Abstract

We numerically investigate the chaos synchronization and message transmission between two mutual coupling semiconductor lasers (MCSLs) subject to identical unidirectional injections (UIs) from an external cavity semiconductor laser (ECSL). The synchronization between the MCSLs is realized through injection locking in conjunction with symmetric operation. The simulation results show that stable isochronal synchronization between the MCSLs can be achieved under proper driving injections. This type of synchronization is robust to parameter mismatch up to tens of percentage and frequency detuning of several tens of gigahertz, which is much better than those of the MCSLs systems with self-feedback. Moreover, the investigations on the mutual chaos pass filtering effects and the message transmission indicate that the isochronal synchronization allows mutual message exchange with a bit rate higher than 10Gb/s, when the chaos modulation technology is adopted. In addition, the MCSLs can synchronize with the ECSL for proper UI and MC, which provides an opportunity for array chaos synchronization and chaos communication networks. Finally, leader/laggard synchronization can also be achieved in the proposed system.

© 2010 IEEE

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  1. L. M. Pecora, T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-825 (1990).
  2. S. J. Li, G. Alvarez, G. R. Chen, "Breaking a chaos-based secure communication scheme designed by an improved modulation method," Chao, Solitons Fractals 25, 109-120 (2005).
  3. F. Zhang, P. L. Chu, "Effect of transmission fiber on chaos communication system based on erbium-doped fiber ring laser," J. Lightw. Technol. 21, 3334-3343 (2003).
  4. X. F. Li, W. Pan, B. Luo, D. Ma, "Chaos synchronization and communication of cascade-coupled semiconductor lasers," J. Lightw. Technol. 24, 4936-4945 (2006).
  5. F. Y. Lin, M. C. Tsai, "Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers," Opt. Express 15, 302-311 (2007).
  6. T. Heil, J. Mulet, I. Fischer, C. R. Mirraso, M. Peil, P. Colet, W. Elsäßer, "On/off phase shift keying for chaos-encrypted communication using external-cavity semiconductor lasers," IEEE J. Quantum Electron. 38, 1162-1170 (2002).
  7. S. Zhou, H. Li, Z. Z. Zhu, "Chaos control and synchronization in a fractional neuron network system," Chaos, Solitons Fractals 36, 973-984 (2008).
  8. R. Mislovaty, E. Klein, I. Kanter, W. Kinzel, "Public channel cryptography by synchronization of neural networks and chaotic maps," Phys. Rev. Lett. 91, 118701-1-118701-4 (2003).
  9. E. Klein, R. Mislovaty, I. Kanter, W. Kinzel, "Public-channel cryptography using chaos synchronization," Phys. Rev. E 2, 016204-1-016204-4 (2005).
  10. I. Kanter, E. Kopelowitz, W. Kinzel, "Public channel cryptography: Chaos synchronization and Hilbert's tenth problem," Phys. Rev. Lett. 101, 084102-1-084102-4 (2008).
  11. J. Ohtsubo, "Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback," IEEE J. Quantum Electron. 38, 1141-1154 (2002).
  12. A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature 437, 343-346 (2005).
  13. M. P. Vaughan, I. Henning, M. J. Adams, L. J. Rivers, P. Cannard, I. F. Lealman, "Mutual optical injection in coupled DBR laser pairs," Opt. Express 17, 2033-2041 (2009).
  14. X. F. Li, W. Pan, B. Luo, D. Ma, "Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers," Semicond. Sci. Technol. 21, 25-34 (2005).
  15. J. Mulet, C. Masoller, C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 063815-1-063815-12 (2002).
  16. S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Topics Quantum Electron. 10, 936-943 (2004).
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  18. E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, I. Kanter, "Stable isochronal synchronization of mutually coupled chaotic lasers," Phys. Rev. E 73, 066214-1-066214-4 (2006).
  19. M. C. Chiang, H. F. Chen, J. M. Liu, "Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 41, 1333-1340 (2005).
  20. R. Vicente, C. R. Mirasso, I. Fischer, "Simultaneous bidirectional message transmission in a chaos-based communication scheme," Opt. Lett. 32, 403-405 (2007).
  21. X. F. Li, W. Pan, B. Luo, D. Ma, "Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization," IEEE J. Quantum Electron. 42, 953-960 (2006).
  22. W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, Z. Zhou, "Chaos synchronization communication using extremely unsymmetrical bidirectional injections," Opt. Lett. 33, 237-239 (2008).
  23. I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, J. Garcia-Ojalvo, "Zero-lag long-range synchronization via dynamical relaying," Phys. Rev. Lett. 97, 123902-1-123902-4 (2006).
  24. R. Vicente, I. Fischer, C. R. Mirasso, "Synchronization properties of three-coupled semiconductor lasers," Phys. Rev. E 78, 066202-1-066202-11 (2008).
  25. B. B. Zhou, R. Roy, "Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillator," Phys. Rev. E 75, 026205-1-026205-5 (2007).
  26. S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, K. A. Shore, "Identification of the optimum time-delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).
  27. N. Jiang, W. Pan, L. S. Yan, B. Luo, L. Yang, S. Y. Xiang, D. Zheng, "Two chaos synchronization schemes and public-channel message transmission in a mutually coupled semiconductor lasers system," Opt. Commun. 282, 2217-2222 (2009).
  28. M. C. Soriano, F. Ruiz-Oliveras, P. Coler, C. R. Mirasso, "Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback," Phys. Rev. E 78, 046218-1-046218-8 (2008).
  29. A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, D. Syvridis, "Feedback phase in optically generated chaos: A sceret key for cryptographic applications," IEEE. J. Quantum Electron. 44, 119-124 (2008).
  30. E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, I. Kanter, "Public-channel cryptograph based on mutual chaos pass filters," Phys. Rev. E 74, 046201–1-046201-4 (2006).
  31. A. Sanchez-Diaz, C. R. Mirasso, P. Colet, P. Garcia-Fernandez, "Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers," IEEE J. Quantum Electron. 35, 292-297 (1999).
  32. J. M. Liu, H. F. Chen, S. Tang, "Synchronized chaotic optical communications at high bit-rates," IEEE J. Quantum Electron. 38, 1184-1196 (2002).
  33. V. Annovazzi-Lodi, M. Benedetti, S. Merlo, T. Perez, P. Colet, C. R. Mirasso, "Message encryption by phase modulation of a chaotic optical carrier," IEEE Photon. Technol. Lett. 19, 76-79 (2007).
  34. D. Kanakidis, A. Argyris, D. Syvridis, "Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration," J. Lightw. Technol. 21, 750-758 (2003).
  35. D. Kanakidis, A. Argyris, A. Bogris, D. Syvridis, "Influence of the decoding process on the performance of chaos encrypted optical communication systems," J. Lightw. Technol. 24, 335-341 (2006).
  36. A. Bogris, K. E. Chlouverakis, A. Argyris, D. Syvridis, "Enhancement of the encryption efficiency of chaotic communications based on all-optical feedback chaos generation by means of subcarrier modulation," Lasers Electro-Opt. Int. Quantum Electron. Conf., CLEOE-IQEC, Eur. Conf. (2007) pp. 1-1.
  37. A. B. Wang, Y. C. Wang, H. C. He, "Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback," IEEE Photon. Technol. Lett. 20, 1633-1635 (2008).
  38. Y. Takiguchi, K. Ohyagi, J. Ohtsubo, "Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback," Opt. Lett. 28, 319-321 (2003).
  39. R. Vicente, T. Perez, C. R. Mirasso, "Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers," IEEE. J. Quantum Electron. 38, 1197-1204 (2002).

2009 (2)

M. P. Vaughan, I. Henning, M. J. Adams, L. J. Rivers, P. Cannard, I. F. Lealman, "Mutual optical injection in coupled DBR laser pairs," Opt. Express 17, 2033-2041 (2009).

N. Jiang, W. Pan, L. S. Yan, B. Luo, L. Yang, S. Y. Xiang, D. Zheng, "Two chaos synchronization schemes and public-channel message transmission in a mutually coupled semiconductor lasers system," Opt. Commun. 282, 2217-2222 (2009).

2008 (7)

M. C. Soriano, F. Ruiz-Oliveras, P. Coler, C. R. Mirasso, "Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback," Phys. Rev. E 78, 046218-1-046218-8 (2008).

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, D. Syvridis, "Feedback phase in optically generated chaos: A sceret key for cryptographic applications," IEEE. J. Quantum Electron. 44, 119-124 (2008).

W. L. Zhang, W. Pan, B. Luo, X. H. Zou, M. Y. Wang, Z. Zhou, "Chaos synchronization communication using extremely unsymmetrical bidirectional injections," Opt. Lett. 33, 237-239 (2008).

R. Vicente, I. Fischer, C. R. Mirasso, "Synchronization properties of three-coupled semiconductor lasers," Phys. Rev. E 78, 066202-1-066202-11 (2008).

I. Kanter, E. Kopelowitz, W. Kinzel, "Public channel cryptography: Chaos synchronization and Hilbert's tenth problem," Phys. Rev. Lett. 101, 084102-1-084102-4 (2008).

S. Zhou, H. Li, Z. Z. Zhu, "Chaos control and synchronization in a fractional neuron network system," Chaos, Solitons Fractals 36, 973-984 (2008).

A. B. Wang, Y. C. Wang, H. C. He, "Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback," IEEE Photon. Technol. Lett. 20, 1633-1635 (2008).

2007 (4)

F. Y. Lin, M. C. Tsai, "Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers," Opt. Express 15, 302-311 (2007).

B. B. Zhou, R. Roy, "Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillator," Phys. Rev. E 75, 026205-1-026205-5 (2007).

R. Vicente, C. R. Mirasso, I. Fischer, "Simultaneous bidirectional message transmission in a chaos-based communication scheme," Opt. Lett. 32, 403-405 (2007).

V. Annovazzi-Lodi, M. Benedetti, S. Merlo, T. Perez, P. Colet, C. R. Mirasso, "Message encryption by phase modulation of a chaotic optical carrier," IEEE Photon. Technol. Lett. 19, 76-79 (2007).

2006 (7)

D. Kanakidis, A. Argyris, A. Bogris, D. Syvridis, "Influence of the decoding process on the performance of chaos encrypted optical communication systems," J. Lightw. Technol. 24, 335-341 (2006).

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, I. Kanter, "Public-channel cryptograph based on mutual chaos pass filters," Phys. Rev. E 74, 046201–1-046201-4 (2006).

X. F. Li, W. Pan, B. Luo, D. Ma, "Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization," IEEE J. Quantum Electron. 42, 953-960 (2006).

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, I. Kanter, "Stable isochronal synchronization of mutually coupled chaotic lasers," Phys. Rev. E 73, 066214-1-066214-4 (2006).

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, K. A. Shore, "Identification of the optimum time-delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, J. Garcia-Ojalvo, "Zero-lag long-range synchronization via dynamical relaying," Phys. Rev. Lett. 97, 123902-1-123902-4 (2006).

X. F. Li, W. Pan, B. Luo, D. Ma, "Chaos synchronization and communication of cascade-coupled semiconductor lasers," J. Lightw. Technol. 24, 4936-4945 (2006).

2005 (5)

S. J. Li, G. Alvarez, G. R. Chen, "Breaking a chaos-based secure communication scheme designed by an improved modulation method," Chao, Solitons Fractals 25, 109-120 (2005).

E. Klein, R. Mislovaty, I. Kanter, W. Kinzel, "Public-channel cryptography using chaos synchronization," Phys. Rev. E 2, 016204-1-016204-4 (2005).

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature 437, 343-346 (2005).

X. F. Li, W. Pan, B. Luo, D. Ma, "Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers," Semicond. Sci. Technol. 21, 25-34 (2005).

M. C. Chiang, H. F. Chen, J. M. Liu, "Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 41, 1333-1340 (2005).

2004 (1)

S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Topics Quantum Electron. 10, 936-943 (2004).

2003 (4)

F. Zhang, P. L. Chu, "Effect of transmission fiber on chaos communication system based on erbium-doped fiber ring laser," J. Lightw. Technol. 21, 3334-3343 (2003).

R. Mislovaty, E. Klein, I. Kanter, W. Kinzel, "Public channel cryptography by synchronization of neural networks and chaotic maps," Phys. Rev. Lett. 91, 118701-1-118701-4 (2003).

D. Kanakidis, A. Argyris, D. Syvridis, "Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration," J. Lightw. Technol. 21, 750-758 (2003).

Y. Takiguchi, K. Ohyagi, J. Ohtsubo, "Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback," Opt. Lett. 28, 319-321 (2003).

2002 (5)

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

J. M. Liu, H. F. Chen, S. Tang, "Synchronized chaotic optical communications at high bit-rates," IEEE J. Quantum Electron. 38, 1184-1196 (2002).

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

J. Mulet, C. Masoller, C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 063815-1-063815-12 (2002).

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

2001 (1)

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

1999 (1)

A. Sanchez-Diaz, C. R. Mirasso, P. Colet, P. Garcia-Fernandez, "Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers," IEEE J. Quantum Electron. 35, 292-297 (1999).

1990 (1)

L. M. Pecora, T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-825 (1990).

Chao, Solitons Fractals (1)

S. J. Li, G. Alvarez, G. R. Chen, "Breaking a chaos-based secure communication scheme designed by an improved modulation method," Chao, Solitons Fractals 25, 109-120 (2005).

Chaos, Solitons Fractals (1)

S. Zhou, H. Li, Z. Z. Zhu, "Chaos control and synchronization in a fractional neuron network system," Chaos, Solitons Fractals 36, 973-984 (2008).

IEEE J. Quantum Electron. (7)

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

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

M. C. Chiang, H. F. Chen, J. M. Liu, "Experimental synchronization of mutually coupled semiconductor lasers with optoelectronic feedback," IEEE J. Quantum Electron. 41, 1333-1340 (2005).

X. F. Li, W. Pan, B. Luo, D. Ma, "Mismatch robustness and security of chaotic optical communications based on injection-locking chaos synchronization," IEEE J. Quantum Electron. 42, 953-960 (2006).

S. Peters-Flynn, P. S. Spencer, S. Sivaprakasam, I. Pierce, K. A. Shore, "Identification of the optimum time-delay for chaos synchronization regimes of semiconductor lasers," IEEE J. Quantum Electron. 42, 427-434 (2006).

A. Sanchez-Diaz, C. R. Mirasso, P. Colet, P. Garcia-Fernandez, "Encoded Gbit/s digital communications with synchronized chaotic semiconductor lasers," IEEE J. Quantum Electron. 35, 292-297 (1999).

J. M. Liu, H. F. Chen, S. Tang, "Synchronized chaotic optical communications at high bit-rates," IEEE J. Quantum Electron. 38, 1184-1196 (2002).

IEEE J. Sel. Topics Quantum Electron. (1)

S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Topics Quantum Electron. 10, 936-943 (2004).

IEEE Photon. Technol. Lett. (2)

V. Annovazzi-Lodi, M. Benedetti, S. Merlo, T. Perez, P. Colet, C. R. Mirasso, "Message encryption by phase modulation of a chaotic optical carrier," IEEE Photon. Technol. Lett. 19, 76-79 (2007).

A. B. Wang, Y. C. Wang, H. C. He, "Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback," IEEE Photon. Technol. Lett. 20, 1633-1635 (2008).

IEEE. J. Quantum Electron. (2)

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

A. Bogris, P. Rizomiliotis, K. E. Chlouverakis, A. Argyris, D. Syvridis, "Feedback phase in optically generated chaos: A sceret key for cryptographic applications," IEEE. J. Quantum Electron. 44, 119-124 (2008).

J. Lightw. Technol. (4)

D. Kanakidis, A. Argyris, D. Syvridis, "Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration," J. Lightw. Technol. 21, 750-758 (2003).

D. Kanakidis, A. Argyris, A. Bogris, D. Syvridis, "Influence of the decoding process on the performance of chaos encrypted optical communication systems," J. Lightw. Technol. 24, 335-341 (2006).

F. Zhang, P. L. Chu, "Effect of transmission fiber on chaos communication system based on erbium-doped fiber ring laser," J. Lightw. Technol. 21, 3334-3343 (2003).

X. F. Li, W. Pan, B. Luo, D. Ma, "Chaos synchronization and communication of cascade-coupled semiconductor lasers," J. Lightw. Technol. 24, 4936-4945 (2006).

Nature (1)

A. Argyris, D. Syvrids, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, K. A. Shore, "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature 437, 343-346 (2005).

Opt. Commun. (1)

N. Jiang, W. Pan, L. S. Yan, B. Luo, L. Yang, S. Y. Xiang, D. Zheng, "Two chaos synchronization schemes and public-channel message transmission in a mutually coupled semiconductor lasers system," Opt. Commun. 282, 2217-2222 (2009).

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

J. Mulet, C. Masoller, C. R. Mirasso, "Modeling bidirectionally coupled single-mode semiconductor lasers," Phys. Rev. A 65, 063815-1-063815-12 (2002).

Phys. Rev. E (6)

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, I. Kanter, "Stable isochronal synchronization of mutually coupled chaotic lasers," Phys. Rev. E 73, 066214-1-066214-4 (2006).

R. Vicente, I. Fischer, C. R. Mirasso, "Synchronization properties of three-coupled semiconductor lasers," Phys. Rev. E 78, 066202-1-066202-11 (2008).

B. B. Zhou, R. Roy, "Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillator," Phys. Rev. E 75, 026205-1-026205-5 (2007).

M. C. Soriano, F. Ruiz-Oliveras, P. Coler, C. R. Mirasso, "Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback," Phys. Rev. E 78, 046218-1-046218-8 (2008).

E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh, L. Khaykovich, W. Kinzel, I. Kanter, "Public-channel cryptograph based on mutual chaos pass filters," Phys. Rev. E 74, 046201–1-046201-4 (2006).

E. Klein, R. Mislovaty, I. Kanter, W. Kinzel, "Public-channel cryptography using chaos synchronization," Phys. Rev. E 2, 016204-1-016204-4 (2005).

Phys. Rev. Lett. (5)

I. Kanter, E. Kopelowitz, W. Kinzel, "Public channel cryptography: Chaos synchronization and Hilbert's tenth problem," Phys. Rev. Lett. 101, 084102-1-084102-4 (2008).

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

L. M. Pecora, T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-825 (1990).

R. Mislovaty, E. Klein, I. Kanter, W. Kinzel, "Public channel cryptography by synchronization of neural networks and chaotic maps," Phys. Rev. Lett. 91, 118701-1-118701-4 (2003).

I. Fischer, R. Vicente, J. M. Buldu, M. Peil, C. R. Mirasso, M. C. Torrent, J. Garcia-Ojalvo, "Zero-lag long-range synchronization via dynamical relaying," Phys. Rev. Lett. 97, 123902-1-123902-4 (2006).

Semicond. Sci. Technol. (1)

X. F. Li, W. Pan, B. Luo, D. Ma, "Nonlinear dynamics of two mutually injected external-cavity semiconductor lasers," Semicond. Sci. Technol. 21, 25-34 (2005).

Other (1)

A. Bogris, K. E. Chlouverakis, A. Argyris, D. Syvridis, "Enhancement of the encryption efficiency of chaotic communications based on all-optical feedback chaos generation by means of subcarrier modulation," Lasers Electro-Opt. Int. Quantum Electron. Conf., CLEOE-IQEC, Eur. Conf. (2007) pp. 1-1.

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