Abstract

We experimentally and numerically observe synchronization of two semiconductor lasers commonly driven by a chaotic semiconductor laser subject to optical feedback. Under condition that the relaxation oscillation frequency is matched between the two response lasers, but mismatched between the drive and the two response lasers, we show that it is possible to observe strongly correlated synchronization between the two response lasers even when the correlation between the drive and response lasers is low. We also show that the cross correlation between the two responses is larger than that between drive and responses over a wide parameter region.

© 2007 Optical Society of America

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  1. G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279,1198-1200 (1998).
    [CrossRef] [PubMed]
  2. J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998).
    [CrossRef]
  3. S. Sivaprakasam and K. A. Shore, "Signal masking for chaotic optical communication using external-cavity diode lasers," Opt. Lett. 24, 1200-1202 (1999).
    [CrossRef]
  4. K. Kusumoto and J. Ohtsubo, "1.5-GHz message transmission based on synchronization of chaos in semiconductor lasers," Opt. Lett. 27, 989-991 (2002).
    [CrossRef]
  5. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
    [CrossRef] [PubMed]
  6. U. M. Maurer, "Secret key agreement by public discussion from common information," IEEE Trans. Inf. Theory 39, 733-742 (1993).
    [CrossRef]
  7. J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
    [CrossRef]
  8. A. Uchida, P. Davis, and S. Itaya, "Generation of information theoretic secure keys using a chaotic semiconductor laser," Appl. Phys. Lett. 83, 3213-3215 (2003).
    [CrossRef]
  9. H. D. I. Abarbanel, N. F. Rulkov and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Phys. Rev. E 53, 4528-4535 (1996).
    [CrossRef]
  10. R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
    [CrossRef]
  11. A. Uchida, K. Higa, T. Shiba, S. Yoshimori, F. Kuwashima, and H. Iwasawa, "Generalized synchronization of chaos in He-Ne lasers," Phys. Rev. E 68, 016215-1—016215-7 (2003).
    [CrossRef]
  12. D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
    [CrossRef]
  13. A. Uchida, R. McAllister, R. Meucci, and R. Roy, "Generalized synchronization of chaos in identical systems with hidden degrees of freedom," Phys. Rev. Lett. 91, 174101-1—174101-4 (2003).
    [CrossRef]
  14. I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Zero-lag long-range synchronization via dynamical relaying," Phys. Rev. Lett. 97, 123902-1—123902-4 (2006).
    [CrossRef]
  15. B. B. Zhou and R. Roy, "Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators," Phys. Rev. E 75, 026205-1—026205-5 (2007).</jrn>
    [CrossRef]

2006 (1)

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
[CrossRef]

2005 (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

2003 (1)

A. Uchida, P. Davis, and S. Itaya, "Generation of information theoretic secure keys using a chaotic semiconductor laser," Appl. Phys. Lett. 83, 3213-3215 (2003).
[CrossRef]

2002 (1)

2001 (1)

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
[CrossRef]

1999 (1)

1998 (3)

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279,1198-1200 (1998).
[CrossRef] [PubMed]

J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998).
[CrossRef]

D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
[CrossRef]

1996 (1)

H. D. I. Abarbanel, N. F. Rulkov and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Phys. Rev. E 53, 4528-4535 (1996).
[CrossRef]

1993 (1)

U. M. Maurer, "Secret key agreement by public discussion from common information," IEEE Trans. Inf. Theory 39, 733-742 (1993).
[CrossRef]

Abarbanel, H. D. I.

H. D. I. Abarbanel, N. F. Rulkov and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Phys. Rev. E 53, 4528-4535 (1996).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Arai, K.

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
[CrossRef]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Colet, P.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Davis, P.

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
[CrossRef]

A. Uchida, P. Davis, and S. Itaya, "Generation of information theoretic secure keys using a chaotic semiconductor laser," Appl. Phys. Lett. 83, 3213-3215 (2003).
[CrossRef]

Dykstra, R.

D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
[CrossRef]

Fischer, I.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Garcia-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Goedgebuer, J.-P.

J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998).
[CrossRef]

Hamilton, M. W.

D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
[CrossRef]

Heckenberg, N. R.

D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
[CrossRef]

Hernandez-Garcia, E.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
[CrossRef]

Itaya, S.

A. Uchida, P. Davis, and S. Itaya, "Generation of information theoretic secure keys using a chaotic semiconductor laser," Appl. Phys. Lett. 83, 3213-3215 (2003).
[CrossRef]

Kusumoto, K.

Larger, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998).
[CrossRef]

Maurer, U. M.

U. M. Maurer, "Secret key agreement by public discussion from common information," IEEE Trans. Inf. Theory 39, 733-742 (1993).
[CrossRef]

Mirasso, C. R.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
[CrossRef]

Muramatsu, J.

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
[CrossRef]

Ohtsubo, J.

Pesquera, L.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Piro, O.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
[CrossRef]

Porte, H.

J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998).
[CrossRef]

Roy, R.

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279,1198-1200 (1998).
[CrossRef] [PubMed]

Rulkov, N. F.

H. D. I. Abarbanel, N. F. Rulkov and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Phys. Rev. E 53, 4528-4535 (1996).
[CrossRef]

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

S. Sivaprakasam and K. A. Shore, "Signal masking for chaotic optical communication using external-cavity diode lasers," Opt. Lett. 24, 1200-1202 (1999).
[CrossRef]

Sivaprakasam, S.

Sushchik, M. M.

H. D. I. Abarbanel, N. F. Rulkov and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Phys. Rev. E 53, 4528-4535 (1996).
[CrossRef]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Tang, D. Y.

D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
[CrossRef]

Toral, R.

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
[CrossRef]

Uchida, A.

A. Uchida, P. Davis, and S. Itaya, "Generation of information theoretic secure keys using a chaotic semiconductor laser," Appl. Phys. Lett. 83, 3213-3215 (2003).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279,1198-1200 (1998).
[CrossRef] [PubMed]

Yoshimura, K.

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

A. Uchida, P. Davis, and S. Itaya, "Generation of information theoretic secure keys using a chaotic semiconductor laser," Appl. Phys. Lett. 83, 3213-3215 (2003).
[CrossRef]

Chaos (1)

R. Toral, C. R. Mirasso, E. Hernandez-Garcia, O. Piro, "Analytical and numerical studies of noise-induced synchronization of chaotic systems," Chaos 11, 665-673 (2001).
[CrossRef]

IEEE Trans. Inf. Theory (2)

U. M. Maurer, "Secret key agreement by public discussion from common information," IEEE Trans. Inf. Theory 39, 733-742 (1993).
[CrossRef]

J. Muramatsu, K. Yoshimura, K. Arai, and P. Davis, "Secret key capacity for optimally correlated sources under sampling attack," IEEE Trans. Inf. Theory 52, 5140-5151 (2006).
[CrossRef]

Nature (1)

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fiber-optic links," Nature 438, 343-346 (2005).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. E (2)

H. D. I. Abarbanel, N. F. Rulkov and M. M. Sushchik, "Generalized synchronization of chaos: The auxiliary system approach," Phys. Rev. E 53, 4528-4535 (1996).
[CrossRef]

D. Y. Tang, R. Dykstra, M. W. Hamilton, and N. R. Heckenberg, "Observation of generalized synchronization of chaos in a driven chaotic system," Phys. Rev. E 57, 5247-5251 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

J.-P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998).
[CrossRef]

Science (1)

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279,1198-1200 (1998).
[CrossRef] [PubMed]

Other (4)

A. Uchida, K. Higa, T. Shiba, S. Yoshimori, F. Kuwashima, and H. Iwasawa, "Generalized synchronization of chaos in He-Ne lasers," Phys. Rev. E 68, 016215-1—016215-7 (2003).
[CrossRef]

A. Uchida, R. McAllister, R. Meucci, and R. Roy, "Generalized synchronization of chaos in identical systems with hidden degrees of freedom," Phys. Rev. Lett. 91, 174101-1—174101-4 (2003).
[CrossRef]

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Zero-lag long-range synchronization via dynamical relaying," Phys. Rev. Lett. 97, 123902-1—123902-4 (2006).
[CrossRef]

B. B. Zhou and R. Roy, "Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators," Phys. Rev. E 75, 026205-1—026205-5 (2007).</jrn>
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup for common-chaotic-signal induced synchronization in three semiconductor lasers. Amp, electronic amplifier; BS, beam splitter; FC, fiber collimator; ISO, optical isolator; L, lens; λ/2, half wave plate; M, mirror; NDF, neutral density filter; OSC, digital oscilloscope; PD, photodetector; SA, radio-frequency spectrum analyzer; SL, semiconductor laser.

Fig. 2.
Fig. 2.

Experimental result of temporal waveforms and corresponding correlation plots for (a), (b) Drive and Response 1, (c), (d) Drive and Response 2, and (e), (f) Response 1 and Response 2. The coupling delay time (4.0 ns) between the two temporal waveforms is compensated in (a)-(d). The cross correlation values are (b) 0.711, (d) 0.659, and (f) 0.947.

Fig. 3.
Fig. 3.

Experimental result of RF spectra for (a) Drive, (b) Response 1, and (c) Response 2.

Fig. 4.
Fig. 4.

Experimental result for the cross correlation between each pair of lasers as a function of (a) the relaxation oscillation frequency of the Response lasers and (b) the optical wavelength detuning between Drive and Response lasers. Solid black curve: Drive and Response 1, dotted blue curve: Drive and Response 2, dashed red curve: Response 1 and Response 2.

Fig. 5.
Fig. 5.

Numerical result of the cross correlation between two of three lasers as a function of (a) the relaxation oscillation frequency of two Responses and (b) the optical wavelength detuning between Drive and one of Responses. Solid black curve: Drive and Response 1, dotted blue curve: Drive and Response 2, dashed red curve: Response 1 and Response 2.

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