OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 12 — Dec. 1, 2000
  • pp: 2481–2485

Phase-space interferences as the source of negative values of the Wigner distribution function

Daniela Dragoman  »View Author Affiliations


JOSA A, Vol. 17, Issue 12, pp. 2481-2485 (2000)
http://dx.doi.org/10.1364/JOSAA.17.002481


View Full Text Article

Acrobat PDF (175 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

It is shown that the negative values of the Wigner distribution function in classical optics are a consequence of the phase-space interference among the Gaussian beams into which an arbitrary light distribution (or a superposition of light distributions) can be decomposed. These elementary Gaussian beams partition the phase space in wave optics in adjacent, interacting, finite-area cells, in contrast to geometrical optics, where the phase space is continuous and a light beam can be decomposed into a number of perfectly localized, non-interacting rays.

© 2000 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.4560) Fourier optics and signal processing : Data processing by optical means
(100.0100) Image processing : Image processing
(100.2960) Image processing : Image analysis

Citation
Daniela Dragoman, "Phase-space interferences as the source of negative values of the Wigner distribution function," J. Opt. Soc. Am. A 17, 2481-2485 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-12-2481


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).
  2. V. Buzek and P. L. Knight, “Quantum interference, superposition states of light, and nonclassical effects,” in Progress in Optics, XXXIV, E. Wolf, ed. (Elsevier, Amsterdam, 1995), pp. 1–158.
  3. D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” in Progress in Optics, XXXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1997), pp. 1–56.
  4. K. B. Wolf and A. L. Rivera, “Holographic information in the Wigner function,” Opt. Commun. 144, 36–42 (1997).
  5. H. Konno and P. S. Lomdahl, “The Wigner transform of solitons solutions for the nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 63, 3967–3973 (1994).
  6. L. Cohen, “Time-frequency distributions—a review,” Proc. IEEE 77, 941–981 (1989).
  7. D. Dragoman, “Wigner-distribution-function representation of the coupling coefficient,” Appl. Opt. 34, 6758–6763 (1995).
  8. D. Dragoman, “Phase space representation of modes in optical waveguides,” J. Mod. Opt. 42, 1815–1823 (1995).
  9. D. Gabor, “Theory of communication,” J. Inst. Electr. Eng. 93 (III), 429–457 (1946).
  10. M. J. Bastiaans, “The expansion of an optical signal into a discrete set of Gaussian beams,” Optik (Stuttgart) 57, 95–102 (1980).
  11. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  12. P. Flandrin, Temps-Fréquence (Hermès, Paris, 1993).
  13. R. L. Hudson, “When is the Wigner quasi-probability density non negative?” Rep. Math. Phys. 6, 249–252 (1974).
  14. A. J. E. M. Janssen, “A note on Hudson’s theorem about functions with non-negative Wigner distributions,” SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 15, 170–176 (1984).
  15. M. J. Bastiaans, “Gabor’s signal expansion applied to partially coherent light,” Opt. Commun. 86, 14–18 (1991).
  16. S. Qian and D. Chen, “Decomposition of the Wigner–Ville distribution and time-frequency distribution series,” IEEE Trans. Signal Process. 42, 2836–2842 (1994).
  17. F. Pedersen, “The Gabor expansion based positive distribution,” Proc. IEEE 3, 1565–1568 (1998).
  18. M. J. Bastiaans, “The Wigner distribution function of partially coherent light,” Opt. Acta 28, 1215–1224 (1981).
  19. M. J. Bastiaans, “Uncertainty principle for partially coherent light,” J. Opt. Soc. Am. 73, 251–255 (1983).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited