Chaos-Based Secure Optical Communications Using Semiconductor Lasers

  • Alexandre Locquet


The advent of chaos theory in the last decade has definitively separated the notions of determinism and predictability. A nonlinear dynamical system that displays a chaotic steady-state behavior is purely deterministic, but its long-term behavior cannot be predicted because of the property of sensitivity to initial conditions (SIC). This property of chaotic systems implies that two states, initially very close to each other, become very different as time elapses. Since it is impossible to know the state of a system with arbitrarily high precision, the SIC property also implies that, in practice, it is impossible to predict the long-term evolution of a chaotic system. One of the most promising applications of chaos theory, which exploits both the deterministic and unpredictable aspects of chaotic behavior, is chaos-based secure communications.


Chaotic System Semiconductor Laser Optical Feedback Chaotic Signal Slave Laser 
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  1. 24.1.
    H. Fujisaka, T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems, Prog. Theor. Phys. 69, 32–47 (1983)MATHCrossRefMathSciNetGoogle Scholar
  2. 24.2.
    H. Fujisaka, T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems. II. The mapping approach, Prog. Theor. Phys. 70, 1240–1248 (1983)MATHCrossRefMathSciNetGoogle Scholar
  3. 24.3.
    T. Yamada, H. Fujisaka: Stability theory of synchronized motion in coupled-oscillator systems. III. Mapping model for continuous system, Prog. Theor. Phys. 72, 885–894 (1984)CrossRefGoogle Scholar
  4. 24.4.
    L.M. Pecora, T.L. Carroll: Synchronization in chaotic systems, Phys. Rev. Lett. 64, 821–824 (1990)CrossRefMathSciNetGoogle Scholar
  5. 24.5.
    L.M. Pecora, T.L. Carroll: Synchronizing chaotic circuits, IEEE Trans. Circ. Syst. 38, 453–456 (1991)CrossRefGoogle Scholar
  6. 24.6.
    N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, H.D.I. Abarbanel: Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E 51, 980–994 (1995)CrossRefGoogle Scholar
  7. 24.7.
    A. Pikovsky, M. Rosenblum, J. Kurths: Synchronization – a Universal Concept in Nonlinear Science (Cambridge Univ. Press, Cambridge 2003)Google Scholar
  8. 24.8.
    S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladeres, C.S. Zhou: The synchronization of chaotic systems, Phys. Rep. 366, 1–101 (2002)MATHCrossRefMathSciNetGoogle Scholar
  9. 24.9.
    A.V. Oppenheim, G.W. Wornell, S.H. Isabelle, K.M. Cuomo: Signal processing in the context of chaotic signals, Proc. ICASSP (1992) pp. 117–120Google Scholar
  10. 24.10.
    L. Kocarev, K.S. Halle, K. Eckert, L.O. Chua, U. Parlitz: Experimental demonstration of secure communications via chaotic synchronization, Int. J. Bifurc. Chaos 2, 709–713 (1992)MATHCrossRefGoogle Scholar
  11. 24.11.
    K.M. Cuomo, A.V. Oppenheim: Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett. 71, 65–68 (1993)CrossRefGoogle Scholar
  12. 24.12.
    H. Dedieu, M.P. Kennedy, M. Hasler: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits, IEEE Trans. Circ. Syst. II 40, 634–642 (1993)CrossRefGoogle Scholar
  13. 24.13.
    G.P. Agrawal, N.K. Dutta: Semiconductor lasers, 2nd edn. (Van Nostrand Reinhold, New York 1993)Google Scholar
  14. 24.14.
    F.T. Arecchi, G.L. Lippi, G.P. Puccioni, J.R. Tredicce: Deterministic chaos in lasers with injected signal, Opt. Commun. 51, 308–314 (1984)CrossRefGoogle Scholar
  15. 24.15.
    K.T. Alligood, T.D. Sauer, J.A. Yorke: CHAOS. An Introduction to Dynamical Systems (Springer, New York 1996)MATHGoogle Scholar
  16. 24.16.
    F.T. Arecchi, R. Meucci, G. Puccioni, J.R. Tredicce: Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser, Phys. Rev. Lett. 49, 1217–1220 (1982)CrossRefGoogle Scholar
  17. 24.17.
    J. Ohtsubo: Semiconductor Lasers, Stability, Instability and Chaos (Springer, Berlin Heidelberg 2006)Google Scholar
  18. 24.18.
    R. Lang: Injection locking properties of a semiconductor laser, IEEE J. Quantum Electron. 18, 976–983 (1982)CrossRefGoogle Scholar
  19. 24.19.
    J.K. Hale, S.M. Verduyn Lunel: Introduction to Functional Differential Equations (Springer, New York 1993)MATHGoogle Scholar
  20. 24.20.
    S. Tang, J.M. Liu: 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
  21. 24.21.
    R. Lang, K. Kobayashi: External optical feedback effects on semiconductor injection laser properties, IEEE J. Quantum Electron. 16, 347–355 (1980)CrossRefGoogle Scholar
  22. 24.22.
    G.H.M. van Tartwijk, G.P. Agrawal: Laser instabilities: a modern perspective, Prog. Quantum Electron. 22, 43–122 (1998)CrossRefGoogle Scholar
  23. 24.23.
    D. Lenstra, B.H. Verbeek, A.J. Den Boef: Coherence collapse in single-mode semiconductor lasers due to optical feedback, IEEE J. Quantum Electron. 21, 674–679 (1985)CrossRefGoogle Scholar
  24. 24.24.
    V. Ahlers, U. Parlitz, W. Lauterborn: Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers, Phys. Rev. A 58, 7208–7213 (1998)Google Scholar
  25. 24.25.
    R. Vicente, J. Daudén, P. Colet, R. Toral: Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop, IEEE J. Quantum Electron. 41, 541–548 (2005)CrossRefGoogle Scholar
  26. 24.26.
    A.P.A. Fischer, M. Yousefi, D. Lenstra, M.W. Carter, G. Vemuri: Experimental and theoretical study of semiconductor laser dynamics due to filtered optical feedback, IEEE J. Sel. Top. Quantum Electron. 10, 944–954 (2004)CrossRefGoogle Scholar
  27. 24.27.
    P. Celka: Chaotic synchronization and modulation of nonlinear time-delayed feedback optical systems, IEEE Trans. Circ. Syst. I 42, 455–463 (1995)CrossRefGoogle Scholar
  28. 24.28.
    N. Gastaud, S. Poinsot, L. Larger, J.M. Merolla, M. Hanna, J.-P. Goedgeuer, F. Malassenet: Electro-optical chaos for multi-10 Gbit/s optical transmissions, Electron. Lett. 40, 898–899 (2004)CrossRefGoogle Scholar
  29. 24.29.
    J.-P. Goedgebuer, P. Lévy, L. Larger, C.C. Chen, W.T. Rhodes: Optical communication with synchronized hyperchaos generated electrooptically, IEEE J. Quantum Electron. 38, 1178–1183 (2002)CrossRefGoogle Scholar
  30. 24.30.
    L. Larger, J.P. Goedgebuer, J.M. Merolla: Chaotic oscillator in wavelength: a new setup for investigating differential difference equations describing nonlinear dynamics, IEEE J. Quantum Electron. 34, 594–601 (1998)CrossRefGoogle Scholar
  31. 24.31.
    E. Genin, L. Larger, J.P. Goedgebuer, M.W. Lee, R. Ferriere, X. Bavard: Chaotic oscillations of the optical phase for multigigahertz-bandwidth secure communications, IEEE J. Quantum Electron. 40, 294–298 (2004)CrossRefGoogle Scholar
  32. 24.32.
    L. Larger, M.W. Lee, J.-P. Goedgebuer, W. Elflein, T. Erneux: Chaos in coherence modulation: bifurcations of an oscillator generating optical delay fluctuations, J. Opt. Soc. Am. B 18, 1063–1068 (2001)CrossRefGoogle Scholar
  33. 24.33.
    R. Roy, K.S. Thornburg: Experimental synchronization of chaotic lasers, Phys. Rev. Lett. 72, 2009–2012 (1994)CrossRefGoogle Scholar
  34. 24.34.
    T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu: Observation of synchronization in laser chaos, Phys. Rev. Lett. 72, 3502–3505 (1994)CrossRefGoogle Scholar
  35. 24.35.
    P. Celka: Synchronization of chaotic optical dynamical systems through 700 m of single mode fiber, IEEE Trans. Circ. Syst. I 43, 869–872 (1996)CrossRefGoogle Scholar
  36. 24.36.
    J.P. Goedgebuer, L. Larger, H. Porte: Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode, Phys. Rev. Lett. 80, 2249–2252 (1998)CrossRefGoogle Scholar
  37. 24.37.
    S. Sivaprakasam, K.A. Shore: Demonstration of optical synchronization of chaotic external-cavity laser diodes, Opt. Lett. 24, 466–468 (1999)CrossRefGoogle Scholar
  38. 24.38.
    H. Fujino, J. Ohtsubo: Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers, Opt. Lett. 25, 625–627 (2000)CrossRefGoogle Scholar
  39. 24.39.
    I. Fischer, Y. Liu, P. Davis: Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication, Phys. Rev. A 62, 011801R-1–011801R-4 (2000)CrossRefGoogle Scholar
  40. 24.40.
    J.M. Liu, H.F. Chen, S. Tang: Optical-communication systems based on chaos in semiconductor lasers, IEEE Trans. Circ. Syst. I 48, 1475–1483 (2001)CrossRefGoogle Scholar
  41. 24.41.
    S. Tang, J.M. Liu: Synchronization of high-frequency chaotic optical pulses, Opt. Lett. 26, 596–598 (2001)CrossRefGoogle Scholar
  42. 24.42.
    P. Colet, R. Roy: Digital communication with synchronized chaotic lasers, Opt. Lett. 19, 2056–2058 (1994)CrossRefGoogle Scholar
  43. 24.43.
    G.D. VanWiggeren, R. Roy: Optical communication with chaotic waveforms, Phys. Rev. Lett. 81, 3547–3550 (1998)CrossRefGoogle Scholar
  44. 24.44.
    G.D. VanWiggeren, R. Roy: Communication with chaotic lasers, Science 279, 1198–1200 (1998)CrossRefGoogle Scholar
  45. 24.45.
    S. Sivaprakasam, K.A. Shore: Signal masking for chaotic optical communication using external-cavity diode lasers, Opt. Lett. 24, 1200–1202 (2000)CrossRefGoogle Scholar
  46. 24.46.
    H.U. Voss: Anticipating chaotic synchronization, Phys. Rev. E. 61, 5115–5119 (2000)CrossRefGoogle Scholar
  47. 24.47.
    A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, K.A. Shore: Chaos-based communications at high bit rates using commercial fibre-optic links, Nature 438, 343–346 (2005)CrossRefGoogle Scholar
  48. 24.48.
    S. Tang, J.M. Liu: Message-encoding at 2.5 Gbit/s through synchronization of chaotic pulsing semiconductor lasers, Opt. Lett. 26, 1843–1845 (2001)CrossRefGoogle Scholar
  49. 24.49.
    S. Tang, H.F. Chen, S.K. Hwang, J.M. Liu: Message encoding and decoding through chaos modulation in chaotic optical communications, IEEE Trans. Circ. Syst. I 49, 163–169 (2001)CrossRefGoogle Scholar
  50. 24.50.
    H.F. Chen, J.M. Liu: Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation, IEEE J. Quantum Electron. 36, 27–34 (2000)CrossRefGoogle Scholar
  51. 24.51.
    J.M. Liu, H.F. Chen, S. Tang: Synchronized chaotic optical communications at high bit rates, IEEE J. Quantum Electron. 38, 1184–1196 (2002)CrossRefGoogle Scholar
  52. 24.52.
    V. Annovazzi-Lodi, S. Donati, A. Scirè: Synchronization of chaotic injected-laser systems and its application to optical cryptography, IEEE J. Quantum Electron. 32, 953–959 (1996)CrossRefGoogle Scholar
  53. 24.53.
    A. Locquet, F. Rogister, M. Sciamanna, P. Mégret, M. Blondel: Two types of synchronization in unidirectionally coupled chaotic external-cavity semiconductor lasers, Phys. Rev. E 64, 045203-1–045203-4 (2001)CrossRefGoogle Scholar
  54. 24.54.
    A. Locquet, C. Masoller, C.R. Mirasso: Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers, Phys. Rev. E 65, 056205-1–056205-4 (2002)CrossRefGoogle Scholar
  55. 24.55.
    A. Murakami, J. Ohtsubo: Synchronization of feedback-induced chaos in semiconductor lasers by optical injection, Phys. Rev. A 65, 033826-1–033826-7 (2002)CrossRefGoogle Scholar
  56. 24.56.
    Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, J.M. Liu: Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers, IEEE J. Quantum Electron. 39, 269–278 (2003)CrossRefGoogle Scholar
  57. 24.57.
    J. Revuelta, C.R. Mirasso, P. Colet, L. Pesquera: Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers, IEEE Photon. Technol. Lett. 14, 140–142 (2002)CrossRefGoogle Scholar
  58. 24.58.
    H. Kantz, T. Schreiber: Nonlinear Time Series Analysis, 2nd edn. (Cambridge Univ. Press, Cambridge 2004)MATHGoogle Scholar
  59. 24.59.
    U. Parlitz, L. Kocarev, A. Tstojanovski, H. Preckel: Encoding messages using chaotic synchronization, Phys. Rev. E 53, 4351–4361 (1996)CrossRefGoogle Scholar
  60. 24.60.
    M.W. Lee, L. Larger, V. Udaltsov, E. Genin, J.P. Goedgebuer: Demonstration of a chaos generator with two time delays, Opt. Lett. 29, 325–327 (2004)CrossRefGoogle Scholar
  61. 24.61.
    R. Hegger, M.J. Bünner, H. Kantz, A. Giaquinta: Identifying and modeling delay feedback systems, Phys. Rev. Lett. 81, 558–561 (1998)CrossRefGoogle Scholar
  62. 24.62.
    M.J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, A. Politi: Reconstruction of systems with delayed feedback: I. Theory, Eur. Phys. J. D 10, 165–176 (2000)CrossRefGoogle Scholar
  63. 24.63.
    M.J. Bünner, M. Ciofini, A. Giaquinta, R. Hegger, H. Kantz, R. Meucci, A. Politi: Reconstruction of systems with delayed feedback: II. Application, Eur. Phys. J. D 10, 177–187 (2000)CrossRefGoogle Scholar
  64. 24.64.
    D. Rontani, A. Locquet, M. Sciamanna, D.S. Citrin, S. Ortin: Time-delay identification in a chaotic semiconductor laser with optical feedback: a dynamical point of view, IEEE J. Quantum Electron. 45, 879–891 (2009)CrossRefGoogle Scholar
  65. 24.65.
    C. Zhou, C.H. Lai: Extracting messages masked by chaotic signals of time-delay systems, Phys. Rev. E 60, 320–323 (1999)CrossRefGoogle Scholar
  66. 24.66.
    V.S. Udaltsov, J.P. Goedgebuer, L. Larger, J.B. Cuenot, P. Levy, W.T. Rhodes: Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations, Phys. Lett. A 308, 54–60 (2003)MATHCrossRefMathSciNetGoogle Scholar
  67. 24.67.
    G. Alvarez, S. Li: Some basic cryptographic requirements for chaos-based cryptosystems, Int. J. Bifurc. Chaos 16, 2129–2151 (2006)CrossRefMathSciNetGoogle Scholar
  68. 24.68.
    B. Schneier: Applied Cryptography, 2nd edn. (John Wiley and Sons, New York 1996)Google Scholar
  69. 24.69.
    K.M. Short: Steps toward unmasking secure communications, Int. J. Bifurc. Chaos 4, 959–977 (1994)MATHCrossRefGoogle Scholar
  70. 24.70.
    K.M. Short: Unmasking a modulated chaotic communications scheme, Int. J. Bifurc. Chaos 6, 367–375 (1996)MATHCrossRefGoogle Scholar
  71. 24.71.
    K.M. Short, A.T. Parker: Unmasking a hyperchaotic modulated scheme, Phys. Rev. E 58, 1159–1162 (1998)CrossRefGoogle Scholar
  72. 24.72.
    Y. Takiguchi, K. Ohyagi, J. Ohtsubo: Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback, Opt. Lett. 28, 319–321 (2003)CrossRefGoogle Scholar
  73. 24.73.
    L. Kocarev, U. Parlitz: General approach for chaotic synchronization with applications to communication, Phys. Rev. Lett. 74, 5028–5031 (1995)CrossRefGoogle Scholar
  74. 24.74.
    A. Sánchez-Díaz, C.R. Mirasso, P. Colet, P. García-Fernández: Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers, IEEE J. Quantum Electron. 35, 292–297 (1999)CrossRefGoogle Scholar
  75. 24.75.
    A. Locquet, C. Masoller, P. Mégret, M. Blondel: Comparison of two types of synchronization of external-cavity semiconductor lasers, Opt. Lett. 27, 31–33 (2002)CrossRefGoogle Scholar
  76. 24.76.
    A. Bogris, A. Argyris, D. Syvridis: Analysis of the optical amplifier noise effect on electrooptically generated hyperchaos, IEEE J. Quantum Electron. 43, 552–559 (2007)CrossRefGoogle Scholar
  77. 24.77.
    M. Yousefi, Y. Barbarin, S. Beri, E.A.J.M. Bente, M.K. Smith, R. Nötzel, D. Lenstra: New role for nonlinear dynamics and chaos in integrated semiconductor laser technology, Phys. Rev. Lett. 98, 044101-1–044101-4 (2007)CrossRefGoogle Scholar
  78. 24.78.
    A. Argyris, M. Hamacher, K.E. Chlouverakis, A. Bogris, D. Syvridis: Photonic integrated device for chaos application in communications, Phys. Rev. Lett. 100, 194101-1–194101-4 (2008)CrossRefGoogle Scholar
  79. 24.79.
    L.S. Tsimring, M.M. Sushchik: Multiplexing chaotic signals using synchronization, Phys. Lett. A 213, 155–166 (1996)CrossRefGoogle Scholar
  80. 24.80.
    Y. Liu, P. Davis: Dual synchronization of chaos, Phys. Rev. E 61, R2176–R2179 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexandre Locquet
    • 1
  1. 1.Unité Mixte Internationale 2958 Georgia Tech-CNRSGeorgia Tech LorraineMetzFrance

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