OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 26 — Dec. 24, 2007
  • pp: 18326–18338

Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons

Servando Lopez-Aguayo and Julio C. Guti érrez-Vega  »View Author Affiliations

Optics Express, Vol. 15, Issue 26, pp. 18326-18338 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (670 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We introduce a new class of elliptically modulated self-trapped singular beams in isotropic nonlinear media where nonlocality plays a crucial role in their existence. The analytical expressions in the highly nonlocal nonlinear limit of these elliptically shaped self-trapped beams, or ellipticons, is obtained and their existence in more general nonlocal nonlinear media is demonstrated. We show that the ellipticons represent a generalization of several known self-trapped beams, for example vortex solitons, azimuthons, and the Hermite and Laguerre solitons clusters. For the limit of the highly nonlocal nonlinear medium, the ellipticons are described in close form in terms of the InceGauss functions.

© 2007 Optical Society of America

OCIS Codes
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(190.5940) Nonlinear optics : Self-action effects
(350.5030) Other areas of optics : Phase

ToC Category:
Nonlinear Optics

Original Manuscript: November 2, 2007
Revised Manuscript: December 14, 2007
Manuscript Accepted: December 16, 2007
Published: December 20, 2007

Servando Lopez-Aguayo and Julio C. Gutiérrez-Vega, "Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons," Opt. Express 15, 18326-18338 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003) p. 540.
  2. A. W. Snyder and D. J. Mitchell, "Accessible solitons," Science 276, 1538-1541 (1997). [CrossRef]
  3. E. A. Ultanir, G. Stegeman, C. H. Lange, and F. Lederer, "Coherent interactions of dissipative spatial solitons," Opt. Lett. 29, 283-285 (2004). [CrossRef] [PubMed]
  4. C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, "Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions," Phys. Rev. Lett. 82, 876-879 (1999). [CrossRef]
  5. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003). [CrossRef] [PubMed]
  6. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002). [CrossRef]
  7. A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of attraction between dark solitons," Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed]
  8. A. I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, "Stable vortex solitons in nonlocal self-focusing nonlinear media," Phys. Rev E 71, 065603 (2005). [CrossRef]
  9. S. Lopez-Aguayo, A. S. Desyatnikov, Yu. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100-1102 (2006). [CrossRef] [PubMed]
  10. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005). [CrossRef] [PubMed]
  11. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992). [CrossRef] [PubMed]
  12. C. Conti, M. Peccianti and G. Assanto, "Observation of optical spatial solitons in a highly nonlocal medium," Phys. Rev. Lett. 92, 113902 (2004). [CrossRef] [PubMed]
  13. S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, "Azimuthons in nonlocal nonlinear media," Opt. Express 14, 7903-7908 (2006). [CrossRef] [PubMed]
  14. A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: Spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005). [CrossRef] [PubMed]
  15. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, "Laguerre and Hermite Soliton clusters in nonlocal nonlinear media," Phys. Rev. Lett. 98, 053901 (2007). [CrossRef] [PubMed]

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.

Supplementary Material

» Media 1: AVI (1365 KB)     
» Media 2: AVI (1406 KB)     
» Media 3: AVI (1339 KB)     
» Media 4: AVI (1520 KB)     
» Media 5: AVI (1537 KB)     
» Media 6: AVI (2087 KB)     
» Media 7: AVI (2097 KB)     
» Media 8: AVI (537 KB)     
» Media 9: AVI (1459 KB)     
» Media 10: AVI (1374 KB)     
» Media 11: AVI (454 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited