Skip to main content
SpringerLink
Log in

Optical breathers and multiple rogue waves via the modulation instability for a complex Ginzburg–Landau equation in the mode-locked laser operation

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Investigation is made on a complex Ginzburg–Landau equation for the mode-locked laser operation. Optical breathers are numerically derived via the split-step Fourier method. Effects of the modulation instability on the dynamic behaviors of the optical breathers are investigated: when the growth rate of the modulation instability increases, the optical breather splits into two optical breathers earlier, and the two optical breathers separate faster. Via the energy distributions of the optical breathers, we obtain that when the fission phenomenon occurs, the energy decreases more than that of the fusion phenomenon. Multiple rogue waves in the chaotic wave field are obtained via the modulation instability. It is observed that multiple rogue waves occur earlier as the growth rate of the modulation instability becomes larger. Occurrence of the rogue wave can be predicted via the spectrum of the optical chaotic wave field.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G.P. Agarwal, Applications of Nonlinear Fiber Optics (Academic Press, New York, NY, 2001)

  2. A. Biswas, Opt. Quantum Electron. 35, 979 (2003)

    Article  Google Scholar 

  3. A. Biswas, Opt. Commun. 239, 461 (2004)

    Article  ADS  Google Scholar 

  4. A. Biswas, A. Jawad, W. Manrakhan, A.K. Sarma, K.R. Khan, Opt. Laser Technol. 44, 2265 (2012)

    Article  ADS  Google Scholar 

  5. L.F. Mollenauer, R.H. Stolen, J.P. Gordon, Phys. Rev. Lett. 45, 1095 (1980)

    Article  ADS  Google Scholar 

  6. F.K. Abdullaev, J. Garnier, Phys. Rev. E 72, 035603 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  7. J.H. Li, H.N. Chan, K.S. Chiang, K.W. Chow, Commun. Nonlinear Sci. Numer. Simul. 28, 28 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  8. Z.Z. Lan, Appl. Math. Lett. 86, 243 (2018)

    Article  MathSciNet  Google Scholar 

  9. Z.Z. Lan, B. Guo, Appl. Math. Lett. 79, 6 (2018)

    Article  MathSciNet  Google Scholar 

  10. X.Y. Xie, G.Q. Meng, Nonlinear Dyn. 93, 779 (2018)

    Article  Google Scholar 

  11. H.L. Zhen, B. Tian, Y.F. Wang, W.R. Sun, L.C. Liu, Phys. Plasma 21, 073709 (2014)

    Article  ADS  Google Scholar 

  12. H.L. Zhen, B. Tian, Y.F. Wang, H. Zhong, W.R. Sun, Phys. Plasma 21, 012304 (2014)

    Article  ADS  Google Scholar 

  13. H.L. Zhen, B. Tian, Y.F. Wang, D.Y. Liu, Phys. Plasma 22, 0322307 (2015)

    Google Scholar 

  14. W.R. Sun, D.Y. Liu, X.Y. Xie, Chaos 27, 043114 (2017)

    Article  ADS  Google Scholar 

  15. L.C. Zhao, S.C. Li, L. Ling, Phys. Rev. E 89, 023210 (2014)

    Article  ADS  Google Scholar 

  16. C. Yang, W. Liu, Q. Zhou, D. Mihalache, B.A. Malomed, Nonlinear Dyn. 95, 369 (2019)

    Article  Google Scholar 

  17. C. Yang, A.B. Wazwaz, Q. Zhou, W. Liu, Laser Phys. 29, 035401 (2019)

    Article  ADS  Google Scholar 

  18. X. Liu, H. Triki, Q. Zhou, M. Mirzazadeh, W. Liu, A. Biswas, M. Belic, Nonlinear Dyn. 95, 143 (2019)

    Article  Google Scholar 

  19. N. Akhmediev, J.M. Soto-Crespo, A. Ankiewicz, Phys. Rev. A 80, 043818 (2009)

    Article  ADS  Google Scholar 

  20. Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, New York, NY, 2003)

  21. D.J. Kedziora, A. Ankiewicz, N. Akhmediev, Phys. Rev. E 85, 066601 (2012)

    Article  ADS  Google Scholar 

  22. N. Akhmediev, J.M. Soto-crespo, A. Ankiewicz, Phys. Lett. A 373, 2137 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. W.P. Hong, Opt. Commun. 213, 173 (2002)

    Article  ADS  Google Scholar 

  24. A. Choudhuri, K. Porsezian, Phys. Rev. A 85, 033820 (2012)

    Article  ADS  Google Scholar 

  25. N. Jiang, C. Wang, C. Xue, G. Li, S. Lin, K. Qiu, Opt. Express 25, 14359 (2017)

    Article  ADS  Google Scholar 

  26. D.N. Urrios, N.E. Capuj, M.F. Colombano, P.D. Garcia, M. Sledzinska, F. Alzina, A. Griol, A. Martinez, M. Clivia, Nat. Commun. 8, 14965 (2017)

    Article  ADS  Google Scholar 

  27. W. Liu, W. Yu, C. Yang, M. Liu, Y. Zhang, M. Lei, Nonlinear Dyn. 89, 2933 (2017)

    Article  Google Scholar 

  28. W. Chang, J.M. Soto-Crespo, P. Vouzas, N. Akhmediev, Opt. Lett. 40, 2949 (2015)

    Article  ADS  Google Scholar 

  29. N. Akhmediev, J.M. Soto-Crespo, G. Town, Phys. Rev. E 63, 056602 (2001)

    Article  ADS  Google Scholar 

  30. J.M. Soto-Crespo, N. Devine, N.P. Hoffmann, N. Akhmediev, Phys. Rev. E 90, 032902 (2014)

    Article  ADS  Google Scholar 

  31. M. Djoko, T.C. Kofane, Commun. Nonlinear Sci. Numer. Simul. 48, 179 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  32. J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, 2010)

  33. J.W. Demmel, Applied Numerical Linear Algebra (SIAM, Philadelphia, 1997)

  34. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, NY, 2013)

  35. A. Kundu, J. Math. Phys. 25, 3433 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  36. M. Li, J.J. Shui, T. Xu, Appl. Math. Lett. 83, 110 (2018)

    Article  MathSciNet  Google Scholar 

  37. J.M. Soto-Crespo, N. Devine, N.P. Hoffmann, N. Akhmediev, J. Opt. Soc. Am. B 34, 1542 (2017)

    Article  ADS  Google Scholar 

  38. P. Ryczkowski, M. Närhi, C. Billet, J.M. Merolla, G. Genty, J.M. Dudley, Nat. Photonics 12, 221 (2018)

    Article  ADS  Google Scholar 

  39. R. Reigada, A. Sarmiento, K. Lindenberg, Chaos 13, 646 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  40. R. Reigada, A. Sarmiento, K. Lindenberg, Phys. Rev. E 66, 046607 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  41. H.N. Chan, K.W. Chow, Stud. Appl. Math. 139, 78 (2017)

    Article  MathSciNet  Google Scholar 

  42. N. Akhmediev, J.M. Soto-Crespo, N. Devine, N.P. Hoffmann, Physica D 294, 37 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, School of Science, and Automation School, Beijing University of Posts and Telecommunications, 100876, Beijing, P.R. China

    Hui-Min Yin, Bo Tian, Zhong Du & Xin-Chao Zhao

Authors
  1. Hui-Min Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhong Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xin-Chao Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bo Tian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, HM., Tian, B., Du, Z. et al. Optical breathers and multiple rogue waves via the modulation instability for a complex Ginzburg–Landau equation in the mode-locked laser operation. Eur. Phys. J. D 73, 147 (2019). https://doi.org/10.1140/epjd/e2019-100184-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2019-100184-0

Keywords

Search

Navigation