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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 2, Iss. 5 — Mar. 2, 1998
  • pp: 169–172

Fractional Talbot effect in phase space: A compact summation formula

Konrad Banaszek, Krzysztof Wódkiewicz, and Wolfgang P. Schleich  »View Author Affiliations

Optics Express, Vol. 2, Issue 5, pp. 169-172 (1998)

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A phase space description of the fractional Talbot effect, occurring in a one–dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at rational multiples of the Talbot distance is derived. The summation formula shows that the fractional Talbot image in the phase space is generated by a finite sum of spatially displaced Wigner functions of the source field.

© Optical Society of America

OCIS Codes
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Research Papers

Original Manuscript: November 14, 1997
Revised Manuscript: November 6, 1997
Published: March 2, 1998

Konrad Banaszek, Krzysztof Wodkiewicz, and Wolfgang Peter Schleich, "Fractional Talbot effect in phase space: A compact summation formula," Opt. Express 2, 169-172 (1998)

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  1. J. T. Winthrop and C. R. Worthington, "Theory of Fresnel images. I. Plane periodic objects in monochromatic light," J. Opt. Soc. Am. 55, 373-381 (1965).<br> [CrossRef]
  2. M. J. Bastiaans, "The Wigner distribution function applied to optical signals and systems," Opt. Commun. 25, 26-30 (1978).<br> [CrossRef]
  3. I. Sh. Averbukh and N. F. Perelman, "Fractional revivals: universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics," Phys. Lett. A139, 449-453 (1989).<br>
  4. J. P. Guigay, "On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects," Opt. Acta 18, 677-682 (1971).<br> [CrossRef]
  5. M. V. Berry and S. Klein, "Integer, fractional and fractal Talbot effects," J. Mod. Opt. 43, 2139-2164 (1996).<br> [CrossRef]
  6. J. Parker and C. R. Stroud, Jr., "Coherence and decay of Rydberg wave-packets," Phys. Rev. Lett. 56, 716-719 (1986).<br> [CrossRef] [PubMed]
  7. B. Yurke and D. Stoler, "Generating quantum-mechanical superpositions of macroscopically distinguishable states via amplitude dispersion," Phys. Rev. Lett. 57, 13-16 (1986).<br> [CrossRef] [PubMed]
  8. A. Mecozzi and P. Tombesi, "Distinguishable quantum states generated via nonlinear birefrigerence," Phys. Rev. Lett. 58, 1055-1058 (1987).<br> [CrossRef] [PubMed]
  9. K. Tara, G. S. Agarwal, and S. Chaturvedi, "Production of Schr"odinger macroscopic quantum-superposition states in a Kerr medium," Phys. Rev. A 47, 5024-5029 (1993).<br> [CrossRef] [PubMed]
  10. D. L. Aronstein and C. R. Stroud, "Fractional wave-function revivals in the infinite square well," Phys. Rev. A 55, 4526-4537 (1997).<br> [CrossRef]
  11. M. Born and W. Ludwig, "Zur Quantenmechanik des kr"aftefreien Teilchens," Z. Phys. 150, 106-117 (1958).<br> [CrossRef]
  12. P. Stifter, C. Leichte, W. P. Schleich, and J. Marklof, "Das Teilchen im Kasten: Strukturen in der Wahrscheinlichkeitsdichte," Z. Naturforsch. 52a, 377-385 (1997).

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