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Secondary Instabilities and Chaos in Optical Ring Cavities

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Nonlinear Dynamics: Materials, Theory and Experiments

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 173))

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Abstract

The dynamical evolution of the modulational instability is studied in a coherently driven passive optical fiber cavity. We show that periodic pattern generated close to the threshold experience convective and absolute Eckhaus instabilities. In addition to this splitting of the secondary instabilities into convective and absolute instabilities we have observed that the onset of the absolute regime is accompanied by the emergence of spatio-temporal chaos.

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References

  1. M. Tlidi, M. Taki, T. Kolokolnikov, Chaos 17, 037101 (2007)

    Article  ADS  Google Scholar 

  2. N. Akhmediev, A. Ankiewicz, Dissipative Solitons: From Optics to Biology and Medicine (Springer, Berlin, 2008)

    MATH  Google Scholar 

  3. A. Mussot, E. Louvergneaux, N. Akhmediev, F. Reynaud, L. Delage, M. Taki, Phys. Rev. Lett. 101, 113904 (2008)

    Article  ADS  Google Scholar 

  4. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, Nat. Photonics 4, 471 (2010)

    Article  ADS  Google Scholar 

  5. A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, M. Douay, Phys. Lett. A 374, 691 (2010)

    Article  ADS  Google Scholar 

  6. F. Leo, A. Mussot, P. Kockaert, P. Emplit, M. Haelterman, M. Taki, Phys. Rev. Lett. 110, 104103 (2013)

    Article  ADS  Google Scholar 

  7. J.A. Sherratt, M.J. Smith, J.D.M. Rademacher, Proc. Natl. Acad. Sci. USA 106, 10890 (2009)

    Article  ADS  Google Scholar 

  8. L.A. Lugiato, R. Lefever, Phys. Rev. Lett. 58, 2209 (1987)

    Article  ADS  Google Scholar 

  9. M. Haelterman, S. Trillo, S. Wabnitz, Opt. Commun. 91, 401 (1992)

    Article  ADS  Google Scholar 

  10. R. Zambrini, M. San Miguel, C. Durniak, M. Taki. Phys. Rev. E 72, 025603 (2005)

    Google Scholar 

  11. P. Manneville, Instabilities, Chaos and Turbulence (Imperial College Press, London, 1994)

    MATH  Google Scholar 

  12. I.S. Aranson, L. Kramer, Rev. Mod. Phys. 74, 99 (2002)

    Article  ADS  Google Scholar 

  13. I.S. Aranson, L. Aranson, L. Kramer, A. Weber, Phy. Rev. A 46, 2992 (1992)

    Article  ADS  Google Scholar 

  14. P. Huerre, P.A. Monkewitz, Annu. Rev. Fluid Mech. 22, 473 (1990)

    Article  ADS  Google Scholar 

  15. C. Bender, S. Orszag, Advanced Mathematical Methods for Scientists and Engineers (MacGraw-Hill, New York, 1978)

    MATH  Google Scholar 

  16. H. Ward, M.N. Ouarzazi, M. Taki, P. Glorieux, Phys. Rev. E 63, 016604 (2000)

    Article  ADS  Google Scholar 

  17. G.S. Triantafyllou, Phys. Fluids 6, 164 (1993)

    Article  ADS  Google Scholar 

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Correspondence to S. Coulibaly .

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Liu, Z., Leo, F., Coulibaly, S., Taki, M. (2016). Secondary Instabilities and Chaos in Optical Ring Cavities. In: Tlidi, M., Clerc, M. (eds) Nonlinear Dynamics: Materials, Theory and Experiments. Springer Proceedings in Physics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-24871-4_12

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