OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 1 — Jan. 1, 2008
  • pp: 171–181

Symmetric array of off-axis singular beams: spiral beams and their critical points

Yana Izdebskaya, Vladlen Shvedov, and Alexander Volyar  »View Author Affiliations

JOSA A, Vol. 25, Issue 1, pp. 171-181 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (597 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We consider conditions of structural stability under which the array of singular beams preserves its topological structure and intensity distribution while slightly perturbing its intrinsic parameters. The orbital angular momentum of the array as a function of the array parameters is a characteristic function, and its extreme points correspond to stable and unstable array states.

© 2008 Optical Society of America

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(260.3160) Physical optics : Interference
(350.5030) Other areas of optics : Phase

ToC Category:
Lasers and Laser Optics

Original Manuscript: July 23, 2007
Revised Manuscript: October 24, 2007
Manuscript Accepted: October 25, 2007
Published: December 19, 2007

Yana Izdebskaya, Vladlen Shvedov, and Alexander Volyar, "Symmetric array of off-axis singular beams: spiral beams and their critical points," J. Opt. Soc. Am. A 25, 171-181 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. S. Soskin and M. V. Vasnetsov, "Singular optics," in Progress in Optics, E.Wolf, ed. (Elsevier North-Holland, 2001), Vol. 42, pp. 219-276. [CrossRef]
  2. V. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228 of Horizons of World Physics (Nova Science, 1999).
  3. V. Garces-Chavez, D. McGloin, M. D. Summers, A. Fernandez-Nieves, G. C. Spalding, G. Cristobal, and K. Dholakia, "The reconstruction of optical angular momentum after distortion in amplitude, phase and polarization," J. Opt. A, Pure Appl. Opt. 6, S235-S238 (2004). [CrossRef]
  4. J. Lin, X.-C. Yuan, X. Peng, and H. B. Niu, "Deterministic approach to the generation of modified helical beams for optical manipulations," Opt. Express 13, 3862-3867 (2005). [CrossRef] [PubMed]
  5. A. Vaziri, G. Weihs, and A. Zelinger, "Superpositions of the orbital angular momentum for applications in quantum experiments," J. Opt. A, Pure Appl. Opt. 4, S47-S51 (2002).
  6. L. Allen, S. M. Barnet, and M. J. Padgett, Optical Angular Momentum (IOP, 2003). [CrossRef]
  7. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solutions," in Progress in Optics, E.Wolf, ed. (Elsevier North-Holland, 2005), Vol. 47, pp. 1-45. [CrossRef]
  8. C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dändliker, "High-resolution experiment of phase singularities produced by computer-generated holograms," Opt. Commun. 242, 163-169 (2004). [CrossRef]
  9. L. E. Helseth, "Optical vortices in focal region," Opt. Commun. 229, 85-91 (2004). [CrossRef]
  10. M. V. Berry, "Optical vortices evolving from helicoidal integer and fractional phase steps," J. Opt. A, Pure Appl. Opt. 6, 259-268 (2004). [CrossRef]
  11. A. E. Siegman, Lasers (University Science, 1986).
  12. F. Gori, G. Gauttari, and C. Padovani, "Bessel-Gaussian beams," Opt. Commun. 64, 491-495 (1987). [CrossRef]
  13. A. P. Kiselev, "The localized light waves: paraxial and exact solution to the wave equation," Opt. Spectrosc. 102, 697-717 (2007). [CrossRef]
  14. J. C. Gutierrez-Vega and M. A. Bandress, "Helmholtz-Gauss waves," J. Opt. Soc. Am. A 22, 289-298 (2005). [CrossRef]
  15. M. Guizar-Sicairos and J. C. Gutierrez-Vega, "Generalized Helmholtz-Gauss beams and its transformation by paraxial optical system," Opt. Lett. 31, 2912-2914 (2006). [CrossRef] [PubMed]
  16. C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, "Helico-conical optical beams: a product of helical and conical phase fronts," Opt. Express 13, 1749-1760 (2005). [CrossRef] [PubMed]
  17. E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A, Pure Appl. Opt. 6, S157-S161 (2004). [CrossRef]
  18. V. V. Kotlyar, R. V. Skidanov, S. N. Khonina, and V. A. Soifer, "Hypergeometric modes," Opt. Lett. 32, 742-744 (2007). [CrossRef] [PubMed]
  19. I. Freund, "Critical point explosions in two-dimensional wave fields," Opt. Commun. 159, 99-117 (1999). [CrossRef]
  20. I. Freund, "Saddle point wave fields," Opt. Commun. 163, 230-242 (1999). [CrossRef]
  21. J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, "Angular momentum of optical vortex array," Opt. Express 14, 938-949 (2006). [CrossRef] [PubMed]
  22. B. Lü and H. Ma, "Beam combination of radial laser array: Hermite-Gaussian model," Opt. Commun. 178, 395-403 (2000). [CrossRef]
  23. I. D. Maleev and G. A. Swartzlander, "Composite optical vortices," J. Opt. Soc. Am. B 20, 1169-1176 (2003). [CrossRef]
  24. Z. Bouchal, "Controlled spatial shaping of nondiffracting patterns and arrays," Opt. Lett. 27, 1376-1378 (2002). [CrossRef]
  25. Ya. Cai and O. Lin, "Decentered elliptical Gaussian beams," Appl. Opt. 41, 4336-4340 (2002). [CrossRef] [PubMed]
  26. C.-S. Cuo, Y. Zhang, Y.-J. Han, J.-P. Ding, and H.-T. Wang, "Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering," Opt. Commun. 259, 449-454 (2006). [CrossRef]
  27. Z. Bouchal and J. Courtial, "The connection of singular and nondiffractive optics," J. Opt. A, Pure Appl. Opt. 6, S184-S188 (2004). [CrossRef]
  28. S. Vyas and P. Senthsilkumaran, "Interferometric vortex array generator," Appl. Opt. 46, 2893-2898 (2007). [CrossRef] [PubMed]
  29. E. G. Abramochkin and V. G. Volostnikov, "Spiral light beams," Phys. Usp. 174, 1273-1300 (2004), http://www.ufn.ru/ufn04/ufn04̱12/ufn0412a.pdf.
  30. E. G. Abramochkin and V. G. Volostnikov, "Spiral-type beams: optical and quantum aspects," Opt. Commun. 125, 302-323 (1996). [CrossRef]
  31. E. G. Abramochkin and V. G. Volostnikov, "Spiral-type beams," Opt. Commun. 102, 336-350 (1993). [CrossRef]
  32. T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Pitman, 1978).
  33. M. V. Berry, "Catastrophe optics: morphologies of caustics and their diffraction patterns," in Progress in Optics XVIII, E.Wolf, ed. (Elsevier North-Holland, 1980), pp. 257-346. [CrossRef]
  34. I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. Lett. 50, 5164-5172 (1994).
  35. Ya. Izdebskaya, V. Shvedov, and A. Volyar, "Generation of higher-order optical vortices by a dielectric wedge," Opt. Lett. 30, 2472-2474 (2005). [CrossRef] [PubMed]
  36. X.-C. Yuan, B. P. S. Ahluwalia, S. H. Tao, W. C. Cheong, L.-S. Zhang, J. Lin, J. Bu, and R. E. Burge, "Wavelength-scalable micro-fabricated wedge for generation of optical vortex beam in optical manipulation," Appl. Phys. B: Lasers Opt. 86, 209-213 (2007). [CrossRef]
  37. M. Abramowitz and I. StegunHandbook of Mathematical Functions (Dover, 1970).
  38. A. Volyar, V. Shvedov, Ya. Izdebskaya, T. Fadeyeva, and A. Rubass, "Structure and orbital angular momentum of singular array of Gaussian beams," Ukr. J. Phys. Opt. 3, 79-88 (2006), www.ifo.lviv.ua.
  39. K. O'Holleran, M. J. Padgett, and M. R. Dennis, "Topology of optical vortex lines formed by the interference of three, four and five plane waves," Opt. Express 14, 3039-3044 (2006). [CrossRef] [PubMed]
  40. Ya. Izdebskaya, T. Fadeyeva, V. Shvedov, and A. Volyar, "Vortex-bearing array of singular beams with very high orbital angular momentum," Opt. Lett. 31, 2523-2525 (2006). [CrossRef] [PubMed]
  41. M. Berry, "Paraxial beams of spinning light," Proc. SPIE 3487, 6-11 (1998).
  42. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Volume 2: Special Functions (Gordon and Breach, 1986).

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