OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 6 — Mar. 19, 2007
  • pp: 2963–2973

Interactions of chirped and chirp-free similaritons in optical fiber amplifiers

Sergey A. Ponomarenko and Govind P. Agrawal  »View Author Affiliations

Optics Express, Vol. 15, Issue 6, pp. 2963-2973 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (426 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We obtain exact self-similar solutions to an inhomogeneous nonlinear Schrödinger equation, describing propagation of optical pulses in fiber amplifiers with distributed dispersion and gain. We show that there exists a one-to-one correspondence between such self-similar waves and solitons of the standard, homogeneous, nonlinear Schrödinger equation if a certain compatibility condition is satisfied. As this correspondence guarantees the stability of the novel self-similar waves, we refer to them as similaritons. We demonstrate that, the character of similariton interactions crucially depends on the sign of the similariton phase chirp. In particular, we show that the similariton interactions can under certain conditions lead to the formation of molecule-like bound states of two similaritons.

© 2007 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

Original Manuscript: January 23, 2007
Revised Manuscript: February 20, 2007
Manuscript Accepted: February 20, 2007
Published: March 19, 2007

Sergey A. Ponomarenko and Govind P. Agrawal, "Interactions of chirped and chirp-free similaritons in optical fiber amplifiers," Opt. Express 15, 2963-2973 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering (Cambridge University Press, Cambridge, UK, 2003).
  2. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, CA, 2003).
  3. L. F. Mollenauer and J. P. Gordon, Solitons in Optical Fibers: Fundamentals and Applications (Academic Press, San Diego, CA, 2006).
  4. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, San Diego, CA, 2007).
  5. H.-H. Chen and C.-S. Liu, ‘Solitons in nonuniform nedia," Phys. Rev. Lett. 37, 693-697 (1976). [CrossRef]
  6. R. Balakrishnan, "Soliton propagation in nonuniform media," Phys. Rev. A 32, 1144-1149 (1985). [CrossRef] [PubMed]
  7. V. N. Serkin and A. Hasegawa, "Exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion," IEEE J. Sel. Top. Quantum Electron 8, 418-431 (2002). [CrossRef]
  8. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, "Nonautonomous Solitons in External Potentials," Phys. Rev. Lett. 98, 074102 (2007). [CrossRef] [PubMed]
  9. G. I. Barenblatt, Scaling, self-similarity, and intermediate asymptotics (Cambridge University Press, Cambridge, UK, 1996).
  10. J. D. Moores, "Nonlinear compression of chirped solitary waves with and without phase modulation, Opt. Lett. 21, 555-557 (1996). [CrossRef] [PubMed]
  11. V. N. Serkin and A. Hasegawa, "Novel soliton solutions of the nonlinear Schr¨odinger equation model," Phys. Rev. Lett. 85, 4502-4505 (2000). [CrossRef] [PubMed]
  12. V. I. Kruglov, A. C. Peacock, J. M. Dudley, J. D. Harvey, "Self-similar propagation of high-power parabolic pulses in optical fiber amplifiers," Opt. Lett. 25, 1753-1755 (2000). [CrossRef]
  13. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, "Exact self-similar solutions of the generalized nonlinear Schr¨odinger equation with distributed coefficients," Phys. Rev. Lett. 90, 113902 (2003). [CrossRef] [PubMed]
  14. C. Finot and G. Millot, "Collisions between similaritons in optical fiber amplifiers," Opt. Express 13, 7653-7665 (2005). [CrossRef] [PubMed]
  15. V. I. Kruglov and J. D. Harvey, "Asymptotically exact parabolic solutions of the generalized nonlinear Schrodinger equation with varying parameters," J. Opt. Soc. Am. B 23, 2541-2550 (2006). [CrossRef]
  16. S. A. Ponomarenko and G. P. Agrawal, "Do solitonlike self-similar waves exist in nonlinear optical media?" Phys. Rev. Lett. 97, 013901 (2006). [CrossRef] [PubMed]
  17. K. E. Strecker, G. B. Partridge, A. G. Truscott, and R. G. Hulet, "Formation and propagation of matter-wave soliton trains," Nature 417, 150-153 (2002). [CrossRef] [PubMed]
  18. V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional selfmodulation of waves in nonlinear media," Sov. Phys. JETP 34, 62-69 (1972).
  19. B. Tian, W. R. Shan, C. Y. Zhang, G. M. Wei, and Y. T. Gao, "Transformations for a generalized variablecoefficient nonlinear Schrodinger model from plasma physics, arterial mechanics and optical fibers with symbolic computation," Eur. Phys. J. B 47, 329-332 (2005). [CrossRef]
  20. G. P. Agrawal, Lightwave technology: Telecommunication Systems (Wiley, Hoboken, NJ, 2005). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited