Abstract

This paper reports the first experimental observation and theoretical description of zero time lag, complete-chaos synchronization using three laser diodes coupled in a unidirectional cascade configuration. The master laser is rendered chaotic by optical feedback from an external mirror. The output intensity of the master laser is injected into an intermediate laser, and the output intensity of this intermediate laser is in turn injected into a slave laser. The distances between the lasers are carefully adjusted such that the times of flight between the lasers are equal to the delay time in the external-cavity of the master laser. When the three lasers are subject to the same optical injection strength it is observed that their output intensities synchronize with zero time lag. The chaos synchronization has been confirmed by time traces and synchronization diagrams of the three laser outputs, and the null lag time has been measured from cross-correlation diagrams. Numerical simulations based on single-mode rate equations are in good qualitative agreement with the experimental observations.

© 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. 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, 801-1-4 (2000).
    [CrossRef]
  3. A. Uchida, S. Yoshimori, M. Shinozuka, T. Ogawa, and F. Kannari, "Chaotic on—>off keying for secure communications," Opt. Lett. 26, 866-868 (2001).
    [CrossRef]
  4. S. Tang and J.-M. Liu, "Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers," Opt. Lett. 26, 1843-1845 (2001).
    [CrossRef]
  5. J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
    [CrossRef]
  6. C. R. Mirasso, J. Mulet, and C. Masoller, "Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photonics Technol. Lett. 14, 456-458 (2002).
    [CrossRef]
  7. T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
    [CrossRef]
  8. J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, "Optically modulated chaotic communication scheme with external-cavity length as a key to security," J. Opt. Soc. Am. B 20, 497-503 (2003).
    [CrossRef]
  9. M. W. Lee, L. Larger, and J.-P. Goedgebuer, "Transmission system using chaotic delays between lightwaves," IEEE J. Quantum Electron. 39, 931-935 (2003).
    [CrossRef]
  10. J. Paul, M. W. Lee, and K. A. Shore, "3.5-GHz signal transmission in an all-optical chaotic communicationscheme using 1550-nm diode lasers," IEEE Photonics Technol. Lett. 17, 920-922 (2005).
    [CrossRef]
  11. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
    [CrossRef]
  12. D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
    [CrossRef]
  13. S. Sivaprakasam and K. A. Shore, "Demonstration of optical synchronization of chaotic external-cavity laser diodes," Opt. Lett. 24, 466-468 (1999).
    [CrossRef]
  14. C. Masoller, "Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 2782-2785 (2001).
    [CrossRef] [PubMed]
  15. S. Tang and J.-M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 101-1-4 (2003).
    [CrossRef]
  16. Y. Liu and P. Davis, "Dual synchronization of chaos," Phys. Rev. E 61, R2176-R2179 (2000).
    [CrossRef]
  17. A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
    [CrossRef]
  18. A. Murakami, "Phase locking and chaos synchronization in injection-locked semiconductor lasers," IEEE J. Quantum Electron. 39, 438-447 (2003).
    [CrossRef]
  19. M. W. Lee and K. A. Shore, "Two-mode chaos synchronization using a multi-mode external-cavity laser diode and two single-mode laser diodes," J. Lightwave Technol. 23, 1068-1073 (2005).
    [CrossRef]
  20. J. Mulet, C. Masoller, and C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 815-1-12 (2002).
    [CrossRef]
  21. J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
    [CrossRef]
  22. T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
    [CrossRef] [PubMed]
  23. N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, "Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 28, 1677-1679 (2003).
    [CrossRef] [PubMed]
  24. Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
    [CrossRef] [PubMed]
  25. I. V. Koryukin and P. Mandel, "Two regimes of synchronization in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65, 201-1-5 (2002).
    [CrossRef]
  26. A. Locquet, C. Masoller, and C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65,205-1-12 (2002).
    [CrossRef]
  27. A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, "Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback," Phys. Rev. E 69, 201-1-9 (2004).
    [CrossRef]
  28. Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
    [CrossRef]
  29. Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
    [CrossRef]
  30. A. Murakami and J. Ohtsubo, "Synchronization of feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 65,826-1-7 (2002).
    [CrossRef]
  31. M. W. Lee, J. Paul, I. Pierce, and K. A. Shore, "Frequency-detuned synchronization switching in chaotic DFB laser diodes," IEEE J. Quantum Electron. 41, 302-307 (2005).
    [CrossRef]
  32. R. Vicente, T. Pérez, 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]
  33. M. W. Lee, J. Paul, S. Sivaprakasam, and K. A. Shore, "Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes," Opt. Lett. 28, 2168-2170 (2003).
    [CrossRef] [PubMed]
  34. S. Sivaprakasam and K. A. Shore, "Cascaded synchronization of external-cavity laser diodes," Opt. Lett. 26, 253-255 (2001).
    [CrossRef]
  35. J. Paul, S. Sivaprakasam, and K. A. Shore, "Dual-channel chaotic optical communications using external-cavity semiconductor lasers," J. Opt. Soc. Am. B 21, 514-521 (2004).
    [CrossRef]
  36. J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
    [CrossRef]

2005

J. Paul, M. W. Lee, and K. A. Shore, "3.5-GHz signal transmission in an all-optical chaotic communicationscheme using 1550-nm diode lasers," IEEE Photonics Technol. Lett. 17, 920-922 (2005).
[CrossRef]

M. W. Lee, J. Paul, I. Pierce, and K. A. Shore, "Frequency-detuned synchronization switching in chaotic DFB laser diodes," IEEE J. Quantum Electron. 41, 302-307 (2005).
[CrossRef]

M. W. Lee and K. A. Shore, "Two-mode chaos synchronization using a multi-mode external-cavity laser diode and two single-mode laser diodes," J. Lightwave Technol. 23, 1068-1073 (2005).
[CrossRef]

2004

2003

J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, "Optically modulated chaotic communication scheme with external-cavity length as a key to security," J. Opt. Soc. Am. B 20, 497-503 (2003).
[CrossRef]

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, "Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 28, 1677-1679 (2003).
[CrossRef] [PubMed]

M. W. Lee, J. Paul, S. Sivaprakasam, and K. A. Shore, "Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes," Opt. Lett. 28, 2168-2170 (2003).
[CrossRef] [PubMed]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

M. W. Lee, L. Larger, and J.-P. Goedgebuer, "Transmission system using chaotic delays between lightwaves," IEEE J. Quantum Electron. 39, 931-935 (2003).
[CrossRef]

S. Tang and J.-M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 101-1-4 (2003).
[CrossRef]

A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
[CrossRef]

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

2002

I. V. Koryukin and P. Mandel, "Two regimes of synchronization in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65, 201-1-5 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65,205-1-12 (2002).
[CrossRef]

C. R. Mirasso, J. Mulet, and C. Masoller, "Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photonics Technol. Lett. 14, 456-458 (2002).
[CrossRef]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

A. Murakami and J. Ohtsubo, "Synchronization of feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 65,826-1-7 (2002).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

R. Vicente, T. Pérez, 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]

J. Mulet, C. Masoller, and C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 815-1-12 (2002).
[CrossRef]

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
[CrossRef]

2001

S. Sivaprakasam and K. A. Shore, "Cascaded synchronization of external-cavity laser diodes," Opt. Lett. 26, 253-255 (2001).
[CrossRef]

A. Uchida, S. Yoshimori, M. Shinozuka, T. Ogawa, and F. Kannari, "Chaotic on—>off keying for secure communications," Opt. Lett. 26, 866-868 (2001).
[CrossRef]

S. Tang and J.-M. Liu, "Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers," Opt. Lett. 26, 1843-1845 (2001).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
[CrossRef]

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
[CrossRef]

C. Masoller, "Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 2782-2785 (2001).
[CrossRef] [PubMed]

2000

Y. Liu and P. Davis, "Dual synchronization of chaos," Phys. Rev. E 61, R2176-R2179 (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, 801-1-4 (2000).
[CrossRef]

1999

1997

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
[CrossRef]

1990

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

Aida, T.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

Breban, R.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
[CrossRef]

Buldú, J. M.

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

Carroll, T. L.

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

Colet, P.

J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
[CrossRef]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

Cuenot, J.-B.

J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
[CrossRef]

Davis, P.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (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, 801-1-4 (2000).
[CrossRef]

Y. Liu and P. Davis, "Dual synchronization of chaos," Phys. Rev. E 61, R2176-R2179 (2000).
[CrossRef]

DeShazer, D. J.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
[CrossRef]

Elsäßer, W.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

Fischer, I.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

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, 801-1-4 (2000).
[CrossRef]

Fujiwara, N.

García-Ojalvo, J.

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

Goedgebuer, J.-P.

M. W. Lee, L. Larger, and J.-P. Goedgebuer, "Transmission system using chaotic delays between lightwaves," IEEE J. Quantum Electron. 39, 931-935 (2003).
[CrossRef]

J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
[CrossRef]

Heil, T.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

Hong, Y.

Kannari, F.

Kinugawa, S.

A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
[CrossRef]

Koryukin, I. V.

I. V. Koryukin and P. Mandel, "Two regimes of synchronization in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65, 201-1-5 (2002).
[CrossRef]

Kurths, J.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
[CrossRef]

Larger, L.

M. W. Lee, L. Larger, and J.-P. Goedgebuer, "Transmission system using chaotic delays between lightwaves," IEEE J. Quantum Electron. 39, 931-935 (2003).
[CrossRef]

J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
[CrossRef]

Lee, M. W.

J. Paul, M. W. Lee, and K. A. Shore, "3.5-GHz signal transmission in an all-optical chaotic communicationscheme using 1550-nm diode lasers," IEEE Photonics Technol. Lett. 17, 920-922 (2005).
[CrossRef]

M. W. Lee and K. A. Shore, "Two-mode chaos synchronization using a multi-mode external-cavity laser diode and two single-mode laser diodes," J. Lightwave Technol. 23, 1068-1073 (2005).
[CrossRef]

M. W. Lee, J. Paul, I. Pierce, and K. A. Shore, "Frequency-detuned synchronization switching in chaotic DFB laser diodes," IEEE J. Quantum Electron. 41, 302-307 (2005).
[CrossRef]

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

M. W. Lee, L. Larger, and J.-P. Goedgebuer, "Transmission system using chaotic delays between lightwaves," IEEE J. Quantum Electron. 39, 931-935 (2003).
[CrossRef]

M. W. Lee, J. Paul, S. Sivaprakasam, and K. A. Shore, "Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes," Opt. Lett. 28, 2168-2170 (2003).
[CrossRef] [PubMed]

Liu, J.-M.

S. Tang and J.-M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 101-1-4 (2003).
[CrossRef]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

S. Tang and J.-M. Liu, "Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers," Opt. Lett. 26, 1843-1845 (2001).
[CrossRef]

Liu, Y.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

Y. Liu and P. Davis, "Dual synchronization of chaos," Phys. Rev. E 61, R2176-R2179 (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, 801-1-4 (2000).
[CrossRef]

Locquet, A.

A. Locquet, C. Masoller, and C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65,205-1-12 (2002).
[CrossRef]

Mandel, P.

I. V. Koryukin and P. Mandel, "Two regimes of synchronization in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65, 201-1-5 (2002).
[CrossRef]

Masoller, C.

C. R. Mirasso, J. Mulet, and C. Masoller, "Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photonics Technol. Lett. 14, 456-458 (2002).
[CrossRef]

J. Mulet, C. Masoller, and C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 815-1-12 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65,205-1-12 (2002).
[CrossRef]

C. Masoller, "Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 2782-2785 (2001).
[CrossRef] [PubMed]

Matsuura, T.

A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
[CrossRef]

Mirasso, C. R.

J. Mulet, C. Masoller, and C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 815-1-12 (2002).
[CrossRef]

C. R. Mirasso, J. Mulet, and C. Masoller, "Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photonics Technol. Lett. 14, 456-458 (2002).
[CrossRef]

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

R. Vicente, T. Pérez, 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]

J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65,205-1-12 (2002).
[CrossRef]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

Mulet, J.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

C. R. Mirasso, J. Mulet, and C. Masoller, "Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photonics Technol. Lett. 14, 456-458 (2002).
[CrossRef]

J. Mulet, C. Masoller, and C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 815-1-12 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

Murakami, A.

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

A. Murakami and J. Ohtsubo, "Synchronization of feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 65,826-1-7 (2002).
[CrossRef]

Nogawa, S.

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, "Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback," Phys. Rev. E 69, 201-1-9 (2004).
[CrossRef]

Ogawa, T.

Ohtsubo, J.

Ott, E.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
[CrossRef]

Paul, J.

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.

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

Pérez, T.

R. Vicente, T. Pérez, 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]

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

Pesquera, L.

J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
[CrossRef]

Pierce, I.

M. W. Lee, J. Paul, I. Pierce, and K. A. Shore, "Frequency-detuned synchronization switching in chaotic DFB laser diodes," IEEE J. Quantum Electron. 41, 302-307 (2005).
[CrossRef]

Pikovsky, A. S.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
[CrossRef]

Revuelta, J.

J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
[CrossRef]

Rhodes, W. T.

J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
[CrossRef]

Rosenblum, M. G.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
[CrossRef]

Roy, R.

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
[CrossRef]

Saito, S.

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

Shibasaki, N.

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, "Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback," Phys. Rev. E 69, 201-1-9 (2004).
[CrossRef]

Shinozuka, M.

Shore, K. A.

M. W. Lee, J. Paul, I. Pierce, and K. A. Shore, "Frequency-detuned synchronization switching in chaotic DFB laser diodes," IEEE J. Quantum Electron. 41, 302-307 (2005).
[CrossRef]

J. Paul, M. W. Lee, and K. A. Shore, "3.5-GHz signal transmission in an all-optical chaotic communicationscheme using 1550-nm diode lasers," IEEE Photonics Technol. Lett. 17, 920-922 (2005).
[CrossRef]

M. W. Lee and K. A. Shore, "Two-mode chaos synchronization using a multi-mode external-cavity laser diode and two single-mode laser diodes," J. Lightwave Technol. 23, 1068-1073 (2005).
[CrossRef]

J. Paul, S. Sivaprakasam, and K. A. Shore, "Dual-channel chaotic optical communications using external-cavity semiconductor lasers," J. Opt. Soc. Am. B 21, 514-521 (2004).
[CrossRef]

Y. Hong, M. W. Lee, P. S. Spencer, and K. A. Shore, "Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 29, 1215-1217 (2004).
[CrossRef] [PubMed]

M. W. Lee, J. Paul, S. Sivaprakasam, and K. A. Shore, "Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes," Opt. Lett. 28, 2168-2170 (2003).
[CrossRef] [PubMed]

J. Paul, S. Sivaprakasam, P. S. Spencer, and K. A. Shore, "Optically modulated chaotic communication scheme with external-cavity length as a key to security," J. Opt. Soc. Am. B 20, 497-503 (2003).
[CrossRef]

S. Sivaprakasam and K. A. Shore, "Cascaded synchronization of external-cavity laser diodes," Opt. Lett. 26, 253-255 (2001).
[CrossRef]

S. Sivaprakasam and K. A. Shore, "Demonstration of optical synchronization of chaotic external-cavity laser diodes," Opt. Lett. 24, 466-468 (1999).
[CrossRef]

Sivaprakasam, S.

Spencer, P. S.

Takiguchi, Y.

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, "Observation of the synchronization of chaos in mutually injected vertical-cavity surface-emitting semiconductor lasers," Opt. Lett. 28, 1677-1679 (2003).
[CrossRef] [PubMed]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

Tang, S.

S. Tang and J.-M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 101-1-4 (2003).
[CrossRef]

S. Tang and J.-M. Liu, "Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers," Opt. Lett. 26, 1843-1845 (2001).
[CrossRef]

Torrent, M. C.

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

Uchida, A.

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, "Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback," Phys. Rev. E 69, 201-1-9 (2004).
[CrossRef]

A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
[CrossRef]

A. Uchida, S. Yoshimori, M. Shinozuka, T. Ogawa, and F. Kannari, "Chaotic on—>off keying for secure communications," Opt. Lett. 26, 866-868 (2001).
[CrossRef]

Vicente, R.

R. Vicente, T. Pérez, 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]

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

Yoshimori, S.

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, "Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback," Phys. Rev. E 69, 201-1-9 (2004).
[CrossRef]

A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
[CrossRef]

A. Uchida, S. Yoshimori, M. Shinozuka, T. Ogawa, and F. Kannari, "Chaotic on—>off keying for secure communications," Opt. Lett. 26, 866-868 (2001).
[CrossRef]

Appl. Phys. Lett.

Y. Liu, Y. Takiguchi, P. Davis, T. Aida, S. Saito, and J.-M. Liu, "Experimental observation of complete chaos synchronization in semiconductor lasers," Appl. Phys. Lett. 80, 4306-4308 (2002).
[CrossRef]

J. M. Buldú, R. Vicente, T. Pérez, C. R. Mirasso, M. C. Torrent, and J. García-Ojalvo, "Periodic entrainment of power dropouts in mutually coupled semiconductor lasers," Appl. Phys. Lett. 81, 5105-5107 (2002).
[CrossRef]

IEEE J. Quantum Electron.

M. W. Lee, J. Paul, I. Pierce, and K. A. Shore, "Frequency-detuned synchronization switching in chaotic DFB laser diodes," IEEE J. Quantum Electron. 41, 302-307 (2005).
[CrossRef]

R. Vicente, T. Pérez, 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]

Y. Liu, P. Davis, Y. Takiguchi, T. Aida, S. Saito, and J.-M. Liu, "Injection locking and synchronization of periodic and chaotic signals in semiconductor lasers," IEEE J. Quantum Electron. 39, 269-278 (2003).
[CrossRef]

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

J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and W. T. Rhodes, "Chaos shift keying with an optoelectronic encryption system using chaos in wavelength," IEEE J. Quantum Electron. 37, 849-855 (2001).
[CrossRef]

T. Heil, J. Mulet, I. Fischer, C. R. Mirasso, M. Peil, P. Colet, and W. Elsäßer, "ON/OFF phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
[CrossRef]

M. W. Lee, L. Larger, and J.-P. Goedgebuer, "Transmission system using chaotic delays between lightwaves," IEEE J. Quantum Electron. 39, 931-935 (2003).
[CrossRef]

IEEE Photonics Technol. Lett.

J. Paul, M. W. Lee, and K. A. Shore, "3.5-GHz signal transmission in an all-optical chaotic communicationscheme using 1550-nm diode lasers," IEEE Photonics Technol. Lett. 17, 920-922 (2005).
[CrossRef]

C. R. Mirasso, J. Mulet, and C. Masoller, "Chaos shift-keying encryption in chaotic external-cavity semiconductor lasers using a single-receiver scheme," IEEE Photonics Technol. Lett. 14, 456-458 (2002).
[CrossRef]

J. Revuelta, C. R. Mirasso, P. Colet, and L. Pesquera, "Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers," IEEE Photonics Technol. Lett. 14, 140-142 (2002).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

J. Mulet, C. Masoller, and C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 815-1-12 (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, 801-1-4 (2000).
[CrossRef]

A. Murakami and J. Ohtsubo, "Synchronization of feedback-induced chaos in semiconductor lasers by optical injection," Phys. Rev. A 65,826-1-7 (2002).
[CrossRef]

Phys. Rev. E

Y. Liu and P. Davis, "Dual synchronization of chaos," Phys. Rev. E 61, R2176-R2179 (2000).
[CrossRef]

A. Uchida, S. Kinugawa, T. Matsuura, and S. Yoshimori, "Dual synchronization of chaos in one-way coupled microchip lasers," Phys. Rev. E 67, 220-1-8 (2003).
[CrossRef]

I. V. Koryukin and P. Mandel, "Two regimes of synchronization in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65, 201-1-5 (2002).
[CrossRef]

A. Locquet, C. Masoller, and C. R. Mirasso, "Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers," Phys. Rev. E 65,205-1-12 (2002).
[CrossRef]

A. Uchida, N. Shibasaki, S. Nogawa, and S. Yoshimori, "Transient characteristics of chaos synchronization in a semiconductor laser subject to optical feedback," Phys. Rev. E 69, 201-1-9 (2004).
[CrossRef]

Phys. Rev. Lett.

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

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, "From phase to lag synchronization in coupled chaotic oscillators," Phys. Rev. Lett. 78, 4193-4196 (1997).
[CrossRef]

D. J. DeShazer, R. Breban, E. Ott, and R. Roy, "Detecting phase synchronization in a chaotic laser array," Phys. Rev. Lett. 87, 044-101 (2001).
[CrossRef]

C. Masoller, "Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback," Phys. Rev. Lett. 86, 2782-2785 (2001).
[CrossRef] [PubMed]

S. Tang and J.-M. Liu, "Experimental verification of anticipated and retarded synchronization in chaotic semiconductor lasers," Phys. Rev. Lett. 90, 101-1-4 (2003).
[CrossRef]

T. Heil, I. Fischer, W. Elsäßer, J. Mulet, and C. R. Mirasso, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. ML, master laser; IL, intermediate laser; SL, slave laser; τ, external-cavity round-trip time of the ML; τ c 1 , time of flight of ML–IL; τ c 2 , time of flight of IL–SL; BS, beam splitter; NDF, neutral density filter; M, mirror; OI, optical isolator; CA, coupling attenuator; HWP, half-wave plate; PD, photodetector.

Fig. 2
Fig. 2

Experimental time series of the synchronized chaotic laser outputs.

Fig. 3
Fig. 3

Experimental results. Synchronization diagram (a) of the ML versus the IL, (c) of the ML versus the SL, and (e) of the IL versus the SL; cross-correlation diagram (b) of the ML and the IL, (d) of the ML and the SL, and (f) of the IL and the SL.

Fig. 4
Fig. 4

Numerical results for parameters such that γ M = γ I = γ S = 50 ns 1 . (a) Synchronization diagram of the master laser versus the intermediate laser, (b) the corresponding cross-correlation diagram as a function of time shift Δ t , (c) the synchronization diagram of the master laser versus the slave laser, (d) the corresponding cross-correlation diagram, (e) the synchronization diagram of the intermediate laser versus the slave laser, and (f) the corresponding cross-correlation diagram.

Fig. 5
Fig. 5

Numerically simulated output intensities in complete synchronization (parameters as in Fig. 4).

Fig. 6
Fig. 6

Results of numerical simulations with parameters corresponding to generalized synchronization ( γ T = 50 ns 1 , γ I = γ R = 400 ns 1 ). Synchronization diagram (a) of the ML versus the IL, (c) of the ML versus the SL, and (e) of the IL versus the SL; cross-correlation diagram (b) of the ML and the IL, (d) of the ML and the SL, and (f) of the IL and the SL.

Fig. 7
Fig. 7

Numerically simulated output intensities in the generalized synchronization regime (parameters as in Fig. 6). The arrows indicate the lag times between the synchronized intensities.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

E ̇ M = k ( 1 + j α ) ( N M 1 ) E M + γ T E M ( t τ ) exp ( i ω 0 τ ) + D ξ M ( t ) ,
N ̇ M = γ n ( J N M N M E M 2 ) ,
E ̇ I = k ( 1 + j α ) ( N I 1 ) E I + γ I E M ( t τ c 1 ) exp ( i ω 0 τ c 1 ) + D ξ I ( t ) ,
N ̇ I = γ n ( J N I N I E I 2 ) ,
E ̇ S = k ( 1 + j α ) ( N S 1 ) E S ,
+ γ R E I ( t τ c 2 ) exp ( i ω 0 τ c 2 ) + D ξ S ( t )
N ̇ S = γ n ( J N S N S E S 2 ) .
E I ( t τ ) exp ( i ω 0 τ ) = E M ( t τ c 1 ) exp ( i ω 0 τ c 1 ) ,
E S ( t τ ) exp ( i ω 0 τ ) = E I ( t τ c 2 ) exp ( i ω 0 τ c 2 )
I S ( t ) = I I ( t τ c 2 + τ ) = I M ( t + 2 τ τ c 1 τ c 2 ) .
I M ( t ) = a 1 I I ( t + τ c 1 ) ,               I I ( t ) = a 2 I S ( t + τ c 2 ) ,

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