OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 6 — Mar. 16, 2009
  • pp: 4236–4250

Dissipative ring solitons with vorticity

J. Soto-Crespo, N. Akhmediev, C. Mejía-Cortés, and N. Devine  »View Author Affiliations


Optics Express, Vol. 17, Issue 6, pp. 4236-4250 (2009)
http://dx.doi.org/10.1364/OE.17.004236


View Full Text Article

Enhanced HTML    Acrobat PDF (1731 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.

© 2009 Optical Society of America

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 18, 2008
Revised Manuscript: December 22, 2008
Manuscript Accepted: January 20, 2009
Published: March 3, 2009

Citation
J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortes, and N. Devine, "Dissipative ring solitons with vorticity," Opt. Express 17, 4236-4250 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-6-4236


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. K. Batchelor, An Introduction to Fluid Dynamics, (Cambridge University Press, 1967).
  2. H. Kleinert, Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation, (World Scientific, Singapore, 2008).
  3. J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).
  4. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992). [CrossRef]
  5. J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov "Solitary-wave Vortices in Quadratic Nonlinear Media," J. Opt. Soc. Am. B 15, 625-627 (1998). [CrossRef]
  6. A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999). [CrossRef]
  7. N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007). [CrossRef] [PubMed]
  8. B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002). [CrossRef]
  9. Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008). [CrossRef]
  10. D. N. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Observation of polychromatic vortex solitons," Opt. Lett. 33, 1851 (2008). [CrossRef] [PubMed]
  11. V. Tikhonenko, Y. Kivshar, V.V. Steblina, and A.A. Zozulya, "Vortex solitons in a saturable optical medium," J. Opt. Soc. Am. B 15, 79-86 (1998). [CrossRef]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005). [CrossRef] [PubMed]
  13. J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008). [CrossRef]
  14. J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004). [CrossRef]
  15. T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004). [CrossRef] [PubMed]
  16. G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992). [CrossRef] [PubMed]
  17. V. Tikhonenko and N. Akhmediev, "Excitation of vortex solitons in a Gaussian beam configuration," Opt. Commun. 126, 108 (1996). [CrossRef]
  18. I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001). [CrossRef]
  19. Q1. H. Michinel, J. Campo-T’aboas, M. L. Quiroga-Teixeiro, J. R. Salgueiro and R. Garc’ıa-Fern’andez, "Excitation of stable vortex solitons in nonlinear cubic-quintic materials," J. Opt. B: Quantum Semiclass. Opt. 3, 314-317 (2001). [CrossRef]
  20. H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004). [CrossRef]
  21. S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003). [CrossRef]
  22. N. N. Rosanov, "Solitons in laser systems with saturable absorption," in: Dissipative solitons, (Eds.) N. Akhmediev and A. Ankiewicz, Lecture Notes in Physics, V. 661, Springer, Heidelberg, 2005.
  23. L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001). [CrossRef]
  24. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008). [CrossRef]
  25. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991). [CrossRef] [PubMed]
  26. A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008). [CrossRef]
  27. N. Akhmediev. J. M. Soto-Crespo, and G. Town, "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach," Phys. Rev. E 63, 056602 (2001). [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.

Supplementary Material


» Media 1: MPG (1406 KB)     
» Media 2: MPG (1406 KB)     
» Media 3: MPG (1406 KB)     
» Media 4: MPG (1125 KB)     
» Media 5: MPG (1125 KB)     
» Media 6: MPG (1124 KB)     
» Media 7: MPG (1125 KB)     

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited