OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 20, Iss. 11 — Nov. 1, 2003
  • pp: 2338–2348

Solitons in regular and random split-step systems

Rodislav Driben, Boris A. Malomed, and Pak L. Chu  »View Author Affiliations

JOSA B, Vol. 20, Issue 11, pp. 2338-2348 (2003)

View Full Text Article

Acrobat PDF (1198 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Fundamental properties of solitons in the recently introduced split-step model (SSM) are investigated. The SSM is a system that consists of periodically alternating dispersive and nonlinear segments, a period being of the same order of magnitude as the soliton’s dispersion length. The model including fiber loss and gain can always be reduced to its lossless version. First, we develop a variational approximation that makes it possible to explain the existence of SSM solitons that were originally found solely in numerical form. Overall dynamic behavior of a SSM is described by a phase diagram that identifies an established state (stationary soliton, breather with long-period oscillations, splitting into several pulses, or decay into radiation) depending on the amplitude and the width of the initial pulse. In particular, strong saturation in the dependence of the amplitude of the established soliton on the amplitude of the initial pulse is found. The results clearly show some similarities and drastic differences between the SSM and the ordinary soliton model based on the nonlinear Schrödinger equation. A random version of the SSM is introduced, with the length of the system’s cell uniformly distributed in some interval, which is a relevant case for applications to fiber-optic telecommunication networks. It is found that the dynamics of the SSM solitons as well as interactions between them in random systems (both single-channel and multichannel systems) are virtually the same as in their regular counterparts.

© 2003 Optical Society of America

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

Rodislav Driben, Boris A. Malomed, and Pak L. Chu, "Solitons in regular and random split-step systems," J. Opt. Soc. Am. B 20, 2338-2348 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. J. H. B. Nijhof, N. J. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 33, 1726–1727 (1997).
  2. A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900–902 (1998).
  3. I. Gabitov and S. K. Turitsyn, “Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation,” Opt. Lett. 21, 327–329 (1996).
  4. M. J. Ablowitz and G. Biondini, “Multiscale pulse dynamics in communication systems with strong dispersion management,” Opt. Lett. 23, 1668–1670 (1998).
  5. B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Prog. Opt. 43, 69–191 (2002).
  6. C. Paré and P.-A. Belanger, “Spectral domain analysis of dispersion management without averaging,” Opt. Lett. 25, 881–883 (2000).
  7. M. Nakazawa and H. Kubota, “Optical soliton communication in a positively and negatively dispersion-allocated optical-fiber transmission-line,” Electron. Lett. 31, 216–217 (1995).
  8. L. Torner, “Walkoff-compensated dispersion-mapped quadratic solitons,” IEEE Photon. Technol. Lett. 11, 1268–1270 (1999).
  9. L. Torner, S. Carrasco, J.-P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
  10. L. Bergé, V. K. Mezentsev, J. Juul Rasmussen, P. L. Christiansen, and Yu. B. Gaididei, “Self-guiding light in layered nonlinear media,” Opt. Lett. 25, 1037–1039 (2000).
  11. I. Towers and B. A. Malomed, “Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity,” J. Opt. Soc. Am. B 19, 537–543 (2002).
  12. F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, “Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length,” Phys. Rev. A 67, 013605 (2003).
  13. A. Kaplan, B. V. Gisin, and B. A. Malomed, “Stable propagation and all-optical switching in planar waveguide-antiwaveguide periodic structures,” J. Opt. Soc. Am. B 19, 522–528 (2002).
  14. R. Driben and B. A. Malomed, “Split-step solitons in long fiber links,” Opt. Commun. 185, 439–456 (2000).
  15. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992).
  16. S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Comblike dispersion-profiled fiber for soliton pulse train generation,” Opt. Lett. 19, 539–541 (1994).
  17. H. Toda, Y. Furukawa, T. Kinoshita, Y. Kodama, and A. Hasegawa, “Optical soliton transmission experiment in a comb-like dispersion profiled fiber loop,” IEEE Photon. Technol. Lett. 9, 1415–1417 (1997).
  18. H. Toda, Y. Inada, Y. Kodama, and A. Hasegawa, “10 Gbit/s optical soliton transmission experiment in a comb-like dispersion profiled fiber loop,” IEICE Trans. Commun. E82-B, 1541–1543 (1999).
  19. M. Gutin, U. Mahlab, and B. A. Malomed, “Shaping NRZ pulses and suppression of the inter-symbol interference by a second-harmonic-generating module,” Opt. Commun. 200, 401–414 (2001).
  20. R. Driben, B. A. Malomed, M. Gutin, and U. Mahlab, “Implementation of nonlinearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules,” Opt. Commun. 218, 93–104 (2003).
  21. R. Driben and B. A. Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun. 197, 481–489 (2001).
  22. B. A. Malomed and A. Berntson, “Propagation of an optical pulse in a fiber link with random dispersion management,” J. Opt. Soc. Am. B 18, 1243–1251 (2001).
  23. V. V. Konotop and L. Vázquez, Nonlinear Random Waves (World Scientific: Singapore, 1994).
  24. F. Kh. Abdullaev and B. B. Baizakov, “Disintegration of a soliton in a dispersion-managed optical communication line with random parameters,” Opt. Lett. 25, 93–95 (2000).
  25. J. Garnier, “Stabilization of dispersion-managed solitons in random optical fibers by strong dispersion management,” Opt. Commun. 206, 411–438 (2002).
  26. G. P. Agrawal, Nonlinear Fiber Optics (Academic San Diego, Calif., 1995).
  27. J. Satsuma and N. Yajima, “Initial value problem for one-dimensional self modulation of nonlinear waves in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284 (1974).
  28. D. Anderson, M. Lisak, and T. Reichel, “Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system,” J. Opt. Soc. Am. B 5, 207–210 (1988).
  29. R. Driben and B. A. Malomed, “Equilibrium and nonequilibrium solitons in a lossy split-step system with lumped amplification,” Phys. Lett. A 301, 19–26 (2002).
  30. J. Atai and B. A. Malomed, “Solitary waves in systems with separated Bragg grating and nonlinearity,” Phys. Rev. E 64, 066617 (2001).
  31. J. Atai and B. A. Malomed, “Spatial solitons in a medium composed of self-focusing and self-defocusing layers,” Phys. Lett. A 298, 140–148 (2002).

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