The European Physical Journal Special Topics

, Volume 223, Issue 13, pp 2847–2856

A numerical bifurcation study of a basic model of two coupled lasers with saturable absorption

Regular Article Bifurcations and Chaos
Part of the following topical collections:
  1. Advanced Computational and Experimental Techniques in Nolinear Dynamics. Guest Editors: Elbert E.N. Macau and Carlos L. Pando Lambruschini (Eds.)

Abstract

We consider a basic rate-equation model for the gains and intensities of two identical lasers that are mutually coupled via fast saturable absorbers. A numerical bifurcation study with the software package AUTO reveals the prevalence of multistability between different types of stable solutions of the system, including stationary states and in-phase, anti-phase and intermediate-phase oscillations.

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References

  1. 1.
    N.B. Abraham, P. Mandel, L.M. Narducci, Progress in Optics XXV, E. Wolf (eds.), North-Holland, Amsterdam, 1 (1988)Google Scholar
  2. 2.
    F.T. Arecchi, R. Meucci, G. Puccioni, et al., Phys. Rev. Lett. 49, 1217 (1982)ADSCrossRefGoogle Scholar
  3. 3.
    S. Barbay, R. Kuszelewicz, A.M. Yacomotti, Opt. Lett. 36, 4476 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    A. Barsella, C. Lepers, D. Dangoisse, P. Glorieux, T. Erneux, Opt. Commun. 165, 251 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    C. Bonatto, J. C. Garreau, J.A.C. Gallas, Phys. Rev. Lett. 95, 143905 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    T.W. Carr, T. Erneux, IEEE J. Quant. Electron. 37, 1171 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    E.J. Doedel, B.E. Oldeman, et al., AUTO-07P: Continuation, bifurcation software for ordinary differential equations, Vol. 8, Concordia University, Montréal, Canada (2011)Google Scholar
  8. 8.
    E.J. Doedel, B.E. Oldeman, C.L. Pando L., IJBC 21, 305 (2011)ADSMathSciNetMATHGoogle Scholar
  9. 9.
    E.J. Doedel, C.L. Pando L., IJBC 22, 1250238 (2012)MathSciNetGoogle Scholar
  10. 10.
    J.L. Dubbeldam, B. Krauskopf, Opt. Commun. 159, 325 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    J.L. Dubbeldam, B. Krauskopf, D. Lenstra, Phys. Rev. E 60 6580 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    T. Erneux, P. Glorieux, Laser Dynamics (Cambridge University Press, New York, 2010)Google Scholar
  13. 13.
    H. Erzgräber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, W. Elsäßer, Opt. Commun. 255, 286 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    H. Erzgräber, B. Krauskopf, D. Lenstra, SIAM J. Appl. Dynam. Syst. 5, 30 (2006)ADSCrossRefMATHGoogle Scholar
  15. 15.
    Ch. Harder, K.Y. Lau, A. Yariv, Appl. Phys. Lett. 39, 382 (1981)ADSCrossRefGoogle Scholar
  16. 16.
    M.T. Hill, et al., IEEE Trans. Neural Net. 13, 1504 (2002)CrossRefGoogle Scholar
  17. 17.
    A. Huber, P. Szmolyan, SIAM J. Appl. Dyn. Syst. 4, 607 (2005)ADSCrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    E.M. Izhikevich Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (MIT Press, Cambridge MA, 2007)Google Scholar
  19. 19.
    S. Jalil, I. Belykh, A. Shilnikov, Phys. Rev. E 85, 036214 (2012)ADSCrossRefGoogle Scholar
  20. 20.
    U. Keller, Nature 424, 831 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    B. Krauskopf, H.M. Osinga, J. Galán-Vioque (eds.), Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems (Springer-Verlag, New York, 2007)Google Scholar
  22. 22.
    G.J. Lasher, Solid Sate Electron. 7, 707 (1964)ADSCrossRefGoogle Scholar
  23. 23.
    P. Mandel, Theoretical Problems in Cavity Nonlinear Optics (Cambridge University Press, New York, 2005)Google Scholar
  24. 24.
    J.D. Murray, Mathematical Biology, 2nd ed. (Springer-Verlag, New York, 1993)Google Scholar
  25. 25.
    J. Ohtsubo, Semiconductor Lasers (Springer-Verlag, Berlin, 2006)Google Scholar
  26. 26.
    A. Penzkofer, Appl. Phys. B: Photophys. Laser Chem. 46, 43 (1988)ADSCrossRefGoogle Scholar
  27. 27.
    A. Scire, C.J. Tessone, P. Colet, IEEE J. Quantum Electron. 41, 272 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    F. Selmi, S. Haddadi, R. Braive, I. Sagnes, G. Beaudoin, R. Kuszelewicz, A.M. Yacomotti, S. Barbay, Self-pulsing and fast excitable response in micropillar and nano-lasers with saturable absorber, Proceedings of Sixth Rio De La Plata Workshop on Laser Dynamics and Nonlinear Photonics, IEEE Explore (2013)Google Scholar
  29. 29.
    T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu, Phys. Rev. Lett. 72, 3502 (1994)ADSCrossRefGoogle Scholar
  30. 30.
    I. Susa, T. Erneux, A. Barsella, C. Lepers, D. Dangoisse, P. Glorieux, Phys. Rev. A 63, 013815 (2000)ADSCrossRefGoogle Scholar
  31. 31.
    H.G. Winful, Y.C. Chen, J.M. Liu, Appl. Phys. Lett. 48, 616 (1986)ADSCrossRefGoogle Scholar
  32. 32.
    A.M. Yacomotti, S. Haddadi, S. Barbay, Phys. Rev. A 87, 041804(R) (2013)ADSCrossRefGoogle Scholar
  33. 33.
    M. Yamada, IEEE J. Quant. Electron. 29, 1330 (1993)ADSCrossRefGoogle Scholar
  34. 34.
    M.C. Soriano, J. Garcia-Ojalvo, C.R. Mirasso, I. Fischer, Rev. Mod. Phys. 85, 421 (2013)ADSCrossRefGoogle Scholar
  35. 35.
    F. Selmi, R. Braive, G. Beaudoin, I. Sagnes, R. Kuszelewicz, S. Barbay, Phys. Rev. Lett. 112, 183902 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    B. Ibarz, J.M. Casado, M.A.F. Sanjuán, Phys. Reports 501, 1 (2011)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Department of Computer ScienceConcordia UniversityMontréalCanada
  2. 2.Department of MathematicsThe University of AucklandAucklandNew Zealand
  3. 3.Instituto de FísicaBenemérita Universidad Autónoma de PueblaPueblaMéxico

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