Skip to main content
Springer Nature Link
Log in

Frequency conversion dynamics of vector modulation instability in normal-dispersion high-birefringence fibers

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We investigate the frequency conversion associated with the nonlinear stage of vector modulational instability in high-birefringence fibers with normal group-velocity dispersion. A complex heteroclinic structure of instability reveals all possible dynamic trajectories of frequency conversion. It is shown that different Fermi–Pasta–Ulam recurrent regimes are separated by Akhmediev breathers corresponding to a separatrix on the heteroclinic structure. We also demonstrate that the optimal frequency conversion unexpectedly occurs outside the parametric gain bandwidth when the input light is polarized close to 45° from a principal axis of the fiber, whereas the optimal conversion frequency gradually shifts into the gain region when the polarization direction of input light tilts toward the principal axis of the fiber.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Kip, D., Soljacic, M., Segev, M., Eugenieva, E., Christodoulides, D.N.: Modulation instability and pattern formation in spatially incoherent light beams. Science 290, 495 (2000)

    Article  Google Scholar 

  2. Erkintalo, M., Hammani, K., Kibler, B., Finot, C., Akhmediev, N., Dudley, J.M., Genty, G.: Higher-order modulation instability in nonlinear fiber optics. Phys. Rev. Lett. 107, 253901 (2011)

    Article  Google Scholar 

  3. Solli, D., Herink, G., Jalali, B., Ropers, C.: Fluctuations and correlations in modulation instability. Nat. Photonics 6, 463 (2012)

    Article  Google Scholar 

  4. Tang, B., Deng, K.: Discrete breathers and modulational instability in a discrete φ4 nonlinear lattice with next-nearest-neighbor couplings. Nonlinear Dyn. 88, 2417 (2017)

    Article  MathSciNet  Google Scholar 

  5. Zakharov, V.E., Ostrovsky, L.A.: Modulation instability: the beginning. Physica D 238, 540 (2009)

    Article  MathSciNet  Google Scholar 

  6. Dudley, J., Dias, F., Erkintalo, M., Genty, G.: Instabilities, breathers and rogue waves in optics. Nat. Photonics 8, 755 (2014)

    Article  Google Scholar 

  7. Akhmediev, N., Soto-Crespo, J.M., Ankiewicz, A.: Extreme waves that appear from nowhere: on the nature of rogue waves. Phys. Lett. A 373, 2137 (2009)

    Article  MathSciNet  Google Scholar 

  8. Zakharov, V., Gelash, A.: Nonlinear stage of modulation instability. Phys. Rev. Lett. 111, 054101 (2013)

    Article  Google Scholar 

  9. Mussot, A., Kudlinski, A., Droques, M., Szriftgiser, P., Akhmediev, N.: Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses. Phys. Rev. X 4, 011054 (2014)

    Google Scholar 

  10. Pierangeli, D., Flammini, M., Zhang, L., Marcucci, G., Agranat, A., Grinevich, P., Santini, P., Conti, C., DelRe, E.: Observation of Fermi–Pasta–Ulam–Tsingou recurrence and its exact dynamics. Phys. Rev. X 8, 041017 (2018)

    Google Scholar 

  11. Mussot, A., Naveau, C., Conforti, M., Kudlinski, A., Copie, F., Szriftgiser, P., Trillo, S.: Fibre multi-wave mixing combs reveal the broken symmetry of Fermi–Pasta–Ulam recurrence. Nat. Photonics 12, 303 (2018)

    Article  Google Scholar 

  12. Liu, C., Yang, Z.Y., Yang, W.L.: Growth rate of modulation instability driven by superregular breathers. Chaos 28, 083110 (2018)

    Article  MathSciNet  Google Scholar 

  13. Gelash, A., Zakharov, V.: Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability. Nonlinearity 27, R1 (2014)

    Article  MathSciNet  Google Scholar 

  14. Hammani, K., Wetzel, B., Kibler, B., Fatome, J., Finot, C., Millot, G., Akhmediev, N., Dudley, J.: Spectral dynamics of modulation instability described using Akhmediev breather theory. Opt. Lett. 36, 2140 (2011)

    Article  Google Scholar 

  15. Frisquet, B., Kibler, B., Millot, G.: Collision of Akhmediev breathers in nonlinear fiber optics. Phys. Rev. X 3, 041032 (2013)

    Google Scholar 

  16. Liu, C., Yang, Z., Zhao, L., Xin, G., Yang, W.: Optical rogue waves generated on Gaussian background beam. Opt. Lett. 39, 1057 (2014)

    Article  Google Scholar 

  17. Wang, X., Wei, J., Wang, L., Zhang, J.: Baseband modulation instability, rogue waves and state transitions in a deformed Fokas–Lenells equation. Nonlinear Dyn. 97, 343 (2019)

    Article  Google Scholar 

  18. Yin, H.M., Tian, B., Zhang, C.R., Du, X.X., Zhao, X.C.: Optical breathers and rogue waves via the modulation instability for a higher-order generalized nonlinear Schrödinger equation in an optical fiber transmission system. Nonlinear Dyn. 97, 843 (2019)

    Article  Google Scholar 

  19. Trillo, S., Wabnitz, S.: Dynamics of the nonlinear modulational instability in optical fibers. Opt. Lett. 16, 986 (1991)

    Article  Google Scholar 

  20. Conforti, M., Mussot, A., Kudlinski, A., Nodari, S., Dujardin, G., De Biévre, S., Armaroli, A., Trillo, S.: Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation. Phys. Rev. Lett. 117, 013901 (2016)

    Article  Google Scholar 

  21. Bendahmane, A., Mussot, A., Kudlinski, A., Szriftgiser, P., Conforti, M., Wabnitz, S., Trillo, S.: Optimal frequency conversion in the nonlinear stage of modulation instability. Opt. Express 23, 30861 (2015)

    Article  Google Scholar 

  22. Agrawal, G.P.: Nonlinear Fiber Optics, 5th edn. Academic, Cambridge (2013)

    MATH  Google Scholar 

  23. Guo, D., Tian, S.F., Zhang, T.T., Li, J.: Modulation instability analysis and soliton solutions of an integrable coupled nonlinear Schrödinger system. Nonlinear Dyn. 94, 2749 (2018)

    Article  Google Scholar 

  24. Zhao, L.C.: Beating effects of vector solitons in Bose–Einstein condensates. Phys. Rev. E 97, 062201 (2018)

    Article  Google Scholar 

  25. Zhao, L., Duan, L., Gao, P., Yang, Z.: Vector rogue waves on a double-plane wave background. EPL 125, 40003 (2019)

    Article  Google Scholar 

  26. Li, J.T., Han, J.Z., Du, Y.D., Dai, C.Q.: Controllable behaviors of Peregrine soliton with two peaks in a birefringent fiber with higher-order effects. Nonlinear Dyn. 82, 1393 (2015)

    Article  MathSciNet  Google Scholar 

  27. Seve, E., Millot, G., Trillo, S., Wabnitz, S.: Large-signal enhanced frequency conversion in birefringent optical fibers: theory and experiments. JOSA B 15, 2537 (1998)

    Article  Google Scholar 

  28. Cappellini, G., Trillo, S.: Bifurcations and three-wave-mixing instabilities in nonlinear propagation in birefringent dispersive media. Phys. Rev. A 44, 7509 (1991)

    Article  Google Scholar 

  29. Zhang, Y., Yang, C., Yu, W., Mirzazadeh, M., Zhou, Q., Liu, W.: Interactions of vector anti-dark solitons for the coupled nonlinear Schrödinger equation in inhomogeneous fibers. Nonlinear Dyn. 94, 1351 (2018)

    Article  Google Scholar 

  30. Millot, G., Wabnitz, S.: Nonlinear polarization effects in optical fibers: polarization attraction and modulation instability. JOSA B 31, 2754 (2014)

    Article  Google Scholar 

  31. Millot, G., Seve, E., Wabnitz, S., Haelterman, M.: Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber. Opt. Lett. 23, 511 (1998)

    Article  Google Scholar 

  32. Seve, E., Millot, G., Wabnitz, S.: Buildup of terahertz vector dark-soliton trains from induced modulation instability in highly birefringent optical fiber. Opt. Lett. 23, 1829 (1998)

    Article  Google Scholar 

  33. Gilles, M., Bony, P., Garnier, J., Picozzi, A., Guasoni, M., Fatome, J.: Polarization domain walls in optical fibres as topological bits for data transmission. Nat. Photonics 11, 102 (2017)

    Article  Google Scholar 

  34. Lecaplain, C., Grelu, P., Wabnitz, S.: Polarization-domain-wall complexes in fiber lasers. JOSA B 30, 211 (2013)

    Article  Google Scholar 

  35. Seve, E., Millot, G., Trillo, S.: Strong four-photon conversion regime of cross-phase-modulation-induced modulational instability. Phys. Rev. E 61, 3139 (2000)

    Article  Google Scholar 

  36. De Angelis, C., Santagiustina, M., Trillo, S.: Four-photon homoclinic instabilities in nonlinear highly birefringent media. Phys. Rev. A 51, 774 (1995)

    Article  Google Scholar 

  37. Guasoni, M., Wabnitz, S.: Nonlinear polarizers based on four-wave mixing in high-birefringence optical fibers. JOSA B 29, 1511 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) (12004309, 11875220, 11975183, 11425522), and by Scientific Research Program Funded by Shaanxi Provincial Education Department (20JK0947).

Author information

Authors and Affiliations

  1. School of Physics, Northwest University, Xi’an, 710069, China

    Xiankun Yao, Zhan-Ying Yang & Wen-Li Yang

  2. Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi’an, 710069, China

    Xiankun Yao, Zhan-Ying Yang & Wen-Li Yang

  3. Institute of Modern Physics, Northwest University, Xi’an, 710069, China

    Wen-Li Yang

Authors
  1. Xiankun Yao
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Zhan-Ying Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Wen-Li Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Zhan-Ying Yang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, X., Yang, ZY. & Yang, WL. Frequency conversion dynamics of vector modulation instability in normal-dispersion high-birefringence fibers. Nonlinear Dyn 103, 1035–1041 (2021). https://doi.org/10.1007/s11071-020-06181-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-06181-6

Keywords