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Dynamics of Liénard Optoelectronic Oscillators

  • Bruno RomeiraEmail author
  • José Figueiredo
  • Charles N. Ironside
  • Julien Javaloyes
Part of the Studies in Computational Intelligence book series (SCI, volume 483)

Abstract

In this chapter we present a comprehensive study on the dynamics of novel nonlinear optoelectronic oscillators (OEO) modeled by Liénard OEO systems. The OEO dynamical systems are based on negative differential resistance resonant tunneling diode oscillators incorporating a photoconductive region and laser diodes. The modeling results are in a good agreement with the wide variety dynamics that has been observed in recent experimental work spanning from self-sustained relaxation oscillations to injection locking and chaotic behaviors in both electrical and optical domains. Potential applications range from generation of periodic and chaotic signals for chaos-based communication schemes to highly stabilized OEOs for microwave-photonic systems.

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References

  1. 1.
    Strogatz, S.H.: Nonlinear Dynamics and Chaos. Addison-Wesley, New York (1994)Google Scholar
  2. 2.
    Simpson, T.B., Liu, J.M., Huang, K.F., Tai, K.: Nonlinear dynamics induced by external optical injection in semiconductor lasers. Quantum and Semiclassical Optics 9, 765–784 (1997)CrossRefGoogle Scholar
  3. 3.
    Wieczorek, S., Krauskopf, B., Lenstra, D.: A unifying view of bifurcations in a semiconductor laser subject to optical injection. Optics Communications 172, 1–6 (1999)CrossRefGoogle Scholar
  4. 4.
    Lang, R., Kobayashi, K.: External optical feedback effects on semiconductor injection laser properties. IEEE J. Quantum Electron. 16, 347–355 (1980)CrossRefGoogle Scholar
  5. 5.
    Dahmani, B., Hollberg, L., Drullinger, R.: Frequency stabilization of semiconductor-lasers by resonant optical feedback. Optics Letters 12, 7876 (1987)CrossRefGoogle Scholar
  6. 6.
    Mork, J., Tromborg, B., Mark, J.: Chaos in semiconductor-lasers with optical feedback - theory and experiment. IEEE J. Quantum Electron. 28, 93 (1992)CrossRefGoogle Scholar
  7. 7.
    Tang, S., Liu, J.M.: Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback. IEEE J. Quantum Electron. 37, 329–336 (2001)CrossRefGoogle Scholar
  8. 8.
    Ohtsubo, J.: Semiconductor Lasers: Stability, Instability and Chaos. Springer (2005)Google Scholar
  9. 9.
    Ikeda, K., Kondo, K., Akimoto, O.: Successive higher-harmonic bifurcations in systems with delayed feedback. Phys. Rev. Lett. 49, 1467–1470 (1982)CrossRefGoogle Scholar
  10. 10.
    Murphy, T.E., Cohen, A.B., Ravoori, B., Schmitt, K.R.B., Setty, A.V., Sorrentino, F., Williams, C.R.S., Ott, E., Roy, R.: Complex dynamics and synchronization of delayed-feedback nonlinear oscillators. Phil. Trans. R. Soc. A. 368, 343–366 (2010)zbMATHCrossRefGoogle Scholar
  11. 11.
    Yao, X.Y., Maleki, L.: Optoelectronic oscillator for photonic systems. IEEE J. Quantum Electron. 32, 1141–1149 (1996)CrossRefGoogle Scholar
  12. 12.
    Callan, K.E., Illing, L., Gao, Z., Gauthier, D.J., Schöll, E.: Broadband chaos generated by an optoelectronic oscillator. Phys. Rev. Lett. 104, 113901 (2010)CrossRefGoogle Scholar
  13. 13.
    Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fisher, I., Garcia-Ojalvo, J., Mirasso, C., Pesquera, L., Shore, K.A.: Chaos-based communications at high bit rates using commercial fibre-optic links. Nature 438, 343–346 (2005)CrossRefGoogle Scholar
  14. 14.
    Kouomou, Y.C., Colet, P., Larger, L., Gastaud, N.: Chaotic breathers in delayed electro-optical systems. Phys. Rev. Lett. 95, 203903 (2005)CrossRefGoogle Scholar
  15. 15.
    Illing, L., Gauthier, D.J., Roy, R.: Controlling optical chaos, spatiotemporal dynamics, and patterns. Advances in Atomic, Molecular, and Optical Physics 54, 615–697 (2006)CrossRefGoogle Scholar
  16. 16.
    Peil, M., Jacquot, M., Chembo, Y.K., Larger, L., Erneux, T.: Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators. Phys. Rev. E 79, 45201 (2009)CrossRefGoogle Scholar
  17. 17.
    Figueiredo, J.M.L., Romeira, B., Slight, T.J., Ironside, C.N.: Resonant tunnelling optoelectronic circuits. In: Kim, K.Y. (ed.) Advances in Optical and Photonic Devices (2010), http://www.intechopen.com/articles/show/title/resonant-tunnelling-optoelectronic-circuits
  18. 18.
    Romeira, B., Figueiredo, J.M.L., Ironside, C.N., Kelly, A.E., Slight, T.J.: Optical control of a resonant tunneling diode microwave-photonic oscillator. IEEE Photon. Technol. Lett. 22, 1610–1612 (2010)CrossRefGoogle Scholar
  19. 19.
    Romeira, B., Seunarine, K., Ironside, C.N., Kelly, A.E., Figueiredo, J.M.L.: Self-Synchronized optoelectronic oscillator based on an RTD photo-detector and a laser diode. IEEE Photon. Technol. Lett. 23, 1148–1150 (2011)CrossRefGoogle Scholar
  20. 20.
    Slight, T.J., Romeira, B., Wang, L., Figueiredo, J.M.L., Wasige, E., Ironside, C.N.: A Liénard oscillator resonant tunnelling-laser diode hybrid integrated circuit: model and experiment. IEEE J. Quantum Electron. 44, 1158–1163 (2008)CrossRefGoogle Scholar
  21. 21.
    Romeira, B., Figueiredo, J.M.L., Slight, T.J., Wang, L., Wasige, E., Ironside, C.N., Kelly, A.E., Green, R.: Nonlinear dynamics of resonant tunneling optoelectronic circuits for wireless/optical interfaces. IEEE J. Quantum Electron. 45, 1436–1445 (2009)CrossRefGoogle Scholar
  22. 22.
    Romeira, B., Figueiredo, J.M.L., Ironside, C.N., Slight, T.J.: Chaotic dynamics in resonant tunneling optoelectronic voltage controlled oscillators. IEEE Photon. Technol. Lett. 21, 1819–1821 (2009)CrossRefGoogle Scholar
  23. 23.
    Brown, E.R., McMahon, O.B., Mahoney, L.J., Molvar, K.M.: SPICE model of the resonant-tunneling diode. Electronics Lett. 32, 938–940 (1996)CrossRefGoogle Scholar
  24. 24.
    Schulman, J., Santos, H., Chow, D.: Physics-Based RTD current-voltage equation. IEEE Electron Device Lett. 17, 220–222 (1996)CrossRefGoogle Scholar
  25. 25.
    Mena, P.V., Kang, S., DeTemple, T.A.: Rate-equation-based laser models with a single solution regime. J. Lightw. Technol. 15, 717–730 (1997)CrossRefGoogle Scholar
  26. 26.
    Liénard, A.: Etude des oscillations entretenues. Rev. Gen. Electr. 28, 901–946 (1928)Google Scholar
  27. 27.
    Lins, A., Melo, W., Pugh, C.: On Liénards equation. Lecture Notes in Mathematics, vol. 597. Springer, New York (1977)Google Scholar
  28. 28.
    Hale, J.K.: Theory of functional differential equations. Springer, New York (1977)zbMATHCrossRefGoogle Scholar
  29. 29.
    Van der Pol, B.: A theory of the amplitude of free and forced triode vibrations. Radio Rev. 710, 754–762 (1920)Google Scholar
  30. 30.
    Van der Pol, B., Van der Mark, J.: Frequency demultiplication. Nature 120, 363–364 (1927)CrossRefGoogle Scholar
  31. 31.
    Arnold, V.I.: Geometrical methods in the theory of ordinary differential equations. Springer, New York (1983)zbMATHCrossRefGoogle Scholar
  32. 32.
    Zuckerman, H.S., Montgomery, H.L., Niven, I.M., Niven, A.: An Iintroduction to the theory of numbers. John Wiley, New York (1991)Google Scholar
  33. 33.
    Bennett, S., Snowden, C.M., Iezekiel, S.: Nonlinear dynamics in directly modulated multiple-quantum-well laser diodes. IEEE J. Quantum Electron. 33, 2076–2083 (1997)CrossRefGoogle Scholar
  34. 34.
    Liu, H.F., Ngai, W.F.: Nonlinear dynamics of a directly modulated 1.55 μm InGaAsP distributed feedback semiconducor laser. IEEE J. Quantum Electron. 29, 1668–1675 (1993)CrossRefGoogle Scholar
  35. 35.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical recipes: the art of scientific computing. Cambridge University Press (2007)Google Scholar
  36. 36.
    Yao, X.S., Maleki, L.: Multiloop optoelectronic oscillator. IEEE J. Quantum Electron. 36, 79–84 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bruno Romeira
    • 1
    Email author
  • José Figueiredo
    • 1
  • Charles N. Ironside
    • 2
  • Julien Javaloyes
    • 3
  1. 1.Center of Electronics Optoelectronics and Telecommunications, Department of PhysicsUniversity of the AlgarveFaroPortugal
  2. 2.School of EngineeringUniversity of GlasgowGlasgowUnited Kingdom
  3. 3.Departament de FisicaUniversitat de les Illes BalearesPalmaSpain

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