OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 14, Iss. 10 — Oct. 1, 1997
  • pp: 2550–2562

Amalgamation of interacting light beamlets in Kerr-type media

L. Bergé, M. R. Schmidt, J. Juul Rasmussen, P. L. Christiansen, and K. Ø. Rasmussen  »View Author Affiliations

JOSA B, Vol. 14, Issue 10, pp. 2550-2562 (1997)

View Full Text Article

Acrobat PDF (423 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The interaction of optical filaments in bulk self-focusing media is investigated theoretically and numerically. The nature of this interaction is shown to vary with the incident individual powers and relative phases of the beamlets.By means of virial arguments supported by numerical results it is found that three distinct evolution regimes characterize two in-phase interacting filaments:(i) When each filament has a power below <i>N</i><sub>c</sub>/4, where <i>N</i><sub>c</sub> is the critical self-focusing threshold for a single wave, both filaments disperse along their propagation axis. (ii)When their respective powers lie between <i>N</i><sub>c</sub>/4and <i>N</i><sub>c</sub>, they fuse into a single central lobe that may self-focus until collapse, depending on their initial separation distance. The critical distance below which a central lobe forms and collapses is estimated analytically. (iii) When their incident powers both exceed <i>N</i><sub>c</sub>, initially separated filaments individually self-focus without mutual interaction. In contrast to in-phase beamlets, two light cells with opposite phase are shown to never coalesce. The extension of the self-focusing dynamics to optical filaments in bulk media with anomalous group-velocity dispersion is discussed.

© 1997 Optical Society of America

L. Bergé, M. R. Schmidt, J. Juul Rasmussen, P. L. Christiansen, and K. Ø. Rasmussen, "Amalgamation of interacting light beamlets in Kerr-type media," J. Opt. Soc. Am. B 14, 2550-2562 (1997)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964); P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005 (1965); V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” Zh. Eksp. Teor. Fiz. Pis'ma Red. 3, 471 (1966) [JETP Lett. JTPLA2 3, 307 (1966)].
  2. E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103 (1986).
  3. See, for a review, J. Juul Rasmussen and K. Rypdal, “Blow-up in nonlinear Schrödinger equations I. A general review,” Phys. Scr. 33, 481 (1986).
  4. R. McLeod, K. Wagner, and S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254 (1995).
  5. N. Akhmediev and J. M. Soto-Crespo, “Generation of a train of three-dimensional optical solitons in a self-focusingmedium,” Phys. Rev. A 47, 1358 (1993).
  6. A. I. D'yachenko, V. E. Zakharov, A. N. Pushkarev, V. F. Shvets, and V. V. Yan'kov, “Soliton turbulence in non-integrable wave systems,” Zh. Eksp. Teor. Fiz. 96, 2026 (1989) [Sov. Phys. JETP 69, 1144 (1989)]; V. E. Zakharov, A. N. Pushkarev, V. F. Shvets, and V. V. Yan'kov, “Soliton turbulence,” Pis'ma Zh. Eksp. Teor. Fiz. 48, 79 (1988) [JETP Lett. 48, 83 (1988)]; for a review on optical turbulence, see A. I. D'yachenko, A. C. Newell, A. N. Pushkarev, and V. E. Zakharov, “Optical turbulence: weak turbulence, condensates and collapsing filamentsin the nonlinear Schrödinger equation,” Physica D PDNPDT 57, 96 (1992).
  7. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628 (1973); “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24, 178 (1974); B. R. Suydam, “Effect of refractive-index nonlinearity on the optical quality of high-powerlaser beams,” IEEE J. Quantum Electron. IEJQA7 QE-11, 225 (1975).
  8. S. Hüller, Ph. Mounaix, and D. Pesme, “Numerical simulation of filamentation and its interplay with SBS inunderdense plasmas,” Phys. Scr. T63, 151 (1996).
  9. M. J. Landman, G. C. Papanicolaou, C. Sulem, P. L. Sulem, and X. P. Wang, “Stability of isotropic singularities for the nonlinear Schrödingerequation,” Physica D 47, 393 (1991).
  10. C. J. McKinstrie and D. A. Russel, “Nonlinear focusing of coupled waves,” Phys. Rev. Lett. 61, 2929 (1988).
  11. T. Okamawari, A. Hasegawa, and Y. Kodama, “Analyses of soliton interactions by means of a perturbed inverse-scatteringtransform,” Phys. Rev. A 51, 3203 (1995).
  12. V. I. Karpman and V. V. Solov'ev, “A perturbational approach to the two-soliton systems,” Physica D 3, 487 (1981).
  13. K. A. Gorshkov and L. A. Ostrovsky, “Interactions of solitons in non-integrable systems: direct perturbationmethod and applications,” Physica D 3, 428 (1981).
  14. D. Anderson and M. Lisak, “Bandwidth limits due to mutual pulse interaction in optical solitoncommunication systems,” Opt. Lett. 11, 174 (1986).
  15. J. P. Gordon, “Interaction forces among solitons in optical fibers,” Opt. Lett. 8, 596 (1983).
  16. I. M. Uzunov, V. S. Gerdjikov, M. Gölles, and F. Lederer, “On the description of N-soliton interaction in opticalfibers,” Opt. Commun. 125, 237 (1996).
  17. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetrybreaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
  18. V. Tikhonenko, J. Christov, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in asaturable nonlinear medium,” Phys. Rev. Lett. 76, 2698 (1996).
  19. D. E. Edmundson and R. H. Enns, “Fully three-dimensional collisions of bistable light bullets,” Opt. Lett. 18, 1609 (1993).
  20. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15, 1282 (1990).
  21. L. Bergé and J. Juul Rasmussen, “Multi-splitting and collapse of self-focusing anisotropic beams innormal/anomalous dispersive media,” Phys. Plasmas 3, 824 (1996).
  22. J. S. Hesthaven, J. P. Lynov, A. H. Nielsen, J. Juul Rasmussen, M. R. Schmidt, E. A. Shapiro, and S. K. Turitsyn, “Dynamics of a nonlinear dipole vortex,” Phys. Fluids 7, 2220 (1995).
  23. Yu. B. Gaididei, K. Ø. Rasmussen, and P. L. Christiansen, “Nonlinear excitations in two-dimensional molecular structures withimpurities,” Phys. Rev. E 52, 2951 (1995).
  24. K. Rypdal and J. Juul Rasmussen, “Stability of solitary structures in the nonlinear Schrödingerequation,” Phys. Scr. 40, 192 (1989).
  25. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transversemodulation instability,” Europhys. Lett. 35, 25 (1996).
  26. N. N. Akhmediev, V. I. Korneev, and R. F. Nabiev, “Modulation instability of the ground state of the nonlinear wave equation:optical machine gun,” Opt. Lett. 17, 393 (1992).
  27. P. G. Saffman, Vortex Dynamics (CambridgeU. Press, Cambridge, 1992).

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