Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Long-range interactions between optical solitons

Nature Physics volume 2, pages 769–774 (2006)Cite this article

Abstract

Solitons are self-localized wave packets arising from a robust balance between dispersion and nonlinearity. They are a universal phenomenon, exhibiting properties typically associated with particles. Thus far, interactions between solitons have been observed only between neighbouring solitons at close proximity. Here, we study interactions between solitons in highly non-local nonlinear media, and demonstrate experimentally attraction between solitons propagating in different samples, where their optical fields never overlap and the interaction is mediated solely by a non-optical wire. This increases the soliton interaction range by orders of magnitude, and breaks the close-proximity and nearest-neighbour limitations on soliton interactions. We also experiment with three-dimensional interactions between solitons that are far apart, where the solitons capture each other into a spiralling motion with a circular orbit, and a tangential velocity that does not depend on the separation between solitons. Our study suggests that these phenomena could be used in the construction of novel model systems for studying the behaviour of complex nonlinear networks.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Experimental observation of planar interactions between solitons that are far apart in non-local nonlinear media.
Figure 2: Experimental observation of three-dimensional spiralling interactions between widely separated solitons.
Figure 3: Experimental and theoretical comparisons of 3D interactions between solitons and between high-power non-soliton beams.
Figure 4: Experimental demonstration of the interaction between two solitons propagating in separate samples, with the interaction mediated by wiring.

Similar content being viewed by others

References

  1. Stegeman, G. I. & Segev, M. Optical spatial solitons and their interactions: Universality and diversity. Science 286, 1518–1523 (1999).

    Article  Google Scholar 

  2. Zabusky, N. J. & Kruskal, M. D. Interaction of ‘Solitons’ in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15, 240–243 (1965).

    Article  ADS  Google Scholar 

  3. Shih, M. & Segev, M. Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons. Opt. Lett. 21, 1538–1540 (1996).

    Article  ADS  Google Scholar 

  4. Krolikowski, W. & Holmstrom, S. A. Fusion and birth of spatial solitons upon collision. Opt. Lett. 22, 369–371 (1997).

    Article  ADS  Google Scholar 

  5. Królikowski, W., Luther-Davies, B., Denz, C. & Tschudi, T. Annihilation of photorefractive solitons. Opt. Lett. 23, 97–99 (1998).

    Article  ADS  Google Scholar 

  6. Shih, M., Segev, M. & Salamo, G. Three-dimensional spiraling of interacting spatial solitons. Phys. Rev. Lett. 78, 2551–2554 (1997).

    Article  ADS  Google Scholar 

  7. Tikhonenko, V., Christou, J. & Luther-Davies, B. Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium. Phys. Rev. Lett. 76, 2698–2701 (1996).

    Article  ADS  Google Scholar 

  8. Firth, W. J. & Skryabin, D. V. Optical solitons carrying orbital angular momentum. Phys. Rev. Lett. 79, 2450–2453 (1997).

    Article  ADS  Google Scholar 

  9. Torner, L. & Petrov, D.V. Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation. Electron. Lett. 33, 608–610 (1997).

    Article  Google Scholar 

  10. Petrov, D. V. et al. Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal. Opt. Lett. 23, 1444–1447 (1998).

    Article  ADS  Google Scholar 

  11. Gordon, J. P. Interaction forces among solitons in optical fibers. Opt. Lett. 8, 596–598 (1983).

    Article  ADS  Google Scholar 

  12. Litvak, A. G., Mironov, V. A., Fraiman, G. M. & Yunakovskii, A. D. Thermal self-effect of wave beams in a plasma with a nonlocal nonlinearity. Fiz. Plazmy 1, 60–71 (1975).

    ADS  Google Scholar 

  13. Ultanir, E. A., Stegeman, G. I., Lange, C. H. & Lederer, F. Interactions of dissipative spatial solitons. Opt. Lett. 29, 283–285 (2004).

    Article  ADS  Google Scholar 

  14. Strogatz, S. H. Exploring complex networks. Nature 410, 268–276 (2001).

    Article  ADS  Google Scholar 

  15. Dabby, F. W. & Whinnery, J. R. Thermal self-focusing of laser beams in lead glasses. Appl. Phys. Lett. 13, 284–286 (1968).

    Article  ADS  Google Scholar 

  16. Litvak, A. G. Self-focusing of powerful light beams by thermal effects. JETP Lett. 4, 230–233 (1966).

    ADS  Google Scholar 

  17. Suter, D. & Blasberg, T. Stabilization of transverse solitary waves by a nonlocal response of the nonlinear medium. Phys. Rev. A 48, 4583–4587 (1993).

    Article  ADS  Google Scholar 

  18. Segev, M., Crosignani, B., Yariv, A. & Fischer, B. Spatial solitons in photorefractive media. Phys. Rev. Lett. 68, 923–926 (1992).

    Article  ADS  Google Scholar 

  19. Ultanir, E. A., Stegeman, G. I., Michaelis, D., Lange, C. H. & Lederer, F. Stable dissipative solitons in semiconductor optical amplifiers. Phys. Rev. Lett. 90, 253903 (2003).

    Article  ADS  Google Scholar 

  20. Conti, C., Peccianti, M. & Assanto, G. Route to nonlocality and observation of accessible solitons. Phys. Rev. Lett. 91, 73901 (2003).

    Article  ADS  Google Scholar 

  21. Conti, C., Peccianti, M. & Assanto, G. Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett. 92, 113902 (2004).

    Article  ADS  Google Scholar 

  22. Peccianti, M., Conti, C., Assanto, G., De Luca, A. & Umeton, C. Routing of anisotropic spatial solitons and modulational instability in liquid crystals. Nature 432, 733–737 (2004).

    Article  ADS  Google Scholar 

  23. Rivlin, L. A. Gravitational self-confinement of a photon beam. Quantum Electron. 28, 99–103 (1998).

    Article  ADS  Google Scholar 

  24. Pecseli, H. L. & Rasmussen, J. J. Nonlinear electron waves in strongly magnetized plasmas. Plasma Phys. 22, 421–438 (1980).

    Article  ADS  Google Scholar 

  25. Rao, N. N. & Shukla, P. K. Triple-hump upper-hybrid solitons. Phys. Scripta T 82, 53–59 (1999).

    Article  ADS  Google Scholar 

  26. Dalfovo, F., Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463–512 (1999).

    Article  ADS  Google Scholar 

  27. Turitsyn, S. K. Spatial dispersion of nonlinearity and stability of multidimensional solitons. Theor. Math. Phys. 64, 797–801 (1986).

    Article  Google Scholar 

  28. Rotschild, C., Cohen, O., Manela, O., Segev, M. & Carmon, T. 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).

    Article  ADS  Google Scholar 

  29. Snyder, A. W. & Mitchell, D. J. Accessible solitons. Science 276, 1538–1541 (1997).

    Article  Google Scholar 

  30. Kolchugina, I. A., Mironov, V. A. & Sergeev, A. M. Structure of steady-state solitons in systems with a nonlocal nonlinearity. JETP Lett. 31, 304–307 (1980).

    ADS  Google Scholar 

  31. Peccianti, M., Brzdkiewicz, K. A. & Assanto, G. Nonlocal spatial soliton interactions in nematic liquid crystals. Opt. Lett. 27, 1460–1462 (2002).

    Article  ADS  Google Scholar 

  32. Buryak, A. V., Kivshar, Y. S., Shih, M. F. & Segev, M. Induced coherence and stable soliton spiraling. Phys. Rev. Lett. 82, 81–84 (1999).

    Article  ADS  Google Scholar 

  33. Jakubowski, M. H., Steiglitz, K. & Squier, R. State transformations of colliding optical solitons and possible application to computation in bulk media. Phys. Rev. E 58, 6752–6758 (1998).

    Article  ADS  Google Scholar 

  34. Steiglitz, K. Time-gated Manakov spatial solitons are computationally universal. Phys. Rev. E 63, 016608 (2001).

    Article  ADS  Google Scholar 

  35. Park, J. K., Steiglitz, K. & Thurston, W. P. Soliton-like behavior in automata. Physica D 19, 423–432 (1986).

    Article  ADS  MathSciNet  Google Scholar 

  36. Anastassiou, C. et al. Energy exchange interactions between colliding vector solitons. Phys. Rev. Lett. 83, 2332–2335 (1999).

    Article  ADS  Google Scholar 

  37. Anastassiou, C., Fleischer, J. W., Carmon, T., Segev, M. & Steiglitz, K. Information transfer through cascaded collisions of vector solitons. Opt. Lett. 26, 1498–1500 (2001).

    Article  ADS  Google Scholar 

  38. Soljacic, M., Segev, M. & Menyuk, C. R. Self-similarity and fractals in soliton-supporting systems. Phys. Rev. E 61, R1048–R1051 (2000).

    Article  ADS  Google Scholar 

  39. Sears, S., Soljacic, M., Segev, M., Krylov, D. & Bergman, K. Cantor Set fractals from solitons. Phys. Rev. Lett. 84, 1902–1905 (2000).

    Article  ADS  Google Scholar 

  40. Wu, M., Kalinikos, B. A., Carr, L. D. & Patton, C. E. Observation of spin-wave soliton fractals in magnetic film active feedback rings. Phys. Rev. Lett. 96, 187202 (2006).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the Israeli Science Foundation, the Israel-USA Binational Science Foundation and the German-Israeli DIP Project.

Author information

Authors and Affiliations

  1. Physics Department and Solid State Institute, Technion, Haifa 32000, Israel

    Carmel Rotschild, Barak Alfassi & Mordechai Segev

  2. JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA

    Oren Cohen

Authors
  1. Carmel Rotschild
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Barak Alfassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Oren Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mordechai Segev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mordechai Segev.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rotschild, C., Alfassi, B., Cohen, O. et al. Long-range interactions between optical solitons. Nature Phys 2, 769–774 (2006). https://doi.org/10.1038/nphys445

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys445

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing