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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 29, Iss. 11 — Nov. 1, 2012
  • pp: 3119–3127

Localized nonlinear waves in a two-mode nonlinear fiber

Li-Chen Zhao and Jie Liu  »View Author Affiliations


JOSA B, Vol. 29, Issue 11, pp. 3119-3127 (2012)
http://dx.doi.org/10.1364/JOSAB.29.003119


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Abstract

We find that diverse nonlinear waves, such as soliton, Akhmediev breather, and rogue waves (RWs), can emerge and interplay with each other in a two-mode coupled system. It provides a good platform to study interaction between different kinds of nonlinear waves. In particular, we obtain dark RWs analytically for the first time in the coupled system, and find that two RWs can appear in the temporal-spatial distribution. Possible ways to observe these nonlinear waves are discussed.

© 2012 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(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: August 3, 2012
Revised Manuscript: September 18, 2012
Manuscript Accepted: September 19, 2012
Published: October 23, 2012

Citation
Li-Chen Zhao and Jie Liu, "Localized nonlinear waves in a two-mode nonlinear fiber," J. Opt. Soc. Am. B 29, 3119-3127 (2012)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-11-3119


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References

  1. 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]
  2. T. C. Hernandez, V. E. Villargan, V. N. Serkin, G. M. Aguero, T. L. Belyaeva, M. R. Pena, and L. L. Morales, “Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential: I. Bright solitons,” Quantum Electron. 35, 778–786 (2005). [CrossRef]
  3. P. G. Kevrekidis, G. Theocharis, D. J. Frantzeskakis, and Boris A. Malomed, “Feshbach resonance management for Bose-Einstein condensates,” Phys. Rev. Lett. 90, 230401 (2003). [CrossRef]
  4. K. H. Han and H. J. Shin, “Nonautonomous integrable nonlinear Schrödinger equations with generalized external potentials,” J. Phys. A 42, 335202 (2009). [CrossRef]
  5. L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, “Formation of a matter-wave bright soliton,” Science 296, 1290–1293 (2002). [CrossRef]
  6. W. B. Cardoso, A. T. Avelar, and D. Bazeia, “Modulation of breathers in cigar-shaped Bose-Einstein condensates,” Phys. Lett. A 374, 2640–2645 (2010). [CrossRef]
  7. S. Burger, K. Bongs, S. Dettmer, W. Ertmer, and K. Sengstock, “Dark solitons in Bose-Einstein condensates,” Phys. Rev. Lett. 83, 5198–5201 (1999). [CrossRef]
  8. J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark, L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley, K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. D. Phillips, “Generating solitons by phase engineering of a Bose-Einstein condensate,” Science 287, 97–101 (2000). [CrossRef]
  9. T. Busch, and J. R. Anglin, “Motion of dark solitons in trapped Bose-Einstein condensates,” Phys. Rev. Lett. 84, 2298–2301 (2000). [CrossRef]
  10. C. K. Law, C. M. Chan, P. T. Leung, and M.-C. Chu, “Motional dressed states in a Bose-Einstein condensate: superfluidity at supersonic speed,” Phys. Rev. Lett. 85, 1598–1601 (2000). [CrossRef]
  11. B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark, and E. A. Cornell, “Watching dark solitons decay into vortex rings in a Bose-Einstein condensate,” Phys. Rev. Lett. 86, 2926–2929 (2001). [CrossRef]
  12. B. Wu, J. Liu, and Q. Niu, “Controlled generation of dark solitons with phase imprinting,” Phys. Rev. Lett. 88, 034101 (2002). [CrossRef]
  13. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman and Hall, 1997).
  14. N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, “Extreme waves that appear from nowhere: on the nature of rogue waves,” Phys. Lett. A 373, 2137–2145 (2009). [CrossRef]
  15. V. I. Shrira and V. V. Geogjaev, “What makes the Peregrine soliton so special as a prototype of freak waves?,” J. Eng. Math. 67, 11–22 (2010). [CrossRef]
  16. 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]
  17. Q. H. Park and H. J. Shin, “Systematic construction of multicomponent optical solitons,” Phys. Rev. E 61, 3093–3106 (2000). [CrossRef]
  18. P. Kockaert, P. Tassin, G. V. Sande, I. Veretennicoff, and M. Tlidi, “Negative diffraction pattern dynamics in nonlinear cavities with left-handed materials,” Phys. Rev. A 74, 033822 (2006). [CrossRef]
  19. T. Kanna, and M. Lakshmanan, “Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations,” Phys. Rev. Lett. 86, 5043–5046(2001). [CrossRef]
  20. M. Vijayajayanthi, T. Kanna, and M. Lakshmanan, “Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schrödinger equations,” Phys. Rev. A 77, 013820 (2008). [CrossRef]
  21. M. Vijayajayanthi, T. Kanna, and M. Lakshmanan, “Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing, defocusing and mixed type nonlinearities,” Eur. Phys. J., Spec. Top. 173, 57–80 (2009).
  22. L. C. Zhao and S. L. He, “Matter wave solitons in coupled system with external potentials,” Phys. Lett. A 375, 3017–3020(2011). [CrossRef]
  23. C. Becker, S. Stellmer, P. S. Panahi, S. Dorscher, M. Baumert, E.-M. Richter, J. Kronjager, K. Bongs, and K. Sengstock, “Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates,” Nat. Phys. 4, 496–501 (2008). [CrossRef]
  24. M. G. Forest, S. P. Sheu, and P. C. Wright, “On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrödinger systems,” Phys. Lett. A 266, 24–33 (2000). [CrossRef]
  25. B. L. Guo and L. M. Ling, “Rogue wave, breathers and bright-dark-rogue solutions for the coupled Schrödinger equations,” Chin. Phys. Lett. 28, 110202 (2011). [CrossRef]
  26. B. Crosignani and P. Di Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329–331 (1981). [CrossRef]
  27. V. V. Afanasyev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805–807 (1989). [CrossRef]
  28. M. Haelterman and A. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994). [CrossRef]
  29. Y. V. Bludov, V. V. Konotop, and N. Akhmediev, “Vector rogue waves in binary mixtures of Bose-Einstein condensates,” Eur. Phys. J. Spec. Top. 185, 169–180 (2010). [CrossRef]
  30. B. L. Guo, L. M. Ling, and Q. P. Liu, “Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions,” Phys. Rev. E 85, 026607 (2012). [CrossRef]
  31. Y. Ohta and J. K. Yang, “General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation,” Proc. R. Soc. Lond. Ser. A468, 1716–1740 (2012).
  32. Y. V. Bludov, V. V. Konotop, and N. Akhmediev, “Matter rogue waves,” Phys. Rev. A 80, 033610 (2009). [CrossRef]
  33. 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]
  34. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007). [CrossRef]
  35. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008). [CrossRef]
  36. T. Ueda and W. L. Lath, “Dynamics of coupled solitons in nonlinear optical fibers,” Phys. Rev. A 42, 563–571 (1990). [CrossRef]
  37. 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]
  38. C. Cambournac, T. Sylvestre, H. Maillotte, B. Vanderlinden, P. Kockaert, Ph. Emplit, and M. Haelterman, “Symmetry-breaking instability of multimode vector solitons,” Phys. Rev. Lett. 89, 083901 (2002). [CrossRef]
  39. P. Das, T. S. Raju, U. Roy, and P. K. Panigrahi, “Sinusoidal excitations in two-component Bose-Einstein condensates in a trap,” Phys. Rev. A 79, 015601 (2009). [CrossRef]
  40. E. V. Doktorov, V. M. Rothos, and Y. S. Kivshar, “Full-time dynamics of modulational instability in spinor Bose-Einstein condensates,” Phys. Rev. A 76, 013626 (2007). [CrossRef]
  41. M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901(2011). [CrossRef]
  42. F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012). [CrossRef]

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