Abstract

We numerically demonstrate that stable isochronal chaos synchronization (ICS) can be achieved by adding individual self-feedback or external driving to two multiple time-delayed coupling semiconductor lasers (MTDCSLs). The properties of the ICS, such as the influences of the coupling parameters, the mismatch robustness, the chaos pass filtering effects, and the communication performance in these two MTDCSL configurations, are comparatively studied. Moreover, we show that the proposed schemes afford multichannel chaos-based communication with the chaos modulation technique, which provides a potential method for the realization of chaos communication networks.

© 2011 Optical Society of America

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  1. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  2. S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed optoelectronic feedback,” IEEE J. Quantum Electron. 37, 329–336 (2001).
    [CrossRef]
  3. X. F. Li, W. Pan, B. Luo, and D. Ma, “Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser,” Chaos Solitons Fractals 27, 1387–1394 (2006).
    [CrossRef]
  4. D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24, 335–341 (2006).
    [CrossRef]
  5. F. Y. Lin and M. C. Tsai, “Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers,” Opt. Express 15, 302–311 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
    [CrossRef]
  8. G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
    [CrossRef]
  9. W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239(2008).
    [CrossRef] [PubMed]
  10. A. Murakami and K. A. Shore, “Chaos-pass filtering in injection-locked semiconductor lasers,” Phys. Rev. A 72, 053810 (2005).
    [CrossRef]
  11. A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. M. C. Chiang, H. F. Chen and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 41, 1333–1340 (2005).
    [CrossRef]
  15. T. Heil, I. Fischer, W. Elsasser, 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]
  16. R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32, 403–405 (2007).
    [CrossRef] [PubMed]
  17. N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
    [CrossRef]
  18. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
    [CrossRef]
  19. M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
    [CrossRef]
  20. A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
    [CrossRef] [PubMed]
  21. N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
    [CrossRef]
  22. J. Mulet, C. Masoller, and C. R. Mirasso, “Modeling bidirectionally coupled single-mode semiconductor lasers,” Phys. Rev. A 65, 063815 (2002).
    [CrossRef]
  23. N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
    [CrossRef]
  24. R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three-coupled semiconductor lasers,” Phys. Rev. E 78, 066202 (2008).
    [CrossRef]
  25. M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
    [CrossRef]
  26. A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
    [CrossRef]
  27. J. Paul, M. W. Lee, and K. A. Shore, “Effect of chaos pass filtering on message decoding quality using chaotic external-cavity laser diodes,” Opt. Lett. 29, 2497–2499 (2004).
    [CrossRef] [PubMed]
  28. Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656–2662 (2008).
    [CrossRef]

2010

G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
[CrossRef]

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

2009

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

2008

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239(2008).
[CrossRef] [PubMed]

R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three-coupled semiconductor lasers,” Phys. Rev. E 78, 066202 (2008).
[CrossRef]

M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
[CrossRef]

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
[CrossRef]

Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656–2662 (2008).
[CrossRef]

2007

2006

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

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

D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24, 335–341 (2006).
[CrossRef]

2005

A. Murakami and K. A. Shore, “Chaos-pass filtering in injection-locked semiconductor lasers,” Phys. Rev. A 72, 053810 (2005).
[CrossRef]

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

M. C. Chiang, H. F. Chen and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 41, 1333–1340 (2005).
[CrossRef]

2004

2003

2002

J. Mulet, C. Masoller, and C. R. Mirasso, “Modeling bidirectionally coupled single-mode semiconductor lasers,” Phys. Rev. A 65, 063815 (2002).
[CrossRef]

2001

T. Heil, I. Fischer, W. Elsasser, 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]

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed optoelectronic feedback,” IEEE J. Quantum Electron. 37, 329–336 (2001).
[CrossRef]

1980

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

Annovazzi-Lodi, V.

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Argyris, A.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
[CrossRef]

D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24, 335–341 (2006).
[CrossRef]

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

D. Kanakidis, A. Argyris, and D. Syvridis, “Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration,” J. Lightwave Technol. 21, 750–758 (2003).
[CrossRef]

Aviad, Y.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

Bogris, A.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
[CrossRef]

D. Kanakidis, A. Argyris, A. Bogris, and D. Syvridis, “Influence of the decoding process on the performance of chaos encrypted optical communication systems,” J. Lightwave Technol. 24, 335–341 (2006).
[CrossRef]

Butkovski, M.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

Cao, L.-P.

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Chen, H. F.

M. C. Chiang, H. F. Chen and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 41, 1333–1340 (2005).
[CrossRef]

Chen, J.-G.

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Chiang, M. C.

M. C. Chiang, H. F. Chen and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 41, 1333–1340 (2005).
[CrossRef]

Chlouverakis, K. E.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
[CrossRef]

Colet, P.

M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
[CrossRef]

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Deng, T.

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Elsasser, W.

T. Heil, I. Fischer, W. Elsasser, 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]

Englert, A.

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

Feng, Y.

G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
[CrossRef]

Fischer, I.

R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three-coupled semiconductor lasers,” Phys. Rev. E 78, 066202 (2008).
[CrossRef]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32, 403–405 (2007).
[CrossRef] [PubMed]

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E 76, 045201 (2007).
[CrossRef]

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

T. Heil, I. Fischer, W. Elsasser, 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]

Garcia-Ojalvo, J.

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Gross, N.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsasser, 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]

Jiang, N.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

Kanakidis, D.

Kanter, I.

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Khaykovich, L.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Kinzel, W.

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Klein, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[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]

Kopelowitz, E.

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[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]

Larger, L.

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E 76, 045201 (2007).
[CrossRef]

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Lee, M. W.

Li, G.-H.

G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
[CrossRef]

Li, N. Q.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

Li, X. F.

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

Li, Y. L.

Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656–2662 (2008).
[CrossRef]

Lin, F. Y.

Lin, X.-D.

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Liu, J. M.

M. C. Chiang, H. F. Chen and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 41, 1333–1340 (2005).
[CrossRef]

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed optoelectronic feedback,” IEEE J. Quantum Electron. 37, 329–336 (2001).
[CrossRef]

Luo, B.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239(2008).
[CrossRef] [PubMed]

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

Ma, D.

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

Masoller, C.

J. Mulet, C. Masoller, and C. R. Mirasso, “Modeling bidirectionally coupled single-mode semiconductor lasers,” Phys. Rev. A 65, 063815 (2002).
[CrossRef]

Mirasso, C. R.

R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three-coupled semiconductor lasers,” Phys. Rev. E 78, 066202 (2008).
[CrossRef]

M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
[CrossRef]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32, 403–405 (2007).
[CrossRef] [PubMed]

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

J. Mulet, C. Masoller, and C. R. Mirasso, “Modeling bidirectionally coupled single-mode semiconductor lasers,” Phys. Rev. A 65, 063815 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsasser, 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.

J. Mulet, C. Masoller, and C. R. Mirasso, “Modeling bidirectionally coupled single-mode semiconductor lasers,” Phys. Rev. A 65, 063815 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsasser, 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 and K. A. Shore, “Chaos-pass filtering in injection-locked semiconductor lasers,” Phys. Rev. A 72, 053810 (2005).
[CrossRef]

Pan, W.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239(2008).
[CrossRef] [PubMed]

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

Paul, J.

Peil, M.

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E 76, 045201 (2007).
[CrossRef]

Pesquera, L.

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Reidler, I.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

Rizomiliotis, P.

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
[CrossRef]

Rosenbluh, M.

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

Ruiz-Oliveras, F.

M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
[CrossRef]

Shore, K. A.

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

A. Murakami and K. A. Shore, “Chaos-pass filtering in injection-locked semiconductor lasers,” Phys. Rev. A 72, 053810 (2005).
[CrossRef]

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

J. Paul, M. W. Lee, and K. A. Shore, “Effect of chaos pass filtering on message decoding quality using chaotic external-cavity laser diodes,” Opt. Lett. 29, 2497–2499 (2004).
[CrossRef] [PubMed]

Sivaprakasam, S.

Soriano, M. C.

M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
[CrossRef]

Syvridis, D.

Syvrids, D.

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Tang, S.

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed optoelectronic feedback,” IEEE J. Quantum Electron. 37, 329–336 (2001).
[CrossRef]

Tsai, M. C.

Vicente, R.

R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three-coupled semiconductor lasers,” Phys. Rev. E 78, 066202 (2008).
[CrossRef]

R. Vicente, C. R. Mirasso, and I. Fischer, “Simultaneous bidirectional message transmission in a chaos-based communication scheme,” Opt. Lett. 32, 403–405 (2007).
[CrossRef] [PubMed]

Wang, A. B.

Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656–2662 (2008).
[CrossRef]

Wang, A.-B.

G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
[CrossRef]

Wang, M. Y.

Wang, Y.

G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
[CrossRef]

Wang, Y. C.

Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656–2662 (2008).
[CrossRef]

Wu, Z.-M.

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Xia, G.-Q.

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Xiang, S. Y.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

Yan, L. S.

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

Yang, L.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

Zhang, W. L.

Zheng, D.

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, W. L. Zhang, S. Y. Xiang, L. Yang, and D. Zheng, “Chaos synchronization and communication in mutually coupled semiconductor lasers driven by a third laser,” J. Lightwave Technol. 28, 1978–1986 (2010).
[CrossRef]

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

Zhou, Z.

Zigzag, M.

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

Zou, X. H.

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, and Z. Zhou, “Chaos synchronization communication using extremely unsymmetrical bidirectional injections,” Opt. Lett. 33, 237–239(2008).
[CrossRef] [PubMed]

Chaos Solitons Fractals

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

Chin. Phys. B

G.-H. Li, A.-B. Wang, Y. Feng, and Y. Wang, “Synchronization and bidirectional communication without delay line using strong mutually coupled semiconductor lasers,” Chin. Phys. B 19, 070515 (2010).
[CrossRef]

IEEE J. Quantum Electron.

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

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed optoelectronic feedback,” IEEE J. Quantum Electron. 37, 329–336 (2001).
[CrossRef]

M. C. Chiang, H. F. Chen and J. M. Liu, “Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback,” IEEE J. Quantum Electron. 41, 1333–1340 (2005).
[CrossRef]

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, and D. Syvridis, “Feedback phase in optically generated chaos: a sceret key for cryptographic applications,” IEEE J. Quantum Electron. 44, 119–124 (2008).
[CrossRef]

IEEE Photon. Technol. Lett.

N. Jiang, W. Pan, L. S. Yan, B. Luo, X. H. Zou, S. Y. Xiang, L. Yang, and D. Zheng, “Multiaccess optical chaos communication using mutually coupled semiconductor lasers subjected to identical external injections,” IEEE Photon. Technol. Lett. 22, 676–678(2010).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Nature

A. Argyris, D. Syvrids, 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 fibre-optic links,” Nature 437, 343–346 (2005).
[CrossRef]

Opt. Commun.

Y. L. Li, Y. C. Wang, and A. B. Wang, “Message filtering characteristics of semiconductor laser as receiver in optical chaos communication,” Opt. Commun. 281, 2656–2662 (2008).
[CrossRef]

T. Deng, G.-Q. Xia, L.-P. Cao, J.-G. Chen, X.-D. Lin, and Z.-M. Wu, “Bidirectional chaos synchronization and communication in semiconductor lasers with optoelectronic feedback,” Opt. Commun. 282, 2243–2249 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. Mulet, C. Masoller, and C. R. Mirasso, “Modeling bidirectionally coupled single-mode semiconductor lasers,” Phys. Rev. A 65, 063815 (2002).
[CrossRef]

A. Murakami and K. A. Shore, “Chaos-pass filtering in injection-locked semiconductor lasers,” Phys. Rev. A 72, 053810 (2005).
[CrossRef]

Phys. Rev. E

N. Jiang, W. Pan, B. Luo, L. S. Yan, S. Y. Xiang, L. Yang, D. Zheng, and N. Q. Li, “Properties of leader/laggard chaos synchronization in mutually coupled external-cavity semiconductor lasers,” Phys. Rev. E 81, 066217 (2010).
[CrossRef]

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, and I. Kanter, “Public-channel cryptography based on mutual chaos pass filters,” Phys. Rev. E 74, 046201 (2006).
[CrossRef]

M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and I. Kanter, “Zero-lag synchronization and multiple time delays in two coupled chaotic systems,” Phys. Rev. E 81, 036215 (2010).
[CrossRef]

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E 76, 045201 (2007).
[CrossRef]

R. Vicente, I. Fischer, and C. R. Mirasso, “Synchronization properties of three-coupled semiconductor lasers,” Phys. Rev. E 78, 066202 (2008).
[CrossRef]

M. C. Soriano, F. Ruiz-Oliveras, P. Colet, and C. R. Mirasso, “Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback,” Phys. Rev. E 78, 046218 (2008).
[CrossRef]

Phys. Rev. Lett.

T. Heil, I. Fischer, W. Elsasser, 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]

A. Englert, W. Kinzel, Y. Aviad, M. Butkovski, I. Reidler, M. Zigzag, I. Kanter, and M. Rosenbluh, “Zero lag synchronization of chaotic systems with time delayed couplings,” Phys. Rev. Lett. 104, 114102 (2010).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematics of the two MTDCSL configurations: (a) self-feedback; (b) external driving. SL, semiconductor laser; R, reflector; DSL, driver SL; OI, optical isolator; OC, optical coupler.

Fig. 2
Fig. 2

Cross correlation between the outputs of SL1 and SL2 as a function of the injection current I: (a) self-feedback with k f = 10 ns 1 ; (b) ED with k i = 60 ns 1 . The coupling delays are T 1 = 5 ns and T 2 = 10 ns , and the coupling strengths are set to σ 1 = σ 2 = 10 ns 1 .

Fig. 3
Fig. 3

Cross correlation of the outputs of the MCSLs as a function of the MC delays: (a) SF with k f = 10 ns 1 ; (b) ED with k i = 60 ns 1 . The coupling strengths for both cases are set to σ 1 = σ 2 = 10 ns 1 .

Fig. 4
Fig. 4

(a) Cross correlation of the outputs of the MCSLs as a function of the MC strengths and the feedback strength for the SF setup; (b) cross correlation of the outputs of the MCSLs in the parameter space of the MC strengths and the driving strength for the ED configuration.

Fig. 5
Fig. 5

Cross correlation of the outputs of the MCSLs as a function of the MC strengths: (a) SF with k f = 10 ns 1 ; (b) ED with k i = 60 ns 1 .

Fig. 6
Fig. 6

Illustrations of the influence of the parameter mismatch on the synchronization performance for the cases of SF (dashed red curve) and ED (solid black curve). Parameters: k f = 10 ns 1 ; σ 1 = σ 2 = 10 ns 1 ; k i = 60 ns 1 .

Fig. 7
Fig. 7

Illustration of the CPF effects of the SF configuration: (a) power difference between the modulated carrier of SL1 on the Path 1 and the output of SL2; (b) power difference between the modulated carrier of SL1 on Path 2 and the output of SL2; (c) power difference between the modulated carrier of SL2 on Path 1 and the output of SL1; (d) power difference between the modulated carrier of SL2 on Path 2 and the output of SL1. Parameters: k f = 10 ns 1 , σ 1 = σ 2 = 10 ns 1 .

Fig. 8
Fig. 8

Illustration of the CPF effects of the ED configuration: (a) power difference between the modulated carrier of SL1 on Path 1 and the output of SL2; (b) power difference between the modulated carrier of SL1 on Path 2 and the output of SL2; (c) power difference between the modulated carrier of SL2 on Path 1 and the output of SL1; (d) power difference between the modulated carrier of SL2 on Path 2 and the output of SL1. Parameters: k i = 60 ns 1 ; σ 1 = σ 2 = 10 ns 1 .

Fig. 9
Fig. 9

Illustrations of the multichannel message exchange for the SF [(a) and (b)] and ED [(c) and (d)] cases: (a) and (c) present the recovery process at the SL1 end, wherein the black dashed and the blue dashed curves represent the original messages of SL2 encrypted on Path 1 and Path 2, respectively, while the solid curves denote the corresponding decrypted messages recovered by SL1; (b) and (d) present the recovery process at the SL2 end, wherein the black dashed and the blue dashed curves represent the original messages of SL1 encrypted on Path 1 and Path 2, respectively, while the solid curves denote the corresponding decrypted messages recovered by SL2. Parameters are the same as those of Figs. 7, 8.

Fig. 10
Fig. 10

Q-factor values of the recovered messages as a function of the bit rate for (a) the SF scheme and (b) the ED scheme. Parameters are the same as those of Figs. 7, 8.

Tables (1)

Tables Icon

Table 1 Values of Parameters Used in Simulations [4, 15]

Equations (8)

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

d E 1 , 2 ( t ) d t = ( 1 + i α ) 2 ( G 1 , 2 1 τ p ) E 1 , 2 ( t ) + k f E 1 , 2 ( t τ f ) exp ( i ϕ f ) + m = 1 n σ m E 2 , 1 ( t T m ) exp ( i ϕ c m ) + 2 β N 1 , 2 ( t ) χ 1 , 2 ,
d N 1 , 2 ( t ) d t = I q N 1 , 2 ( t ) τ e G 1 , 2 | E 1 , 2 ( t ) | 2 .
d E 1 , 2 ( t ) d t = 1 2 ( 1 + i α ) ( G 1 , 2 1 τ p ) E 1 , 2 ( t ) + k i E D ( t τ i ) exp ( i ϕ i ) + m = 1 n σ m E 2 , 1 ( t T m ) exp ( i ϕ c m ) + 2 β N 1 , 2 ( t ) χ 1 , 2 ,
d N 1 , 2 ( t ) d t = I q N 1 , 2 ( t ) τ e G 1 , 2 | E 1 , 2 ( t ) | 2 .
d E D ( t ) d t = 1 2 ( 1 + i α ) ( G D 1 τ p ) E D ( t ) + k f D E D ( t τ f D ) exp ( i ϕ f D ) + 2 β N D ( t ) χ D ,
d N D ( t ) d t = I D q N D ( t ) τ e G D | E D ( t ) | 2 .
G 1 , 2 , D = g [ N 1 , 2 , D ( t ) N 0 ] 1 + s E 1 , 2 , D ( t ) 2 .
C 12 = ( P 1 ( t ) P 1 ( t ) ) · ( P 2 ( t ) P 2 ( t ) ) ( P 1 ( t ) P 1 ( t ) ) 2 · ( P 2 ( t ) P 2 ( t ) ) 2 ,

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