OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 586–595

Multipole composite spatial solitons: theory and experiment

Anton S. Desyatnikov, Dragomir Neshev, Elena A. Ostrovskaya, Yuri S. Kivshar, Glen McCarthy, Wieslaw Krolikowski, and Barry Luther-Davies  »View Author Affiliations

JOSA B, Vol. 19, Issue 3, pp. 586-595 (2002)

View Full Text Article

Acrobat PDF (756 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We discuss the properties of composite (or vector) spatial optical solitons created by the incoherent interaction of two optical beams and associated with higher-order modes guided by a soliton-induced waveguide in a bulk medium. Such stationary (2+1)-dimensional self-trapped localized structures include, in particular, vortex- and dipole-mode vector solitons and also incorporate higher-order multipole spatial solitons in a bulk medium, such as quadrupole solitons and necklace-type composite beams. We overview our theoretical and experimental results for the structure, formation, and stability of these self-trapped composite optical beams and also discuss the effects of anisotropy and of the nonlocality of the photorefractive nonlinearity on their properties. Additionally, we demonstrate, analytically and experimentally, that an array of the dipole-mode vector solitons can be generated as a result of the transverse instability of a quasi-one-dimensional two-hump soliton stripe in a saturable nonlinear optical medium.

© 2002 Optical Society of America

OCIS Codes
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(190.5330) Nonlinear optics : Photorefractive optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Anton S. Desyatnikov, Dragomir Neshev, Elena A. Ostrovskaya, Yuri S. Kivshar, Glen McCarthy, Wieslaw Krolikowski, and Barry Luther-Davies, "Multipole composite spatial solitons: theory and experiment," J. Opt. Soc. Am. B 19, 586-595 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. M. Segev and G. I. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51, 42–48 (1998).
  2. D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988).
  3. S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).
  4. A. W. Snyder, S. J. Hewlett, and J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1015 (1994).
  5. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
  6. See, e.g., M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
  7. M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4560 (1998).
  8. See, e.g., A. W. Snyder and Yu. S. Kivshar, “Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution,” J. Opt. Soc. Am. B 14, 3025–3031 (1997), and references therein.
  9. V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
  10. E. Ostrovskaya, Yu. S. Kivshar, D. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
  11. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
  12. J. J. García-Ripoll, V. Perez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
  13. J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, “Vector solitons in (2+1) dimensions,” Opt. Lett. 25, 643–645 (2000).
  14. T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
  15. A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
  16. L. Gagnon and C. Paré, “Nonlinear radiation modes connected to parabolic graded-index profiles by the lens transformation,” J. Opt. Soc. Am. A 8, 601–607 (1991).
  17. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
  18. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).
  19. W. J. Firth and D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997).
  20. D. V. Skryabin and W. J. Firth, “Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media,” Phys. Rev. E 58, 3916–3930 (1998).
  21. A. Desyatnikov, D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Perez-García, “Multipole spatial vector solitons,” Opt. Lett. 26, 435–437 (2001).
  22. A. Barthelemy, C. Froehly, and M. Shalaby, “Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction,” in Mode-Locked and Other Ultrashort Laser Designs, Amplifiers, and Applications, M. Piche and P. W. Pace, eds., Proc. SPIE 2041, 104–113 (1994).
  23. M. Soljačić, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
  24. See, e.g., A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
  25. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
  26. W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
  27. D. Neshev, G. McCarthy, W. Krolikowski, E. A. Ostrovskaya, G. F. Calvo, F. Agullo-Lopez, and Yu. S. Kivshar, “Dipole-mode vector solitons in anisotropic nonlocal self-focusing media,” Opt. Lett. 26, 1185–1187 (2001).
  28. W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
  29. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
  30. M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
  31. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
  32. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
  33. V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eskp. Teor. Fiz. 65, 997 (1973) [ Sov. Phys. JETP 38, 494–500 (1974)].
  34. E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103–165 (1986).
  35. Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
  36. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
  37. V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129–1131 (1996).
  38. R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
  39. X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
  40. C. Anastassiou, M. Soljacić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85, 4888–4891 (2000).
  41. H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, “Spatial modulational instability in one-dimensional lithium niobate slab waveguides,” Opt. Lett. 25, 1786–1788 (2000).
  42. D. V. Skryabin and W. J. Firth, “Modulational instability of solitary waves in nondegenerate three-wave mixing: the role of phase symmetries,” Phys. Rev. Lett. 81, 3379–3382 (1998).
  43. Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
  44. J. J. García-Ripoll, V. Pérez-García, W. Krolikowski, and Yu. S. Kivshar, “Scattering of light by molecules of light,” arXiv.org # e-print archive, June 29, 2000, http://arXiv.org/ps/ nlin.PS/0006047.
  45. D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).

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