OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 16 — Aug. 8, 2005
  • pp: 6202–6211

Self-organization of spatial solitons

Martin Centurion, Ye Pu, and Demetri Psaltis  »View Author Affiliations

Optics Express, Vol. 13, Issue 16, pp. 6202-6211 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (1300 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present experimental results on the transverse modulation instability of an elliptical beam propagating in a bulk nonlinear Kerr medium, and the formation and self-organization of spatial solitons. We have observed the emergence of order, self organization and a transition to an unstable state. Order emerges through the formation of spatial solitons in a periodic array. If the initial period of the array is unstable the solitons will tend to self-organize into a larger (more stable) period. Finally the system transitions to a disordered state where most of the solitons disappear and the beam profile becomes unstable to small changes in the input energy.

© 2005 Optical Society of America

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Research Papers

Original Manuscript: June 1, 2005
Revised Manuscript: July 29, 2005
Published: August 8, 2005

Martin Centurion, Ye Pu, and Demetri Psaltis, "Self-organization of spatial solitons," Opt. Express 13, 6202-6211 (2005)

Sort:  Journal  |  Reset  


  1. Y. Kivshar, D. Pelinovsky, �??Self-focusing and transverse instabilities of solitary waves,�?? Phys. Rep. 331, 118-195 (2000). [CrossRef]
  2. V. E. Zakharov, A. M. Rubenchik, �??�??Instability of waveguides and solitons in nonlinear media,�??�?? Sov. Phys. JETP 38, 494-500 (1974).
  3. M. Saffman, G. McCarthy and W. Krolikowski, �??Two-dimensional modulational instability in photorefractive media,�?? J. Opt. Soc. Am. B. 6, 387-403 (2004).
  4. H. Maillotte, J. Monneret, A. Barthelemy, C. Froehly, �??�??Laser beam self-splitting into solitons by optical Kerr nonlinearity,�??�?? Opt. Commun. 109, 265-271 (1994) [CrossRef]
  5. R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, S. Wabnitz, �??�??Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,�??�?? Phys. Rev. Lett. 78, 2756-2759 (1997); [CrossRef]
  6. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, D. N. Christodoulides, �??Modulation instability and pattern formation in spatially incoherent light beams,�?? Science 290, 495-498 (2000). [CrossRef] [PubMed]
  7. B. Crosignani, P. Di Porto, �??�??Nonlinear propagation in Kerr media of beams with unequal transverse widths,�??�?? Opt. Lett. 18, 1394-1396 (1993); [CrossRef] [PubMed]
  8. A. V. Mamaev, M. Saffman, A. A. Zozulya, �??�??Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,�??�?? Europhys. Lett. 35, 25-30 (1996); [CrossRef]
  9. G. Fibich, B. Ilan, �??�??Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation,�??�?? J. Opt. Soc. Am. B 17, 1749-1758 (2000); [CrossRef]
  10. A. Dubietis, G. Tamogauskas, G. Fibich G, B. Ilan, �??Multiple filamentation induced by input-beam ellipticity�??, Opt. Lett. 29, 1126-1128 (2004); [CrossRef] [PubMed]
  11. R. Malendevich, L. Jankovic, G. Stegeman, J. S. Aitchison, �??Spatial modulation instability in a Kerr slab waveguide,�?? Opt. Lett. 26, 1879-1881 (2001); [CrossRef]
  12. C. Cambournac, H. Maillotte, E. Lantz, J. M. Dudley, M. Chauvet, �??Spatiotemporal behavior of periodic arrays of spatial solitons in a planar waveguide with relaxing Kerr nonlinearity,�?? J. Opt. Soc. Am. B 19, 574-585 (2002); [CrossRef]
  13. E. Lantz, C. Cambournac, H. Maillotte, �??Spatiotemporal dynamics of soliton arrays generated from spatial noise in a planar waveguide with relaxing Kerr nonlinearity,�?? Opt. Express 10, 942-948 (2002); [PubMed]
  14. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, J. P. Torres, �??�??Eliminating the transverse instabilities of Kerr solitons,�??�?? Phys. Rev. Lett. 85, 4888�??4891 (2000); [CrossRef] [PubMed]
  15. G. I. Stegeman, M. Segev, �??Optical spatial solitons and their interactions: Universality and diversity,�?? Science 286, 1518-1523 (1999). [CrossRef] [PubMed]
  16. A. Barthelemy, S. Maneuf, C. Froehly, �??Soliton Propagation and Self-Confinement of Laser-Beams by Kerr Optical Non-Linearity,�?? , Opt. Commun. 55, 201-206 (1985). [CrossRef]
  17. M. Segev, B. Crosignani, A. Yariv and B. Fischer, �??Spatial Solitons in Photorefractive Media,�?? Phys. Rev. Lett. 68, 923-926 (1992). [CrossRef] [PubMed]
  18. W. E. Torruelas, Z. Wang, D. J. Hagan, E. W. Vanstryland, G. I. Stegeman, L. Torner, C. R. Menyuk, �??Observation of 2-Dimensional Spatial Solitary Waves in a Quadratic Medium,�?? Phys. Rev. Lett. 74, 5036-5039 (1995). [CrossRef]
  19. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, �??Periodic breakup of optical beams due to self-focusing,�?? Appl. Phys. Lett. 23, 628-630 (1973). [CrossRef]
  20. J. P. Gordon, �??Interaction Forces among Solitons in Optical Fibers,�?? Opt. Lett. 8, 596-598 (1983). [CrossRef] [PubMed]
  21. M. Shalaby, F. Reynaud, and A. Barthelemy, �??Experimental observation of spatial soliton interactions with a pi/2 relative phase difference,�?? Opt. Lett. 17, 778-780 (1992). [CrossRef] [PubMed]
  22. M. Petrovi, D. Träger, A. Strinic, M. Belic, J. Schroder, C. Denz, �??Solitonic lattices in photorefractive crystals,�?? Phys. Rev. E 68, 055601 (2003) [CrossRef]
  23. R. Mcleod, K. Wagner and S. Blair, �??(3+1)-Dimensional Optical Soliton Dragging Logic,�?? Phys. Rev. A 52, 3254-3278 (1995). [CrossRef] [PubMed]
  24. M. Peccianti, C. Conti, G. Assanto, A. De Luca, C. Umeton, �??Routing of anisotropic spatial solitons and modulational instability in liquid crystals,�?? Nature 432, 733 (2004). [CrossRef] [PubMed]
  25. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, �??Optically Turbulent Femtosecond Light Guide in Air,�?? Phys. Rev. Lett. 83, 2938-2941 (1999). [CrossRef]
  26. L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Woste, R. Bourayou, R. Sauerbrey, �??Multiple filamentation of Terrawatt laser pulses in air,�?? Phys. Rev. Lett. 92, 225002 (2004). [CrossRef] [PubMed]
  27. H. Schroeder and S. L. Chin, �??Visualization of the evolution of multiple filaments in methanol,�?? Opt. Commun. 234, 399-406 (2004). [CrossRef]
  28. R Boyd, Nonlinear Optics, Academic Press, 2003.
  29. R. A. Ganeev, A. I. Ryasnyansky, M. Baba, M. Suzuki, N. Ishizawa, M. Turu, S. Sakakibara, H. Kuroda, �??Nonlinear refraction in CS2,�?? Appl. Phys. B 78, 433�??438 (2004). [CrossRef]
  30. M. Fujimoto, S. Aoshima, M. Hosoda, and Y. Tsuchiya, �??Femtosecond time-resolved optical polarigraphy: imaging of the propagation dynamics of intense light in a medium,�?? Opt. Lett. 24, 850-852 (1999). [CrossRef]
  31. G. G. Luther, A. C. Newell, and J. V. Moloney, E. M. Wright, �??Short-Pulse Conical Emission and Spectral Broadening in Normally Dispersive Media,�?? Opt. Lett. 19, 789-791 (1994). [CrossRef] [PubMed]
  32. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, �??Conical emission from self-guided femtosecond pulses in air,�?? Opt. Lett. 21, 62-64 (1996). [CrossRef] [PubMed]
  33. M. Centurion, Y. Pu, M. Tsang, D. Psaltis, �??Dynamics of filament formation in a Kerr medium,�?? Phys. Rev. A 71 063811 (2005). [CrossRef]
  34. J. M. Halbout, C. L. Tang, �??�??Femtosecond interferometry for nonlinear optics,�??�?? Appl. Phys. Lett. 40, 765-767 (1982) [CrossRef]
  35. D. McMorrow, W. T. Lotshaw, G. A. Kenneywallace, �??�??Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,�??�?? IEEE J. Quantum Electron. 24, 443-454 (1988)). [CrossRef]
  36. A. Piekara, �??On self-trapping of a laser beam,�?? IEEE J. Quantum Electron. QE-2, 249-250 (1966). [CrossRef]
  37. A. Vinçotte, L. Berge, �??�?(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,�?? Phys. Rev. A 70, 061802 (2004) [CrossRef]
  38. M. Falconieri, G. Salvetti, �??Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2,�?? Appl. Phys. B. 69, 133-136 (1999). [CrossRef]
  39. R.A. Ganeev, A.I. Ryasnyansky, N. Ishizawa, M. Baba, M. Suzuki, M. Turu, S. Sakakibara, H. Kuroda, �??�??Two- and three-photon absorption in CS2,�??�?? Opt. Commun. 231, 431-436 (2004). [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: AVI (79 KB)     
» Media 2: AVI (113 KB)     
» Media 3: AVI (259 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited