Abstract

The effects of unwanted external optical feedback on synchronized chaotic optical communication systems are studied numerically. We consider an open-loop configuration consisting of a transmitter laser with double external optical feedbacks and a receiver laser with optical injection from the transmitter laser. First, including the effects of unwanted optical feedback, the synchronization performances of both the complete synchronization and the generalized synchronization are examined. Then the encoding and decoding performances of the generalized synchronization and the effects of the introduced feedback are investigated, respectively. Finally, we study the control of the unwanted feedback on the dynamics of the transmitter laser and briefly discuss the system security when the transmitter laser is driven to operate in a steady state or periodic oscillation state by the additional feedback.

© 2006 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. S. Tang and J. M. Liu, "Effects of message encoding and decoding on synchronized chaotic optical communications," IEEE J. Quantum Electron. 39, 1468-1475 (2003).
    [CrossRef]
  3. S. F. Yu, "Nonlinear dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 35, 332-341 (1999).
    [CrossRef]
  4. A. Hohl and A. Gavrielides, "Bifurcation cascade in a semiconductor laser subject to optical feedback," Phys. Rev. Lett. 82, 1148-1151 (1999).
    [CrossRef]
  5. S. Tang and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum Electron. 37, 329-336 (2001).
    [CrossRef]
  6. J. B. Gao, S. K. Hwang, and J. M. Liu, "Effects of intrinsic spontaneous-emission noise on the nonlinear dynamics of an optically injected semiconductor laser," Phys. Rev. A 59, 1582-1585 (1999).
    [CrossRef]
  7. V. Ahlers, U. Parlitz, and W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E 58, 7208-7213 (1998).
    [CrossRef]
  8. J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
    [CrossRef]
  9. K. Kusumoto and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
    [CrossRef]
  10. A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
    [CrossRef]
  11. Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
    [CrossRef]
  12. J. M. Buldú, J. Garcia-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
    [CrossRef]
  13. H. F. Chen and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
    [CrossRef]
  14. R. Vicente, T. Perez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
    [CrossRef]
  15. A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
    [CrossRef]
  16. I. Fischer, Y. Liu, and P. Davis, "Synchronization of chaotic semiconductor laser dynamics on sub-ns timescales and its potential for chaos communication," Phys. Rev. A 62, 011801-1-4 (2000).
    [CrossRef]
  17. Y. Takiguchi, H. Fujino, and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in externally injected semiconductor lasers in low-frequency fluctuation regime," Opt. Lett. 24, 1570-1572 (1999).
    [CrossRef]
  18. H. Fujino and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers," Opt. Lett. 25, 625-627 (2000).
    [CrossRef]
  19. M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
    [CrossRef]
  20. H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).
    [CrossRef]
  21. K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
    [CrossRef]
  22. P. S. Spencer, C. R. Mirasso, and K. A. Shore, "Effect of strong optical feedback on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 10, 191-193 (1998).
    [CrossRef]
  23. Y. Liu and J. Ohtsubo, "Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer," IEEE J. Quantum Electron. 33, 1163-1169 (1997).
    [CrossRef]
  24. R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
    [CrossRef]
  25. X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Numerical study of static and dynamic behaviors of VCSELs with polarization-selective optical feedback," IEE Proc. Optoelectron. (to be published).
  26. X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
    [CrossRef]
  27. J. Martin-Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
    [CrossRef]
  28. V. N. Morozov, J. A. Neff, and H. J. Zhou, "Analysis of vertical-cavity surface-emitting laser multimode behavior," IEEE J. Quantum Electron. 33, 980-988 (1997).
    [CrossRef]
  29. X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
    [CrossRef]
  30. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a time series," Physica D 16, 285-317 (1985).
    [CrossRef]

2006 (1)

X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

2005 (1)

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
[CrossRef]

2004 (1)

J. M. Buldú, J. Garcia-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

2003 (4)

A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

S. Tang and J. M. Liu, "Effects of message encoding and decoding on synchronized chaotic optical communications," IEEE J. Quantum Electron. 39, 1468-1475 (2003).
[CrossRef]

K. Kusumoto and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

2002 (3)

J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
[CrossRef]

R. Vicente, T. Perez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef]

2001 (2)

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
[CrossRef]

S. Tang and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum Electron. 37, 329-336 (2001).
[CrossRef]

2000 (3)

H. Fujino and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers," Opt. Lett. 25, 625-627 (2000).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, "Synchronization of chaotic semiconductor laser dynamics on sub-ns timescales and its potential for chaos communication," Phys. Rev. A 62, 011801-1-4 (2000).
[CrossRef]

H. F. Chen and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

1999 (4)

Y. Takiguchi, H. Fujino, and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in externally injected semiconductor lasers in low-frequency fluctuation regime," Opt. Lett. 24, 1570-1572 (1999).
[CrossRef]

J. B. Gao, S. K. Hwang, and J. M. Liu, "Effects of intrinsic spontaneous-emission noise on the nonlinear dynamics of an optically injected semiconductor laser," Phys. Rev. A 59, 1582-1585 (1999).
[CrossRef]

S. F. Yu, "Nonlinear dynamics of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 35, 332-341 (1999).
[CrossRef]

A. Hohl and A. Gavrielides, "Bifurcation cascade in a semiconductor laser subject to optical feedback," Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

1998 (2)

V. Ahlers, U. Parlitz, and W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E 58, 7208-7213 (1998).
[CrossRef]

P. S. Spencer, C. R. Mirasso, and K. A. Shore, "Effect of strong optical feedback on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 10, 191-193 (1998).
[CrossRef]

1997 (3)

Y. Liu and J. Ohtsubo, "Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer," IEEE J. Quantum Electron. 33, 1163-1169 (1997).
[CrossRef]

J. Martin-Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
[CrossRef]

V. N. Morozov, J. A. Neff, and H. J. Zhou, "Analysis of vertical-cavity surface-emitting laser multimode behavior," IEEE J. Quantum Electron. 33, 980-988 (1997).
[CrossRef]

1995 (1)

K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
[CrossRef]

1994 (1)

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).
[CrossRef]

1990 (1)

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

1985 (1)

A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov exponents from a time series," Physica D 16, 285-317 (1985).
[CrossRef]

1980 (1)

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
[CrossRef]

Ahlers, V.

V. Ahlers, U. Parlitz, and W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E 58, 7208-7213 (1998).
[CrossRef]

Aida, T.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
[CrossRef]

Buldú, J. M.

J. M. Buldú, J. Garcia-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

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.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
[CrossRef]

H. F. Chen and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

Davis, P.

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, "Synchronization of chaotic semiconductor laser dynamics on sub-ns timescales and its potential for chaos communication," Phys. Rev. A 62, 011801-1-4 (2000).
[CrossRef]

Deng, G.

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Numerical study of static and dynamic behaviors of VCSELs with polarization-selective optical feedback," IEE Proc. Optoelectron. (to be published).

Elsäßer, W.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef]

Fischer, I.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, "Synchronization of chaotic semiconductor laser dynamics on sub-ns timescales and its potential for chaos communication," Phys. Rev. A 62, 011801-1-4 (2000).
[CrossRef]

Fujino, H.

Gao, J. B.

J. B. Gao, S. K. Hwang, and J. M. Liu, "Effects of intrinsic spontaneous-emission noise on the nonlinear dynamics of an optically injected semiconductor laser," Phys. Rev. A 59, 1582-1585 (1999).
[CrossRef]

Garcia-Ojalvo, J.

J. M. Buldú, J. Garcia-Ojalvo, and M. C. Torrent, "Multimode synchronization and communication using unidirectionally coupled semiconductor lasers," IEEE J. Quantum Electron. 40, 640-650 (2004).
[CrossRef]

Gavrielides, A.

A. Hohl and A. Gavrielides, "Bifurcation cascade in a semiconductor laser subject to optical feedback," Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

Heil, T.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef]

Hohl, A.

A. Hohl and A. Gavrielides, "Bifurcation cascade in a semiconductor laser subject to optical feedback," Phys. Rev. Lett. 82, 1148-1151 (1999).
[CrossRef]

Hwang, S. K.

J. B. Gao, S. K. Hwang, and J. M. Liu, "Effects of intrinsic spontaneous-emission noise on the nonlinear dynamics of an optically injected semiconductor laser," Phys. Rev. A 59, 1582-1585 (1999).
[CrossRef]

Kakiuchida, H.

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Kusumoto, K.

K. Kusumoto and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Lauterborn, W.

V. Ahlers, U. Parlitz, and W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E 58, 7208-7213 (1998).
[CrossRef]

Li, N. H.

X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

Li, X. F.

X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Numerical study of static and dynamic behaviors of VCSELs with polarization-selective optical feedback," IEE Proc. Optoelectron. (to be published).

Liu, J. M.

S. Tang and J. M. Liu, "Effects of message encoding and decoding on synchronized chaotic optical communications," IEEE J. Quantum Electron. 39, 1468-1475 (2003).
[CrossRef]

S. Tang and J. M. Liu, "Chaotic pulsing and quasiperiodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum Electron. 37, 329-336 (2001).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
[CrossRef]

H. F. Chen and J. M. Liu, "Open-loop chaotic synchronization of injection-locked semiconductor lasers with gigahertz range modulation," IEEE J. Quantum Electron. 36, 27-34 (2000).
[CrossRef]

J. B. Gao, S. K. Hwang, and J. M. Liu, "Effects of intrinsic spontaneous-emission noise on the nonlinear dynamics of an optically injected semiconductor laser," Phys. Rev. A 59, 1582-1585 (1999).
[CrossRef]

Liu, Y.

A. Uchida, Y. Liu, and P. Davis, "Characteristics of chaotic masking in synchronized semiconductor lasers," IEEE J. Quantum Electron. 39, 963-970 (2003).
[CrossRef]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, "Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 63, 031802(R) (2001).
[CrossRef]

I. Fischer, Y. Liu, and P. Davis, "Synchronization of chaotic semiconductor laser dynamics on sub-ns timescales and its potential for chaos communication," Phys. Rev. A 62, 011801-1-4 (2000).
[CrossRef]

Y. Liu and J. Ohtsubo, "Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer," IEEE J. Quantum Electron. 33, 1163-1169 (1997).
[CrossRef]

Luo, B.

X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Numerical study of static and dynamic behaviors of VCSELs with polarization-selective optical feedback," IEE Proc. Optoelectron. (to be published).

Ma, D.

X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Numerical study of static and dynamic behaviors of VCSELs with polarization-selective optical feedback," IEE Proc. Optoelectron. (to be published).

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
[CrossRef]

Miguel, M. S.

J. Martin-Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
[CrossRef]

Mirasso, C. R.

R. Vicente, T. Perez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

P. S. Spencer, C. R. Mirasso, and K. A. Shore, "Effect of strong optical feedback on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 10, 191-193 (1998).
[CrossRef]

Morozov, V. N.

V. N. Morozov, J. A. Neff, and H. J. Zhou, "Analysis of vertical-cavity surface-emitting laser multimode behavior," IEEE J. Quantum Electron. 33, 980-988 (1997).
[CrossRef]

Murakami, A.

A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
[CrossRef]

Neff, J. A.

V. N. Morozov, J. A. Neff, and H. J. Zhou, "Analysis of vertical-cavity surface-emitting laser multimode behavior," IEEE J. Quantum Electron. 33, 980-988 (1997).
[CrossRef]

Ohstubo, J.

K. Kusumoto and J. Ohstubo, "Anticipating synchronization based on optical injection-locking in chaotic semiconductor lasers," IEEE J. Quantum Electron. 39, 1531-1536 (2003).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
[CrossRef]

H. Fujino and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers," Opt. Lett. 25, 625-627 (2000).
[CrossRef]

Y. Takiguchi, H. Fujino, and J. Ohtsubo, "Experimental synchronization of chaotic oscillations in externally injected semiconductor lasers in low-frequency fluctuation regime," Opt. Lett. 24, 1570-1572 (1999).
[CrossRef]

Y. Liu and J. Ohtsubo, "Dynamics and chaos stabilization of semiconductor lasers with optical feedback from an interferometer," IEEE J. Quantum Electron. 33, 1163-1169 (1997).
[CrossRef]

H. Kakiuchida and J. Ohtsubo, "Characteristics of a semiconductor laser with external feedback," IEEE J. Quantum Electron. 30, 2087-2097 (1994).
[CrossRef]

Pan, W.

X. F. Li, W. Pan, B. Luo, D. Ma, Y. Wang, and N. H. Li, "Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser," Chaos Solitons Fractals 27, 1387-1394 (2006).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Theoretical analysis of multi-transverse-mode characteristics of vertical-cavity surface-emitting lasers," Semicond. Sci. Technol. 20, 505-513 (2005).
[CrossRef]

X. F. Li, W. Pan, B. Luo, D. Ma, and G. Deng, "Numerical study of static and dynamic behaviors of VCSELs with polarization-selective optical feedback," IEE Proc. Optoelectron. (to be published).

Parlitz, U.

V. Ahlers, U. Parlitz, and W. Lauterborn, "Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers," Phys. Rev. E 58, 7208-7213 (1998).
[CrossRef]

Pecora, L. M.

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

Peil, M.

M. Peil, T. Heil, I. Fischer, and W. Elsäßer, "Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario," Phys. Rev. Lett. 88, 174101-1-4 (2002).
[CrossRef]

Perez, T.

R. Vicente, T. Perez, and C. R. Mirasso, "Open- versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1197-1204 (2002).
[CrossRef]

Petermann, K.

K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE J. Sel. Top. Quantum Electron. 1, 480-489 (1995).
[CrossRef]

Prati, F.

J. Martin-Regalado, F. Prati, M. S. Miguel, and N. B. Abraham, "Polarization properties of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 33, 765-783 (1997).
[CrossRef]

Shore, K. A.

P. S. Spencer, C. R. Mirasso, and K. A. Shore, "Effect of strong optical feedback on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 10, 191-193 (1998).
[CrossRef]

Spencer, P. S.

P. S. Spencer, C. R. Mirasso, and K. A. Shore, "Effect of strong optical feedback on vertical-cavity surface-emitting lasers," IEEE Photon. Technol. Lett. 10, 191-193 (1998).
[CrossRef]

Swift, J. B.

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Figures (10)

Fig. 1
Fig. 1

Schematic setup of a chaotic optical communication system using three typical schemes (CSK, CMS, and CM) for the encoding and decoding processes. Here, m(t) stands for the message.

Fig. 2
Fig. 2

Complete chaos synchronization and the effects of external optical feedback. The time traces and the correlation curves are plotted in the left and the right columns, respectively. (a), (b), and (c) without additional feedback; (d), (e), and (f) with additional feedback. Here L inj = 6 cm, k inj = 1 × 10−3, L ext1 = 3 cm, k ext1 = 1 × 10−3. In (a), (b), and (c), k ext2 = 0. In (d), (e), and (f), k ext2 = 1 × 10−10 and L ext2 = 3 cm.

Fig. 3
Fig. 3

Generalized chaos synchronization and the effects of external optical feedback. (a) and (b) Time traces; (c), (d), and (e) correlation curves. (a), (b), and (c) Without additional feedback; (d) and (e) with additional feedback. Here L inj = 0 cm, k inj = 5 × 10−2, L ext1 = 3 cm, k ext1 = 1 × 10−3, and L ext2 = 3 cm. In (d), k ext2 = 1 × 10−5. In (e), k ext2 = 1 × 10−3.

Fig. 4
Fig. 4

(a) Sent message, (b) transmitter output, (c) receiver output, (d) output difference of transmitter and receiver, (e) recovered message. The CMS scheme is used and the additional feedback is neglected here. The parameters are chosen to be same as those of Fig. 3.

Fig. 5
Fig. 5

Curve a, sent message; curves b–f, the recovered messages for different levels of the additional optical feedback. Here, L ext2 = 3 cm. (b)–(f), the values of k ext2 are 0, 1 × 10−5, 1 × 10−4, 1 × 10−3, and 1 × 10−2, respectively. The other parameters are the same as those of Fig. 3.

Fig. 6
Fig. 6

Variation of the correlation coefficient between the transmitter and the receiver with respect to the feedback coefficient k ext2. The other parameters are chosen to be same as those of Fig. 3.

Fig. 7
Fig. 7

(a) Variation of the maximum Lyapunov exponent and (b) the bifurcation diagram of master laser power with respect to L ext2. Here k ext2 = 1 × 10−3.

Fig. 8
Fig. 8

Sent message and recovered messages for different values of L ext2, which are chosen to be 3 cm + 0.2 μm and 3 cm + 0.23 μm for (b) and (c), respectively. Here k ext2 = 1 × 10−3 and the other parameters are the same as those of Fig. 3.

Fig. 9
Fig. 9

Same as in Fig. 8 but for the CM scheme.

Fig. 10
Fig. 10

As in Fig. 8 but for the CSK scheme.

Tables (1)

Tables Icon

Table 1 Parameters Used in this Study

Equations (20)

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d P m ( t ) d t = ( Γ G m 1 τ p ) P m ( t ) + β sp BN m 2 ( t ) + 2 k ext 1 τ in P m ( t ) P m ( t τ ext 1 ) cos [ θ ext 1 ( t ) ] + 2 k ext 2 τ in P m ( t ) P m ( t τ ext 2 ) cos [ θ ext 2 ( t ) ] ,
d N m ( t ) d t = I q V N m ( t ) τ e G m P m ( t ) ,
d Φ m ( t ) d t = 1 2 β c ( Γ G m 1 τ p ) k ext 1 τ in P m ( t τ ext 1 ) P m ( t ) sin [ θ ext 1 ( t ) ] k ext 2 τ in P m ( t τ ext 2 ) P m ( t ) sin [ θ ext 2 ( t ) ] ,
θ ext 1 , ext 2 ( t ) = ω m τ ext 1 , ext 2 + Φ m ( t ) Φ m ( t τ ext 1 , ext 2 ) ,
τ ext 1 , ext 2 = 2 L ext 1 , ext 2 / C ,
d P s ( t ) d t = ( Γ G s 1 τ p ) P s ( t ) + β sp BN s 2 ( t ) + 2 k inj τ in P s ( t ) P m ( t τ inj ) cos [ θ inj ( t ) ] ,
d N s ( t ) d t = I q V N s ( t ) τ e G s P s ( t ) ,
d Φ s ( t ) d t = 1 2 β c ( Γ G s 1 τ p ) k inj τ in P m ( t τ inj ) P s ( t ) sin [ θ inj ( t ) ] ,
θ inj ( t ) = ω m τ inj + Φ s ( t ) Φ m ( t τ inj ) + t Δ ω ,
τ inj = L inj / C ,
G m , s = v g α N log [ N m , s ( t ) / N 0 ] 1 + ε N L P m , s ( t ) ,
P s ( t ) = P m ( t Δ t ) ,
Φ s ( t ) = Φ m ( t Δ t ) ω 0 Δ t ( mod 2 π ) ,
N s ( t ) = N m ( t Δ t ) ,
k ext1 = k inj ,
Δ ω = 0 ,
Δ t = τ inj τ ext 1 .
P s ( t ) P m ( t Δ t ) ,
Δ t = τ inj .
C ( Δ t ) = { P m ( t Δ t ) P m ( t Δ t ) } { P s ( t ) P s ( t ) } { P m ( t - Δt ) - P m ( t - Δt ) } 2 { P s ( t ) - P s ( t ) } 2 .

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