OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 1 — Jan. 1, 2013
  • pp: 87–94

Rogue waves in optical fibers in presence of third-order dispersion, self-steepening, and self-frequency shift

Adrian Ankiewicz, Jose M. Soto-Crespo, M. Amdadul Chowdhury, and Nail Akhmediev  »View Author Affiliations


JOSA B, Vol. 30, Issue 1, pp. 87-94 (2013)
http://dx.doi.org/10.1364/JOSAB.30.000087


View Full Text Article

Enhanced HTML    Acrobat PDF (1192 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Rogue waves in optical fibers can be mathematically described by the nonlinear Schrödinger equation and its extensions that take into account third-order dispersion, self-steepening, and self-frequency shift. These equations are integrable in special cases such as the Sasa–Satsuma or the Hirota equations. However, approximate polynomial solutions can also be obtained in cases beyond these integrable ones. We present these solutions and confirm their validity using numerical simulations.

© 2012 Optical Society of America

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 12, 2012
Revised Manuscript: October 19, 2012
Manuscript Accepted: October 23, 2012
Published: December 6, 2012

Citation
Adrian Ankiewicz, Jose M. Soto-Crespo, M. Amdadul Chowdhury, and Nail Akhmediev, "Rogue waves in optical fibers in presence of third-order dispersion, self-steepening, and self-frequency shift," J. Opt. Soc. Am. B 30, 87-94 (2013)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-1-87


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air–silica microstructure optical fiber with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]
  2. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001). [CrossRef]
  3. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006). [CrossRef]
  4. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002). [CrossRef]
  5. J. M. Dudley and J. R. Taylor, eds., Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).
  6. K. M. Hilligsoe, H. N. Paulsen, J. Thogersen, S. R. Keiding, and J. J. Larsen, “Initial steps of supercontinuum generation in photonic crystal fibers,” J. Opt. Soc. Am. B 20, 1887–1893 (2003). [CrossRef]
  7. J. Bethge, A. Husakou, F. Mitschke, F. Noack, U. Griebner, G. Steinmeyer, and J. Herrmann, “Two-octave supercontinuum generation in a water-filled photonic crystal fiber,” Opt. Express 18, 6230–6240 (2010). [CrossRef]
  8. A. Mussot and A. Kudlinski, “19.5 W CW-pumped supercontinuum source from 0.65 to 1.38  μm,” Electron. Lett. 45, 29–30 (2009). [CrossRef]
  9. J. C. Travers, “High average power supercontinuum sources,” Pramana J. Phys. 75, 769–785 (2010). [CrossRef]
  10. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007). [CrossRef]
  11. N. Akhmediev and E. Pelinovsky, eds., Issue on “Rogue waves—towards a unifying concept?” Eur. Phys. J. Special Topics 185, 1–266 (2010).
  12. D. V. Skryabin and A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010). [CrossRef]
  13. G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010). [CrossRef]
  14. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009). [CrossRef]
  15. A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009). [CrossRef]
  16. Ch. Mahnke and F. Mitschke, “Possibility of an Akhmediev breather decaying into solitons,” Phys. Rev. A 85, 033808 (2012). [CrossRef]
  17. N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A 373, 675–678 (2009). [CrossRef]
  18. P. Gaillard, “Families of quasi-rational solutions of the NLS equation and multi-rogue waves,” J. Phys. A 44, 435204(2011). [CrossRef]
  19. Y. Ohta and J. Yang, “General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation,” Proc. R. Soc. A 468, 1716–1740 (2012). [CrossRef]
  20. A. Ankiewicz, N. Devine, and N. Akhmediev, “Are rogue waves robust against perturbations?” Phys. Lett. A 373, 3997–4000 (2009). [CrossRef]
  21. B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys. 6, 790–795 (2010). [CrossRef]
  22. D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. B 25, 16–43 (1983). [CrossRef]
  23. S. B. Cavalcanti, J. C. Cressoni, Heber R. da Cruz, and A. S. Gouveia-Neto, “Modulation instability in the region of minimum group-velocity dispersion of single-mode optical fibers via an extended nonlinear Schrödinger equation,” Phys. Rev. A 43, 6162–6165 (1991). [CrossRef]
  24. M. J. Potasek, “Modulation instability in an extended nonlinear Schrödinger equation,” Opt. Lett. 12, 921–923 (1987). [CrossRef]
  25. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman and Hall, 1997).
  26. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973). [CrossRef]
  27. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed., Optics and Photonics series (Academic, 2006), Section 5.5.3.
  28. N. Sasa and J. Satsuma, “New type of soliton solutions for a higher-order nonlinear Schrödinger equation,” J. Phys. Soc. Jpn. 60, 409–417 (1991). [CrossRef]
  29. R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation,” J. Math. Phys. 14, 805–809 (1973). [CrossRef]
  30. D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A 27, 1393–1398 (1983). [CrossRef]
  31. S. Palacios, A. Guinea, J. M. Fernandez-Diaz, and R. D. Crespo, “Dark solitary waves in the nonlinear Schrödinger equation with third order dispersion, self-steepening, and self-frequency shift,” Phys. Rev. E 60, R45–R47 (1999). [CrossRef]
  32. Z. Li, L. Li, H. Tian, and G. Zhou, “New types of solitary wave solutions for the higher order nonlinear Schrödinger equation,” Phys. Rev. Lett. 84, 4096–4099 (2000). [CrossRef]
  33. T. Brugarino and M. Sciacca, “Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics,” Opt. Commun. 262, 250–256 (2006). [CrossRef]
  34. U. Bandelow and N. Akhmediev, “Persistence of rogue waves in extended nonlinear Schrödinger equations: integrable Sasa–Satsuma case,” Phys. Lett. A 376, 1558–1561 (2012). [CrossRef]
  35. A. Ankiewicz, J. M. Soto-Crespo, and N. Akhmediev, “Rogue waves and rational solutions of the Hirota equation,” Phys. Rev. E 81, 046602 (2010). [CrossRef]
  36. N. Akhmediev, V. I. Korneev, and N. V. Mitskevich, “Modulation instability of CW signal in an optical fiber with the 3rd-order dispersion,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 33, 95–100 (1990); Radiofiz 33, 111–117 (1990).

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