soc. Am. A 16, 1970-1973 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-8-1970


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References

  1. A. V. Gaponov-Grekhov, M. I. Rabinovich, Nonlinearities in Action (Springer-Verlag, Berlin, 1991), p. 25.
  2. B. J. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 16 (1962). [CrossRef]
  3. Y. A. Kratsov, Y. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, Berlin, 1990), pp. 29–40.
  4. G. Martı́nez-Niconoff, “Interference between caustics of diffraction fields,” Opt. Lett. 23, 750–752 (1998). [CrossRef]
  5. G. Martı́nez-Niconoff, J. Carranza-Gallardo, A. Cornejo-Rodriguez, “Caustics of diffraction fields,” Opt. Commun. 114, 194–198 (1995). [CrossRef]
  6. V. I. Arnold, Singularities of Caustics and Wave Fronts (Kluwer Academic, Dordrecht, The Netherlands, 1990) p. 17.
  7. M. V. Berry, 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.
  8. N. Piskunov, Calculo Diferencial e Integral (Mir, Moscow, 1977), p. 216.
  9. R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley, New York, 1981), p. 319.

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