Abstract

Topologies of two, three and four time-delay-coupled chaotic semiconductor lasers are experimentally and theoretically found to show new types of synchronization. Generalized zero-lag synchronization is observed for two lasers separated by long distances even when their self-feedback delays are not equal. Generalized sub-lattice synchronization is observed for quadrilateral geometries while the equilateral triangle is zero-lag synchronized. Generalized zero-lag synchronization, without the limitation of precisely matched delays, opens possibilities for advanced multi-user communication protocols.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
    [CrossRef] [PubMed]
  2. O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
    [CrossRef] [PubMed]
  3. I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
    [CrossRef]
  4. R. Vardi, A. Wallach, E. Kopelowitz, M. Abeles, S. Marom, and I. Kanter, “Synthetic reverberating activity patterns embedded in networks of cortical neurons,” Arxiv preprint arXiv:1201.0339 (2012).
  5. M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
    [CrossRef] [PubMed]
  6. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
    [CrossRef]
  7. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
    [CrossRef]
  8. A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
    [CrossRef]
  9. I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
    [CrossRef] [PubMed]
  10. G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88(9), 097903 (2002).
    [CrossRef] [PubMed]
  11. A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
    [CrossRef] [PubMed]
  12. B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
    [CrossRef] [PubMed]
  13. B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
    [CrossRef] [PubMed]
  14. M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 045201 (2007).
    [CrossRef] [PubMed]
  15. D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
    [CrossRef]
  16. Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
    [CrossRef] [PubMed]
  17. M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
    [CrossRef] [PubMed]
  18. 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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
    [CrossRef] [PubMed]
  19. K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
    [CrossRef] [PubMed]
  20. V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7208–7213 (1998).
    [CrossRef]
  21. Y. Takiguchi, H. Fujino, and J. Ohtsubo, “Experimental synchronization of chaotic oscillations in externally injected semiconductor lasers in a low-frequency fluctuation regime,” Opt. Lett. 24(22), 1570–1572 (1999).
    [CrossRef] [PubMed]
  22. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
    [CrossRef]
  23. I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
    [CrossRef]
  24. S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
    [CrossRef] [PubMed]
  25. V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
    [CrossRef] [PubMed]
  26. J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (2010).
    [CrossRef] [PubMed]
  27. J. Kestler, W. Kinzel, and I. Kanter, “Sublattice synchronization of chaotic networks with delayed couplings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 035202 (2007).
    [CrossRef] [PubMed]
  28. C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
    [CrossRef]

2011

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[CrossRef]

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

2010

V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
[CrossRef] [PubMed]

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[CrossRef] [PubMed]

2009

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

2008

A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
[CrossRef] [PubMed]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

2007

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (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 Stat. Nonlin. Soft Matter Phys. 76(4), 045201 (2007).
[CrossRef] [PubMed]

J. Kestler, W. Kinzel, and I. Kanter, “Sublattice synchronization of chaotic networks with delayed couplings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 035202 (2007).
[CrossRef] [PubMed]

C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
[CrossRef]

2006

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

2003

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[CrossRef]

2002

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88(9), 097903 (2002).
[CrossRef] [PubMed]

1999

1998

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7208–7213 (1998).
[CrossRef]

1985

D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[CrossRef]

1980

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

Ahlers, V.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7208–7213 (1998).
[CrossRef]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[CrossRef] [PubMed]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

Butkovski, 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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[CrossRef] [PubMed]

Cohen, A. B.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
[CrossRef] [PubMed]

Cohen, D.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

D’Huys, O.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

Dahms, T.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
[CrossRef] [PubMed]

Danckaert, J.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

Davidson, N.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

Davis, P.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[CrossRef]

Den Boef, A.

D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[CrossRef]

Englert, A.

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

Erneux, T.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

Fischer, I.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 045201 (2007).
[CrossRef] [PubMed]

Flunkert, V.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
[CrossRef] [PubMed]

Friedman, M.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

Friesem, A. A.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

Fujino, H.

Garcia-Ojalvo, J.

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (2010).
[CrossRef] [PubMed]

García-Ojalvo, J.

C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
[CrossRef]

Geissler, F.

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[CrossRef]

González, C.

C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
[CrossRef]

Gross, N.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Heiligenthal, S.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

Hicke, K.

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Itaya, S.

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[CrossRef]

Jüngling, T.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

Kanter, I.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

J. Kestler, W. Kinzel, and I. Kanter, “Sublattice synchronization of chaotic networks with delayed couplings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 035202 (2007).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Kestler, J.

J. Kestler, W. Kinzel, and I. Kanter, “Sublattice synchronization of chaotic networks with delayed couplings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 035202 (2007).
[CrossRef] [PubMed]

Khaykovich, L.

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Kinzel, W.

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[CrossRef]

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[CrossRef] [PubMed]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

J. Kestler, W. Kinzel, and I. Kanter, “Sublattice synchronization of chaotic networks with delayed couplings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 035202 (2007).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Klein, E.

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

Kopelowitz, E.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 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 Stat. Nonlin. Soft Matter Phys. 76(4), 045201 (2007).
[CrossRef] [PubMed]

Lauterborn, W.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7208–7213 (1998).
[CrossRef]

Lenstra, D.

D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[CrossRef]

Masoller, C.

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (2010).
[CrossRef] [PubMed]

C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
[CrossRef]

Motter, A. E.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

Murphy, T. E.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
[CrossRef] [PubMed]

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Nixon, M.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

Ohtsubo, J.

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Ott, E.

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

Parlitz, U.

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7208–7213 (1998).
[CrossRef]

Peil, M.

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 045201 (2007).
[CrossRef] [PubMed]

Peleg, Y.

Ravoori, B.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
[CrossRef] [PubMed]

Reidler, I.

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[CrossRef] [PubMed]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

Ronen, E.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (2010).
[CrossRef] [PubMed]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

Roy, R.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (2010).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
[CrossRef] [PubMed]

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88(9), 097903 (2002).
[CrossRef] [PubMed]

Schöll, E.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
[CrossRef] [PubMed]

Setty, A. V.

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Sorrentino, F.

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

Sun, J.

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

Takiguchi, Y.

Torrent, M.

C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
[CrossRef]

Uchida, A.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88(9), 097903 (2002).
[CrossRef] [PubMed]

Vardi, R.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

Verbeek, B.

D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[CrossRef]

Vicente, R.

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

Yanchuk, S.

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
[CrossRef] [PubMed]

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Yoshimura, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

Yoskovits, P.

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[CrossRef] [PubMed]

Zamora-Munt, J.

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (2010).
[CrossRef] [PubMed]

Zigzag, M.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[CrossRef]

I. Kanter, M. Butkovski, Y. Peleg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18(17), 18292–18302 (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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett.

A. Uchida, P. Davis, and S. Itaya, “Generation of information theoretic secure keys using a chaotic semiconductor laser,” Appl. Phys. Lett. 83(15), 3213–3215 (2003).
[CrossRef]

Chaos

O. D’Huys, R. Vicente, T. Erneux, J. Danckaert, and I. Fischer, “Synchronization properties of network motifs: influence of coupling delay and symmetry,” Chaos 18(3), 037116 (2008).
[CrossRef] [PubMed]

Europhys. Lett.

I. Kanter, M. Zigzag, A. Englert, F. Geissler, and W. Kinzel, “Synchronization of unidirectional time delay chaotic networks and the greatest common divisor,” Europhys. Lett. 93(6), 60003 (2011).
[CrossRef]

C. González, C. Masoller, M. Torrent, and J. García-Ojalvo, “Synchronization via clustering in a small delay-coupled laser network,” Europhys. Lett. 79(6), 64003 (2007).
[CrossRef]

IEEE J. Quantum Electron.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980).
[CrossRef]

D. Lenstra, B. Verbeek, and A. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. 21(6), 674–679 (1985).
[CrossRef]

J. Stat. Phys.

I. Kanter, E. Kopelowitz, R. Vardi, M. Zigzag, D. Cohen, and W. Kinzel, “Nonlocal mechanism for synchronization of time delay networks,” J. Stat. Phys. 145(3), 713–733 (2011).
[CrossRef]

Nat. Photonics

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

J. Kestler, W. Kinzel, and I. Kanter, “Sublattice synchronization of chaotic networks with delayed couplings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(3), 035202 (2007).
[CrossRef] [PubMed]

E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaykovich, and I. Kanter, “Stable isochronal synchronization of mutually coupled chaotic lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(6), 066214 (2006).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, A. V. Setty, F. Sorrentino, T. E. Murphy, E. Ott, and R. Roy, “Adaptive synchronization of coupled chaotic oscillators,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(5), 056205 (2009).
[CrossRef] [PubMed]

M. Peil, L. Larger, and I. Fischer, “Versatile and robust chaos synchronization phenomena imposed by delayed shared feedback coupling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 045201 (2007).
[CrossRef] [PubMed]

Y. Aviad, I. Reidler, W. Kinzel, I. Kanter, and M. Rosenbluh, “Phase synchronization in mutually coupled chaotic diode lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(2), 025204 (2008).
[CrossRef] [PubMed]

M. Rosenbluh, Y. Aviad, E. Cohen, L. Khaykovich, W. Kinzel, E. Kopelowitz, P. Yoskovits, and I. Kanter, “Spiking optical patterns and synchronization,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 046207 (2007).
[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 Stat. Nonlin. Soft Matter Phys. 81(3), 036215 (2010).
[CrossRef] [PubMed]

K. Hicke, O. D’Huys, V. Flunkert, E. Schöll, J. Danckaert, and I. Fischer, “Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(5), 056211 (2011).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

V. Ahlers, U. Parlitz, and W. Lauterborn, “Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(6), 7208–7213 (1998).
[CrossRef]

Phys. Rev. Lett.

M. Nixon, M. Friedman, E. Ronen, A. A. Friesem, N. Davidson, and I. Kanter, “Synchronized cluster formation in coupled laser networks,” Phys. Rev. Lett. 106(22), 223901 (2011).
[CrossRef] [PubMed]

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88(9), 097903 (2002).
[CrossRef] [PubMed]

A. B. Cohen, B. Ravoori, T. E. Murphy, and R. Roy, “Using synchronization for prediction of high-dimensional chaotic dynamics,” Phys. Rev. Lett. 101(15), 154102 (2008).
[CrossRef] [PubMed]

B. Ravoori, A. B. Cohen, J. Sun, A. E. Motter, T. E. Murphy, and R. Roy, “Robustness of optimal synchronization in real networks,” Phys. Rev. Lett. 107(3), 034102 (2011).
[CrossRef] [PubMed]

S. Heiligenthal, T. Dahms, S. Yanchuk, T. Jüngling, V. Flunkert, I. Kanter, E. Schöll, and W. Kinzel, “Strong and weak chaos in nonlinear networks with time-delayed couplings,” Phys. Rev. Lett. 107(23), 234102 (2011).
[CrossRef] [PubMed]

V. Flunkert, S. Yanchuk, T. Dahms, and E. Schöll, “Synchronizing distant nodes: a universal classification of networks,” Phys. Rev. Lett. 105(25), 254101 (2010).
[CrossRef] [PubMed]

J. Zamora-Munt, C. Masoller, J. Garcia-Ojalvo, and R. Roy, “Crowd synchrony and quorum sensing in delay-coupled lasers,” Phys. Rev. Lett. 105(26), 264101 (2010).
[CrossRef] [PubMed]

Other

R. Vardi, A. Wallach, E. Kopelowitz, M. Abeles, S. Marom, and I. Kanter, “Synthetic reverberating activity patterns embedded in networks of cortical neurons,” Arxiv preprint arXiv:1201.0339 (2012).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Experimental setup: two mutually coupled SC lasers, LDA and LDB. PD, photodiode; M, mirror. τa and τb are the optical delay times between LDA and LDB and the coupling beam splitter, BS, respectively. τ indicates the optical delay between the BS and mirror, M. (b) Schematic diagram of the experimental configuration. (c) Shifted cross correlation between the chaotic intensities of LDA and LDB. ZLS for identical self feedback and mutual coupling delays, τa = τb (light blue), and generalized ZLS for τa≠τb (dark blue; τab~-1.95 ns) (d) Shifted cross correlation around the mutual delay time between the two lasers. (e) A generalized star configuration of n SC lasers. The output intensity of the lasers with unequal optical delay times, {τk}, is combined with equal weight and reflected by a passive mirror.

Fig. 2
Fig. 2

(a) Experimental setup of four SC lasers in a quadrilateral geometry. The optical time delays between lasers A and B (C and D) and their coupling beam spliter is τa and τbc and τd), respectively. τ is the the optical delay between the two coupling BSs. (b) Schematic diagram of the quadrilateral experimental setup. (c) Shifted cross correlation of the chaotic intensities between lasers A and B (light blue; time shift ~-0.03 ns) and C and D (purple; time shift ~-0.195 ns), indicating generalized ZLS between diagonal pairs.

Fig. 3
Fig. 3

(a) Configuration for numerical simulation with τa=2 ns, τb=4 ns, τc=3 ns, τd=7 ns and τ=11 ns. Pairs of lasers with the same color (light blue and purple) are generalized ZLS as indicated by the relative time in ns units. (b) The transformation from a quadrilateral geometry to a square. Dashed lines represent the effective time delays after compensating for the synchronization time shift. (c) Calculated shifted cross correlation of the chaotic intensities of the quadrilateral geometry, Fig. 3(a).

Fig. 4
Fig. 4

(a) Experimental setup of three SC lasers in an equilateral triangle. Each laser is bidirectionally coupled to two adjacent lasers where τabc. (b) Schematic diagram of the experimental setup. (c) Shifted cross correlation of the chaotic intensities of all three pairs of lasers indicating ZLS.

Equations (2)

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

T A + T B = 2T M
i=m k1 τ i+1 τ i = τ k τ m

Metrics