OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 12 — Dec. 1, 1998
  • pp: 3039–3044

Generalized propagation-invariant wave fields

Rafael Piestun and Joseph Shamir  »View Author Affiliations

JOSA A, Vol. 15, Issue 12, pp. 3039-3044 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (358 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Necessary and sufficient conditions are presented that determine a generalized class of propagation-invariant wave fields. The existence of wave fields with transverse distributions that are periodically reproduced with different azimuthal orientations is demonstrated. These fields are conveniently described in the longitudinal-azimuthal frequency representation. An interesting subclass is characterized by aperiodic rotated self-images, in the sense that they never return to their original orientation along the propagation. Other subclasses include the conventional self-imaging wave fields, the so-called nondiffracting beams, and the rotating wave fields.

© 1998 Optical Society of America

OCIS Codes
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(260.1960) Physical optics : Diffraction theory
(350.7420) Other areas of optics : Waves

Rafael Piestun and Joseph Shamir, "Generalized propagation-invariant wave fields," J. Opt. Soc. Am. A 15, 3039-3044 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. Durnin, “Exact solutions for nondiffracting beams,” J. Opt. Soc. Am. A 4, 651–654 (1987). [CrossRef]
  2. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150–152 (1989). [CrossRef]
  3. A. B. Valyaev, S. G. Krivoshlykov, “Mode properties of Bessel beams,” Sov. J. Quantum Electron. 19, 679–680 (1989). [CrossRef]
  4. P. Szwaykowski, J. Ojeda-Castañeda, “Nondiffracting beams and the self-imaging phenomenon,” Opt. Commun. 83, 1–4 (1991). [CrossRef]
  5. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]
  6. E. Abramochkin, V. Volostnikov, “Spiral-type beams,” Opt. Commun. 102, 336–350 (1993). [CrossRef]
  7. Y. Y. Schechner, R. Piestun, J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996). [CrossRef]
  8. S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: travelling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996). [CrossRef]
  9. C. Paterson, R. Smith, “Helicon waves: propagation-invariant waves in a rotating coordinate system,” Opt. Commun. 124, 131–140 (1996). [CrossRef]
  10. V. V. Kotlyar, V. A. Soifer, S. N. Khonina, “An algorithm for the generation of laser beams with longitudinal periodicity: rotating images,” J. Mod. Opt. 44, 1409–1416 (1997). [CrossRef]
  11. G. Indebetouw, “Polychromatic self-imaging,” J. Mod. Opt. 35, 243–252 (1988). [CrossRef]
  12. J. Turunen, A. Vasara, A. T. Friberg, “Propagation invariance and self-imaging in variable-coherence optics,” J. Opt. Soc. Am. 8, 282–289 (1991). [CrossRef]
  13. Z. Bouchal, R. Horak, J. Wagner, “Propagation-invariant electromagnetic fields: theory and experiment,” J. Mod. Opt. 43, 1905–1920 (1996). [CrossRef]
  14. R. Piestun, Y. Y. Schechner, J. Shamir, “Self-imaging with finite energy,” Opt. Lett. 22, 200–202 (1997). [CrossRef] [PubMed]
  15. R. Piestun, Y. Y. Schechner, J. Shamir, “Generalized self-imaging in free space,” Diffractive Optics ’97, Vol. 12 of European Optical Society Topical Meetings Digest Series (European Optical Society, Orsay, France, 1997), pp. 128–129.
  16. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967). [CrossRef]
  17. W. D. Montgomery, “Algebraic formulation of diffraction applied to self-imaging,” J. Opt. Soc. Am. 58, 1112–1124 (1968). [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  19. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  20. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974). [CrossRef]
  21. G. Indebetouw, “Quasi-self-imaging using aperiodic sequences,” J. Opt. Soc. Am. A 9, 549–558 (1992). [CrossRef]

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