Abstract

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver. The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

© 2009 Optical Society of America

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  1. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
    [CrossRef] [PubMed]
  2. M. Cuomo and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68, (1993).
    [CrossRef] [PubMed]
  3. P. Colet and R. Roy, "Digital communication with synchronized chaotic lasers," Opt. Lett. 19, 2056--2058 (1994).
    [CrossRef] [PubMed]
  4. G.D. Van Wiggeren and R. Roy, "Communications with chaotic lasers," Science 279, 1198-1200 (1998).
    [CrossRef]
  5. S. Sivaprakasam and K. A. Shore, "Signal masking for chaotic optical communication using externalcavity diode lasers," Opt. Lett. 24, 1200-2 (1999).
    [CrossRef]
  6. S. Donati and C. R. Mirasso, "Introduction to the feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1140 (2002).
    [CrossRef]
  7. S. Sivaprakasam and C. Masoller Ottieri, Chaos synchronization, in Unlocking Dynamical Diversity : Semiconductor Lasers with Optical Feedback, D. M. Kane and K. A. Shore, eds., (Wiley & Sons, Chichester, 2005), Chapp. 6, pp. 185-211.
    [CrossRef]
  8. J. Ohtsubo and P. Davis, Chaotic Optical Communication, in Unlocking Dynamical Diversity: Semiconductor Lasers with Optical Feedback, D. M. Kane and K. A. Shore, eds., (Wiley & Sons, Chichester, 2005), Chap. 9, pp. 307-333.
    [CrossRef]
  9. J. M. Liu, H. F. Chen, and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans, Circuits and Syst. I 48, 1475 (2001).
    [CrossRef]
  10. V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
    [CrossRef]
  11. A. Argyris et al., "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature,  438, 343-346 (2005).
    [PubMed]
  12. C. Robilliard, E. H. Huntington, and J. G. Webb, "Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback," IEEE Trans. Circuits Syst. II 53, 722-726 (2006).
    [CrossRef]
  13. C. Robilliard, E. H. Huntington, and M. R. Frater, "Digital transmission for improved synchronization of analog chaos generators in communications systems," Chaos 17, 023130: 1-7 (2007).
    [CrossRef] [PubMed]
  14. D. M. Kane, J. P. Toomey, M. W. Lee, and K. A. Shore, "Correlation dimension signature of wideband chaos synchronization of semiconductor lasers," Opt. Lett. 31, 20-22 (2006).
    [CrossRef] [PubMed]
  15. S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
    [CrossRef]

2007 (1)

C. Robilliard, E. H. Huntington, and M. R. Frater, "Digital transmission for improved synchronization of analog chaos generators in communications systems," Chaos 17, 023130: 1-7 (2007).
[CrossRef] [PubMed]

2006 (3)

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
[CrossRef]

D. M. Kane, J. P. Toomey, M. W. Lee, and K. A. Shore, "Correlation dimension signature of wideband chaos synchronization of semiconductor lasers," Opt. Lett. 31, 20-22 (2006).
[CrossRef] [PubMed]

C. Robilliard, E. H. Huntington, and J. G. Webb, "Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback," IEEE Trans. Circuits Syst. II 53, 722-726 (2006).
[CrossRef]

2005 (1)

A. Argyris et al., "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature,  438, 343-346 (2005).
[PubMed]

2003 (1)

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

2002 (1)

S. Donati and C. R. Mirasso, "Introduction to the feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1140 (2002).
[CrossRef]

2001 (1)

J. M. Liu, H. F. Chen, and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans, Circuits and Syst. I 48, 1475 (2001).
[CrossRef]

1999 (1)

1998 (1)

G.D. Van Wiggeren and R. Roy, "Communications with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

1994 (1)

1993 (1)

M. Cuomo and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68, (1993).
[CrossRef] [PubMed]

1990 (1)

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris et al., "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature,  438, 343-346 (2005).
[PubMed]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Chen, H. F.

J. M. Liu, H. F. Chen, and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans, Circuits and Syst. I 48, 1475 (2001).
[CrossRef]

Colet, P.

Cuenot, J.-B.

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Cuomo, M.

M. Cuomo and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68, (1993).
[CrossRef] [PubMed]

Donati, S.

S. Donati and C. R. Mirasso, "Introduction to the feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1140 (2002).
[CrossRef]

Frater, M. R.

C. Robilliard, E. H. Huntington, and M. R. Frater, "Digital transmission for improved synchronization of analog chaos generators in communications systems," Chaos 17, 023130: 1-7 (2007).
[CrossRef] [PubMed]

Goedgebuer, J.-P.

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Huntington, E. H.

C. Robilliard, E. H. Huntington, and M. R. Frater, "Digital transmission for improved synchronization of analog chaos generators in communications systems," Chaos 17, 023130: 1-7 (2007).
[CrossRef] [PubMed]

C. Robilliard, E. H. Huntington, and J. G. Webb, "Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback," IEEE Trans. Circuits Syst. II 53, 722-726 (2006).
[CrossRef]

Kane, D. M.

Larger, L.

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Lee, M. W.

Levy, P.

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Liu, J. M.

J. M. Liu, H. F. Chen, and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans, Circuits and Syst. I 48, 1475 (2001).
[CrossRef]

Mirasso, C. R.

S. Donati and C. R. Mirasso, "Introduction to the feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1140 (2002).
[CrossRef]

Oppenheim, A. V.

M. Cuomo and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68, (1993).
[CrossRef] [PubMed]

Pecora, L. M.

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Peters-Flynn, S.

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
[CrossRef]

Pierce, I.

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
[CrossRef]

Rhodes, W. T.

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Robilliard, C.

C. Robilliard, E. H. Huntington, and M. R. Frater, "Digital transmission for improved synchronization of analog chaos generators in communications systems," Chaos 17, 023130: 1-7 (2007).
[CrossRef] [PubMed]

C. Robilliard, E. H. Huntington, and J. G. Webb, "Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback," IEEE Trans. Circuits Syst. II 53, 722-726 (2006).
[CrossRef]

Roy, R.

G.D. Van Wiggeren and R. Roy, "Communications with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

P. Colet and R. Roy, "Digital communication with synchronized chaotic lasers," Opt. Lett. 19, 2056--2058 (1994).
[CrossRef] [PubMed]

Shore, K. A.

Sivaprakasam, S.

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
[CrossRef]

S. Sivaprakasam and K. A. Shore, "Signal masking for chaotic optical communication using externalcavity diode lasers," Opt. Lett. 24, 1200-2 (1999).
[CrossRef]

Spencer, P. S.

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
[CrossRef]

Tang, S.

J. M. Liu, H. F. Chen, and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans, Circuits and Syst. I 48, 1475 (2001).
[CrossRef]

Toomey, J. P.

Udaltsov, V. S.

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Van Wiggeren, G.D.

G.D. Van Wiggeren and R. Roy, "Communications with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

Webb, J. G.

C. Robilliard, E. H. Huntington, and J. G. Webb, "Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback," IEEE Trans. Circuits Syst. II 53, 722-726 (2006).
[CrossRef]

Chaos (1)

C. Robilliard, E. H. Huntington, and M. R. Frater, "Digital transmission for improved synchronization of analog chaos generators in communications systems," Chaos 17, 023130: 1-7 (2007).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

S. Donati and C. R. Mirasso, "Introduction to the feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1140 (2002).
[CrossRef]

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, and K. A. Shore, "Identification of the optimum time delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
[CrossRef]

IEEE Trans, Circuits and Syst. I (1)

J. M. Liu, H. F. Chen, and S. Tang, "Optical-communication systems based on chaos in semiconductor lasers," IEEE Trans, Circuits and Syst. I 48, 1475 (2001).
[CrossRef]

IEEE Trans. Circuits Syst. II (1)

C. Robilliard, E. H. Huntington, and J. G. Webb, "Enhancing the Security of Delayed Differential Chaotic Systems With Programmable Feedback," IEEE Trans. Circuits Syst. II 53, 722-726 (2006).
[CrossRef]

Nature (1)

A. Argyris et al., "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature,  438, 343-346 (2005).
[PubMed]

Opt. Lett. (3)

Phys. Lett. A (1)

V. S. Udaltsov, J.-P. Goedgebuer, L. Larger, J.-B. Cuenot, P. Levy, and W. T. Rhodes, "Cracking chaosbased encryption systems ruled by nonlinear time delay differential equations," Phys. Lett. A 308, 54 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

M. Cuomo and A. V. Oppenheim, "Circuit implementation of synchronized chaos with applications to communications," Phys. Rev. Lett. 71, 65-68, (1993).
[CrossRef] [PubMed]

Science (1)

G.D. Van Wiggeren and R. Roy, "Communications with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef]

Other (2)

S. Sivaprakasam and C. Masoller Ottieri, Chaos synchronization, in Unlocking Dynamical Diversity : Semiconductor Lasers with Optical Feedback, D. M. Kane and K. A. Shore, eds., (Wiley & Sons, Chichester, 2005), Chapp. 6, pp. 185-211.
[CrossRef]

J. Ohtsubo and P. Davis, Chaotic Optical Communication, in Unlocking Dynamical Diversity: Semiconductor Lasers with Optical Feedback, D. M. Kane and K. A. Shore, eds., (Wiley & Sons, Chichester, 2005), Chap. 9, pp. 307-333.
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Hybrid electronic/optical synchronized chaos communication system. The transmitter and receiver chaotic electronic circuits (boxed) consist of a delay differential feedback (DDF) chaotic system, as described in the text. The current boosted transmitter signal is added to a dc injection current and is the injection to a semiconductor laser. The optical signal is propagated in free-space and photodetected. The photodetector current is amplified and added to a dc offset before being applied to the receiver circuit which synchronizes with the transmitter. The synchronized receiver signal, v’(t), is subtracted from the optical signal to recover the message.

Fig. 2
Fig. 2

Chaotic signal and synchronized receiver. Fig. 2(a): the output from the chaotic transmitter; and Fig. 2(b): the synchronized receiver, after transmission via the optical carrier. A sinusoidal nonlinearity has been used to the FPGA. Fig. 2(c): the synchronized chaotic receiver signal plotted against the chaotic transmitted signal. Fig. 2(d): the cross correlation coefficient (C3) as a function of the delay (calibrated in data points).

Fig. 3.
Fig. 3.

Message masking and recovery. (a)-(c) show the transmitted, received and recovered message signal time traces. The corresponding frequency spectra (Fig. 3 (d)–(f)) show no evidence of the 20 kHz message in either the transmitted or synchronized signals, while a sharp peak can be seen at the message frequency in that of the recovered signal.

Equations (1)

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C 3 ( Δ ) = [ P tr ( t + Δ ) P tr ] [ P re ( t ) P re ] { [ P tr ( t ) P tr ] 2 [ P re ( t ) P re ] 2 } 1 2

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