Abstract

The caustics of diffraction fields are structures that present a nonlinear phase distribution. The superposition of two caustics presents interesting irradiance distributions, which we analyze within the framework of catastrophe theory. This treatment permits the inclusion of the optical path difference involved in a parametric family, and by employing the geometric theory of diffraction we can analyze the interference patterns in a selective fashion. The theoretical predictions are verified experimentally with a Michelson interferometer.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. XVIII, p. 259.
  2. A. V. Gaponov-Grekhov and M. I. Rabinovich, Nonlinearities in Action (Springer-Verlag, Berlin, 1991).
  3. G. Martinez-Niconoff, J. Carranza-Gallardo, and A. Cornejo-Rodriguez, Opt. Commun. 114, 194 (1995).
    [CrossRef]
  4. R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley Interscience, New York, 1981).
  5. B. J. Keller, J. Opt. Soc. Am. 52, 116 (1962).
    [CrossRef] [PubMed]

1995 (1)

G. Martinez-Niconoff, J. Carranza-Gallardo, and A. Cornejo-Rodriguez, Opt. Commun. 114, 194 (1995).
[CrossRef]

1962 (1)

Berry, M. V.

M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. XVIII, p. 259.

Carranza-Gallardo, J.

G. Martinez-Niconoff, J. Carranza-Gallardo, and A. Cornejo-Rodriguez, Opt. Commun. 114, 194 (1995).
[CrossRef]

Cornejo-Rodriguez, A.

G. Martinez-Niconoff, J. Carranza-Gallardo, and A. Cornejo-Rodriguez, Opt. Commun. 114, 194 (1995).
[CrossRef]

Gaponov-Grekhov, A. V.

A. V. Gaponov-Grekhov and M. I. Rabinovich, Nonlinearities in Action (Springer-Verlag, Berlin, 1991).

Gilmore, R.

R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley Interscience, New York, 1981).

Keller, B. J.

Martinez-Niconoff, G.

G. Martinez-Niconoff, J. Carranza-Gallardo, and A. Cornejo-Rodriguez, Opt. Commun. 114, 194 (1995).
[CrossRef]

Rabinovich, M. I.

A. V. Gaponov-Grekhov and M. I. Rabinovich, Nonlinearities in Action (Springer-Verlag, Berlin, 1991).

Upstill, C.

M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. XVIII, p. 259.

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

G. Martinez-Niconoff, J. Carranza-Gallardo, and A. Cornejo-Rodriguez, Opt. Commun. 114, 194 (1995).
[CrossRef]

Other (3)

R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley Interscience, New York, 1981).

M. V. Berry and C. Upstill, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), Vol. XVIII, p. 259.

A. V. Gaponov-Grekhov and M. I. Rabinovich, Nonlinearities in Action (Springer-Verlag, Berlin, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Selected diffractive rays on the nk plane. (b) Geometric description of the caustic or the separatrix region projected upon the transmittance plane.

Fig. 2
Fig. 2

(a) Schematic diagram of the experimental setup for generating interference between caustics of diffraction fields. (b) Geometric description of the geometry of the interference fringes.

Fig. 3
Fig. 3

Experimental results for the interference: (a) Caustic of the diffraction field for an elliptical curve. (b) Superposition of two coincident caustics of diffraction fields. (c)–(f) Interference between the caustics of diffraction for differents angle tilts.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ϕx, a=A exp ikcatastrophe function=A exp ikcatastrophe germx+pertx, a,
ϕx, y=i=1, 2Ai exp ikcatastrophe germx, y+pertx, y, ai, bi,
I=I1+I2+2 Re[A1A2* exp(ikδ],
ϕx, a, b=A exp ikx44+a1x2+b1x+A exp ikx44+a2x2+b2x,
Ix, a=2I1+Re exp ikx2a1-a2+xb1-b2,
δ=x2Δa+xΔb.

Metrics