Abstract

Chaos data analysis has been performed on the chaotic output power time series data from a synchronized transmitter–receiver pair of semiconductor lasers. The system uses an asymmetric, bidirectional coupling configuration between the master (transmitter), which is a laser diode with optical feedback, and a stand-alone slave semiconductor laser. The correlation dimension of the chaotic time series has a minimum value of 4, which was obtained from high-bandwidth measurements. The correlation dimensions for both the master and the synchronized slave are identical when the cross-correlation coefficient of the synchronized chaos is above 0.9. These results establish correlation dimension analysis as an effective tool for the determination of the quality of wideband chaos synchronization.

© 2006 Optical Society of America

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  1. S. Donati and C. R. Mirasso, eds., feature on optical chaos and application to cryptography, IEEE J. Quantum Electron. 38, 1138-1204 (2002).
    [CrossRef]
  2. Unlocking Dynamic Diversity: Semiconductor Lasers with Optical Feedback, D.M.Kane and K.A.Shore, eds. (Wiley, 2005).
    [CrossRef]
  3. S. Sivaprakasam and K. A. Shore, Opt. Lett. 24, 466 (1999).
    [CrossRef]
  4. F. Fujino and J. Ohtsubo, Opt. Lett. 25, 625 (2000).
    [CrossRef]
  5. C. Mirasso, P. Colet, and P. Garcia-Fernandes, IEEE Photon. Technol. Lett. 8, 299 (1996).
    [CrossRef]
  6. V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
    [CrossRef]
  7. P. Spencer, P. Rees, and I. Pierce, Ref. , Chap. 2, pp. 23-54.
  8. D. Lenstra, G. Vemuri, and M. Yousefi, Ref. , Chap. 3, 55-80.
  9. B. Krauskopf, Ref. , Chap. 5, pp. 147-184.
  10. S. Sivaprakasam and C. Masoller Ottieri, Ref. , Chap. 6, pp. 185-211.
  11. J. Ohtsubo and P. Davis, Ref. , Chap. 9, pp. 307-334.
  12. H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, 1996).
    [CrossRef]
  13. J. C. Sprott and G. Rowlands, Chaos Data Analyzer: the Professional Version (Physics Academic Software, 2003).
  14. J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Chaos analysis of experimental output power time series data from a chaotic semiconductor laser" (in preparation).
  15. F. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617 (1986).
    [CrossRef] [PubMed]
  16. A. Varone, A. Politi, and M. Ciofini, Phys. Rev. A 52, 3176 (1995).
    [CrossRef] [PubMed]
  17. H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
    [CrossRef] [PubMed]
  18. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
    [CrossRef]
  19. S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).
  20. S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
    [CrossRef]

2002

S. Donati and C. R. Mirasso, eds., feature on optical chaos and application to cryptography, IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
[CrossRef]

2000

1999

1998

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

1996

H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
[CrossRef] [PubMed]

C. Mirasso, P. Colet, and P. Garcia-Fernandes, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

1995

A. Varone, A. Politi, and M. Ciofini, Phys. Rev. A 52, 3176 (1995).
[CrossRef] [PubMed]

1986

F. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617 (1986).
[CrossRef] [PubMed]

1983

P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

Abarbanel, H. D.

H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
[CrossRef] [PubMed]

H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, 1996).
[CrossRef]

Ahlers, V.

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Arecchi, F.

F. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617 (1986).
[CrossRef] [PubMed]

Ciofini, M.

A. Varone, A. Politi, and M. Ciofini, Phys. Rev. A 52, 3176 (1995).
[CrossRef] [PubMed]

Colet, P.

C. Mirasso, P. Colet, and P. Garcia-Fernandes, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Davis, P.

J. Ohtsubo and P. Davis, Ref. , Chap. 9, pp. 307-334.

Donati, S.

S. Donati and C. R. Mirasso, eds., feature on optical chaos and application to cryptography, IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

Fujino, F.

Gadomski, W.

F. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617 (1986).
[CrossRef] [PubMed]

Garcia-Fernandes, P.

C. Mirasso, P. Colet, and P. Garcia-Fernandes, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Gills, Z.

H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
[CrossRef] [PubMed]

Grassberger, P.

P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

Kane, D. M.

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Chaos analysis of experimental output power time series data from a chaotic semiconductor laser" (in preparation).

Krauskopf, B.

B. Krauskopf, Ref. , Chap. 5, pp. 147-184.

Lauterborn, W.

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Lee, M. W.

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Chaos analysis of experimental output power time series data from a chaotic semiconductor laser" (in preparation).

S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).

Lenstra, D.

D. Lenstra, G. Vemuri, and M. Yousefi, Ref. , Chap. 3, 55-80.

Liu, C.

H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
[CrossRef] [PubMed]

Meucci, R.

F. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617 (1986).
[CrossRef] [PubMed]

Mirasso, C.

C. Mirasso, P. Colet, and P. Garcia-Fernandes, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Mirasso, C. R.

S. Donati and C. R. Mirasso, eds., feature on optical chaos and application to cryptography, IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

Ohtsubo, J.

F. Fujino and J. Ohtsubo, Opt. Lett. 25, 625 (2000).
[CrossRef]

J. Ohtsubo and P. Davis, Ref. , Chap. 9, pp. 307-334.

Ottieri, C. Masoller

S. Sivaprakasam and C. Masoller Ottieri, Ref. , Chap. 6, pp. 185-211.

Parlitz, U.

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Paul, J.

S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).

Pierce, I.

P. Spencer, P. Rees, and I. Pierce, Ref. , Chap. 2, pp. 23-54.

Politi, A.

A. Varone, A. Politi, and M. Ciofini, Phys. Rev. A 52, 3176 (1995).
[CrossRef] [PubMed]

Procaccia, I.

P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

Rees, P.

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
[CrossRef]

P. Spencer, P. Rees, and I. Pierce, Ref. , Chap. 2, pp. 23-54.

Rowlands, G.

J. C. Sprott and G. Rowlands, Chaos Data Analyzer: the Professional Version (Physics Academic Software, 2003).

Roy, R.

H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
[CrossRef] [PubMed]

Shore, K. A.

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
[CrossRef]

S. Sivaprakasam and K. A. Shore, Opt. Lett. 24, 466 (1999).
[CrossRef]

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Chaos analysis of experimental output power time series data from a chaotic semiconductor laser" (in preparation).

S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).

Sivaprakasam, S.

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
[CrossRef]

S. Sivaprakasam and K. A. Shore, Opt. Lett. 24, 466 (1999).
[CrossRef]

S. Sivaprakasam and C. Masoller Ottieri, Ref. , Chap. 6, pp. 185-211.

S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).

Spencer, P.

P. Spencer, P. Rees, and I. Pierce, Ref. , Chap. 2, pp. 23-54.

Spencer, P. S.

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
[CrossRef]

S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).

Sprott, J. C.

J. C. Sprott and G. Rowlands, Chaos Data Analyzer: the Professional Version (Physics Academic Software, 2003).

Toomey, J. P.

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Chaos analysis of experimental output power time series data from a chaotic semiconductor laser" (in preparation).

Varone, A.

A. Varone, A. Politi, and M. Ciofini, Phys. Rev. A 52, 3176 (1995).
[CrossRef] [PubMed]

Vemuri, G.

D. Lenstra, G. Vemuri, and M. Yousefi, Ref. , Chap. 3, 55-80.

Yousefi, M.

D. Lenstra, G. Vemuri, and M. Yousefi, Ref. , Chap. 3, 55-80.

IEEE J. Quantum Electron.

S. Donati and C. R. Mirasso, eds., feature on optical chaos and application to cryptography, IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, IEEE J. Quantum Electron. 38, 1155 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

C. Mirasso, P. Colet, and P. Garcia-Fernandes, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Opt. Lett.

Phys. Rev. A

F. Arecchi, W. Gadomski, and R. Meucci, Phys. Rev. A 34, 1617 (1986).
[CrossRef] [PubMed]

A. Varone, A. Politi, and M. Ciofini, Phys. Rev. A 52, 3176 (1995).
[CrossRef] [PubMed]

H. D. I. Abarbanel, Z. Gills, C. Liu, and R. Roy, Phys. Rev. A 53, 440 (1996).
[CrossRef] [PubMed]

Phys. Rev. E

V. Ahlers, U. Parlitz, and W. Lauterborn, Phys. Rev. E 58, 7208 (1998).
[CrossRef]

Phys. Rev. Lett.

P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

Other

S. Sivaprakasam, M. W. Lee, J. Paul, P. S. Spencer, and K. A. Shore, "Enhanced chaos synchronization using bi-directional coupling of diode laser" (in preparation).

Unlocking Dynamic Diversity: Semiconductor Lasers with Optical Feedback, D.M.Kane and K.A.Shore, eds. (Wiley, 2005).
[CrossRef]

P. Spencer, P. Rees, and I. Pierce, Ref. , Chap. 2, pp. 23-54.

D. Lenstra, G. Vemuri, and M. Yousefi, Ref. , Chap. 3, 55-80.

B. Krauskopf, Ref. , Chap. 5, pp. 147-184.

S. Sivaprakasam and C. Masoller Ottieri, Ref. , Chap. 6, pp. 185-211.

J. Ohtsubo and P. Davis, Ref. , Chap. 9, pp. 307-334.

H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, 1996).
[CrossRef]

J. C. Sprott and G. Rowlands, Chaos Data Analyzer: the Professional Version (Physics Academic Software, 2003).

J. P. Toomey, D. M. Kane, M. W. Lee, and K. A. Shore, "Chaos analysis of experimental output power time series data from a chaotic semiconductor laser" (in preparation).

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Figures (4)

Fig. 1
Fig. 1

CD versus ED of chaotic output power time series data for the transmitter (master) CSL, comparing sampling periods of 100 ps (20 000 data points) and 50 ps (20 000 data points). The dashed line shows the expected trend for stochastic noise. The horizontal lines at CD values of 4 and 5 are included to facilitate comparison of the CD graph with a flat plateau.

Fig. 2
Fig. 2

Output power time series for the master CSL for a 25 ns time comparing sampling periods of 100 and 50 ps.

Fig. 3
Fig. 3

CD versus ED of a chaotic output power time series for the transmitter (master) CSL and synchronized receiver (slave) laser with a cross-correlation coefficient of 0.93. Other curves as for Fig. 1.

Fig. 4
Fig. 4

CD versus ED of a chaotic output power time series for the transmitter (master) CSL and synchronized receiver (slave) laser with a cross-correlation coefficient of 0.76. Other lines as for Fig. 1.

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