Abstract

Isochrony and time leadership was studied in the synchronized excitable behavior of coupled chaotic diode lasers. Each unit of the system had chaos due to feedback with a fixed delay time. The inter-units coupling signal had a second, independent, characteristic time. Synchronized excitable spikes present isochronous, time leading or time lagging behavior whose stability is shown to depend on a simple relation between the feedback and the coupling times. Experiments on the synchronized low frequency fluctuations of two optically coupled semiconductor lasers and numerical calculations with coupled laser equations verify the predicted stability conditions for synchronization. Synchronism with intermittent time leadership exchange was also observed and characterized.

©2009 Optical Society of America

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References

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    [Crossref] [PubMed]
  6. R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
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  7. J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
    [Crossref]
  8. X. Li, W. Pan, D. Ma, and B. Luo, “Chaos synchronization of unidirectionally injected vertical-cavity surfaceemitting lasers with global and mode-selective coupling,” Opt. Express 14, 3138–3151 ( 2006).
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  9. I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
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    [Crossref] [PubMed]
  20. J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
    [Crossref]
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    [Crossref]
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  23. I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
    [Crossref]
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    [Crossref]
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    [Crossref]
  26. N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
    [Crossref]
  27. M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).
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    [Crossref]

2009 (1)

2008 (2)

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Coarse Grained Variables and Deterministic Chaos in an Excitable System,” Phys. Rev. Lett. 100, 044101-1–044101-4 ( 2008).
[Crossref]

2007 (3)

J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
[Crossref]

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207-1–046207-5 ( 2007).
[Crossref]

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

2006 (7)

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

X. Li, W. Pan, D. Ma, and B. Luo, “Chaos synchronization of unidirectionally injected vertical-cavity surfaceemitting lasers with global and mode-selective coupling,” Opt. Express 14, 3138–3151 ( 2006).
[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 73, 066214-1–066214-4 ( 2006).
[Crossref]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

E. A. Rogers-Dakin, J. García-Ojalvo, D. J. DeShazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 ( 2006).
[Crossref]

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

2005 (1)

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

2004 (3)

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental Deterministic Coherence Resonance,”Phys. Rev. Lett. 93, 144101-1–144101-4 ( 2004).
[Crossref]

J. Mulet, C. R. Mirasso, T. Heil, and I. Fischer, “Synchronization scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quant. Semiclass. Opt. 6, 97–105 ( 2004).
[Crossref]

M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).

2003 (1)

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

2001 (2)

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

C. Masoller, “Anticipation in the Synchronization of Semiconductor Lasers with Optical Feedback,” Phys. Rev. Lett. 86, 2782–2785 ( 2001).
[Crossref] [PubMed]

1999 (1)

1997 (1)

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

1995 (1)

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quant. Semiclass. Opt. 7, 87–143 ( 1995).
[Crossref]

1994 (3)

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Y. Shimizu, “Observation of Synchronization in Laser Chaos,” Phys. Rev. Lett. 72, 3502–3505 ( 1994).
[Crossref] [PubMed]

R. Roy and K. S. Thornburg, “Experimental Synchronization of Chaotic Lasers,” Phys. Rev. Lett. 72, 2009–2012 ( 1994).
[Crossref] [PubMed]

Y. Liu, P.C. de Oliveira, M.B. Danailov, and J. R. Rios Leite, “Chaotic and periodic passive Q switching in coupled CO2 lasers with a saturable absorber,” Phys. Rev. A 50, 3464–3470 ( 1994).
[Crossref] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347–355 ( 1980).
[Crossref]

Al Naimee, K.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Arecchi, F. T.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

Argyris, A.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Ariizumi, H.

Avila, J. F. M.

J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
[Crossref]

Balle, S.

M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).

Boccaletti, S.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

Buldú, J. M.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

Cavalcante, H. L. D. de S.

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Coarse Grained Variables and Deterministic Chaos in an Excitable System,” Phys. Rev. Lett. 100, 044101-1–044101-4 ( 2008).
[Crossref]

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental Deterministic Coherence Resonance,”Phys. Rev. Lett. 93, 144101-1–144101-4 ( 2004).
[Crossref]

Cisak, M.

M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).

Colet, P.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Danailov, M.B.

Y. Liu, P.C. de Oliveira, M.B. Danailov, and J. R. Rios Leite, “Chaotic and periodic passive Q switching in coupled CO2 lasers with a saturable absorber,” Phys. Rev. A 50, 3464–3470 ( 1994).
[Crossref] [PubMed]

Davis, P.

de Oliveira, P.C.

Y. Liu, P.C. de Oliveira, M.B. Danailov, and J. R. Rios Leite, “Chaotic and periodic passive Q switching in coupled CO2 lasers with a saturable absorber,” Phys. Rev. A 50, 3464–3470 ( 1994).
[Crossref] [PubMed]

DeShazer, D. J.

E. A. Rogers-Dakin, J. García-Ojalvo, D. J. DeShazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 ( 2006).
[Crossref]

Elssser, W.

T. Heil, I. Fischer, W. Elssser, J. Mulet, and C. R. Mirasso, “Chaos Synchronization and Spontaneous Symmetry-Breaking in Symmetrically Delay-Coupled Semiconductor Lasers,” Phys. Rev. Lett. 86, 795–798 ( 2001).
[Crossref] [PubMed]

Fischer, I.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

J. Mulet, C. R. Mirasso, T. Heil, and I. Fischer, “Synchronization scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quant. Semiclass. Opt. 6, 97–105 ( 2004).
[Crossref]

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

Fisher, I.

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

Fujino, H.

Garcia-Ojalvo, J.

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

García-Ojalvo, J.

E. A. Rogers-Dakin, J. García-Ojalvo, D. J. DeShazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 ( 2006).
[Crossref]

Giacomelli, G.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

Giudici, M.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

Gollo, L. L

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

Green, C.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

Gross, N.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

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

Heil, T.

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

J. Mulet, C. R. Mirasso, T. Heil, and I. Fischer, “Synchronization scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quant. Semiclass. Opt. 6, 97–105 ( 2004).
[Crossref]

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

Ivanchenko, M. V.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

Kanter, I.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

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

Khaykovich, L.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

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

Kinzel, W.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

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

Klein, E.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

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

Kobayashi, K.

R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347–355 ( 1980).
[Crossref]

Kopelowitz, E.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

Kurths, J.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

A. Pikovsky, M. Rosenblum, and J. Kurths, “Synchronization: A Universal Concept in Nonlinear Sciences,” (Cambridge Nonlinear Science Series, 2003)

Lang, R.

R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347–355 ( 1980).
[Crossref]

Larger, L.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Lenstra, D.

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quant. Semiclass. Opt. 7, 87–143 ( 1995).
[Crossref]

Li, M.

Li, X.

Liu, Y.

Y. Liu, P.C. de Oliveira, M.B. Danailov, and J. R. Rios Leite, “Chaotic and periodic passive Q switching in coupled CO2 lasers with a saturable absorber,” Phys. Rev. A 50, 3464–3470 ( 1994).
[Crossref] [PubMed]

Luo, B.

Ma, D.

Marino, F.

M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).

Martinez Avila, J. F.

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Coarse Grained Variables and Deterministic Chaos in an Excitable System,” Phys. Rev. Lett. 100, 044101-1–044101-4 ( 2008).
[Crossref]

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental Deterministic Coherence Resonance,”Phys. Rev. Lett. 93, 144101-1–144101-4 ( 2004).
[Crossref]

Masoller, C.

C. Masoller, “Anticipation in the Synchronization of Semiconductor Lasers with Optical Feedback,” Phys. Rev. Lett. 86, 2782–2785 ( 2001).
[Crossref] [PubMed]

Meucci, R.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

Mirasso, C. R.

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
[Crossref]

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

J. Mulet, C. R. Mirasso, T. Heil, and I. Fischer, “Synchronization scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quant. Semiclass. Opt. 6, 97–105 ( 2004).
[Crossref]

T. Heil, I. Fischer, W. Elssser, 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. R. Mirasso, T. Heil, and I. Fischer, “Synchronization scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quant. Semiclass. Opt. 6, 97–105 ( 2004).
[Crossref]

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

Nespolo, U.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

Ohtsubo, J.

Oowada, I.

Pan, W.

Peil, M.

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

Pesquera, L.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Pierce, I.

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

Pikovsky, A.

A. Pikovsky, M. Rosenblum, and J. Kurths, “Synchronization: A Universal Concept in Nonlinear Sciences,” (Cambridge Nonlinear Science Series, 2003)

Pipa, Gordon

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

Rees, P.

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

Rios Leite, J. R.

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Coarse Grained Variables and Deterministic Chaos in an Excitable System,” Phys. Rev. Lett. 100, 044101-1–044101-4 ( 2008).
[Crossref]

J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
[Crossref]

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental Deterministic Coherence Resonance,”Phys. Rev. Lett. 93, 144101-1–144101-4 ( 2004).
[Crossref]

Y. Liu, P.C. de Oliveira, M.B. Danailov, and J. R. Rios Leite, “Chaotic and periodic passive Q switching in coupled CO2 lasers with a saturable absorber,” Phys. Rev. A 50, 3464–3470 ( 1994).
[Crossref] [PubMed]

Rogers-Dakin, E. A.

E. A. Rogers-Dakin, J. García-Ojalvo, D. J. DeShazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 ( 2006).
[Crossref]

Rosenbluh, M

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

Rosenbluh, M.

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

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

Rosenblum, M.

A. Pikovsky, M. Rosenblum, and J. Kurths, “Synchronization: A Universal Concept in Nonlinear Sciences,” (Cambridge Nonlinear Science Series, 2003)

Roy, R.

E. A. Rogers-Dakin, J. García-Ojalvo, D. J. DeShazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 ( 2006).
[Crossref]

R. Roy and K. S. Thornburg, “Experimental Synchronization of Chaotic Lasers,” Phys. Rev. Lett. 72, 2009–2012 ( 1994).
[Crossref] [PubMed]

Salvadori, F.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

Schwartz, I. B.

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207-1–046207-5 ( 2007).
[Crossref]

Shaw, L. B.

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207-1–046207-5 ( 2007).
[Crossref]

Shimizu, T. Y.

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Y. Shimizu, “Observation of Synchronization in Laser Chaos,” Phys. Rev. Lett. 72, 3502–3505 ( 1994).
[Crossref] [PubMed]

Shore, K. A.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

Sivaprakasam, S.

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

Spencer, P. S.

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

Sugawara, T.

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Y. Shimizu, “Observation of Synchronization in Laser Chaos,” Phys. Rev. Lett. 72, 3502–3505 ( 1994).
[Crossref] [PubMed]

Syvridis, D.

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Tachikawa, M.

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Y. Shimizu, “Observation of Synchronization in Laser Chaos,” Phys. Rev. Lett. 72, 3502–3505 ( 1994).
[Crossref] [PubMed]

Takiguchi, Y.

Thornburg, K. S.

R. Roy and K. S. Thornburg, “Experimental Synchronization of Chaotic Lasers,” Phys. Rev. Lett. 72, 2009–2012 ( 1994).
[Crossref] [PubMed]

Toral, R.

M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).

Torrent, M. C.

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

Tredicce, J. R.

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

Tsukamoto, T.

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Y. Shimizu, “Observation of Synchronization in Laser Chaos,” Phys. Rev. Lett. 72, 3502–3505 ( 1994).
[Crossref] [PubMed]

Uchida, A.

van Tartwijk, G. H. M.

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quant. Semiclass. Opt. 7, 87–143 ( 1995).
[Crossref]

Vicente, R.

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
[Crossref]

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

Yoshimori, S.

Yoshimura, K.

Yoskovits, P.

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

Zhou, C.

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

IEEE J. Quantum Electron. (1)

R. Lang and K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347–355 ( 1980).
[Crossref]

J. Opt. B: Quant. Semiclass. Opt. (1)

J. Mulet, C. R. Mirasso, T. Heil, and I. Fischer, “Synchronization scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quant. Semiclass. Opt. 6, 97–105 ( 2004).
[Crossref]

Nature (1)

A. Argyris, D. Syvridis, 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 438, 343–346 ( 2005).
[Crossref] [PubMed]

Opt. Commun. (1)

N. Gross, W. Kinzel, I. Kanter, M. Rosenbluh, and L. Khaykovich, “Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers,” Opt. Commun. 264, 464–468 ( 2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

Y. Liu, P.C. de Oliveira, M.B. Danailov, and J. R. Rios Leite, “Chaotic and periodic passive Q switching in coupled CO2 lasers with a saturable absorber,” Phys. Rev. A 50, 3464–3470 ( 1994).
[Crossref] [PubMed]

Phys. Rev. E (6)

R. Meucci, F. Salvadori, M. V. Ivanchenko, K. Al Naimee, C. Zhou, F. T. Arecchi, S. Boccaletti, and J. Kurths, “Synchronization of spontaneous bursting in a CO2 laser,” Phys. Rev. E 74, 066207-10662070-6 ( 2006).
[Crossref]

E. A. Rogers-Dakin, J. García-Ojalvo, D. J. DeShazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 ( 2006).
[Crossref]

I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207-1–046207-5 ( 2007).
[Crossref]

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

J. F. M. Avila, R. Vicente, J. R. Rios Leite, and C. R. Mirasso “Synchronization properties of bidirectionally coupled semiconductor lasers under asymmetric operating conditions”, Phys. Rev. E 75, 066202-1–066202-6 ( 2007).
[Crossref]

M. Giudici, C. Green, G. Giacomelli, U. Nespolo, and J. R. Tredicce, “Andronov bifurcation and excitability in semiconductor lasers with optical feedback,” Phys. Rev. E 55, 6414–6418 ( 1997).
[Crossref]

Phys. Rev. Lett. (10)

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Experimental Deterministic Coherence Resonance,”Phys. Rev. Lett. 93, 144101-1–144101-4 ( 2004).
[Crossref]

J. F. Martinez Avila, H. L. D. de S. Cavalcante, and J. R. Rios Leite, “Coarse Grained Variables and Deterministic Chaos in an Excitable System,” Phys. Rev. Lett. 100, 044101-1–044101-4 ( 2008).
[Crossref]

C. Masoller, “Anticipation in the Synchronization of Semiconductor Lasers with Optical Feedback,” Phys. Rev. Lett. 86, 2782–2785 ( 2001).
[Crossref] [PubMed]

T. Heil, I. Fischer, W. Elssser, J. Mulet, and C. R. Mirasso, “Chaos Synchronization and Spontaneous Symmetry-Breaking in Symmetrically Delay-Coupled Semiconductor Lasers,” Phys. Rev. Lett. 86, 795–798 ( 2001).
[Crossref] [PubMed]

I. Fischer, R. Vicente, J. M. Buldú, M. Peil, and C. R. Mirasso, “Zero-Lag Long-Range Synchronization via Dynamical Relaying,” Phys. Rev. Lett. 97, 123902-1–123902-4 ( 2006).
[Crossref]

M. Cisak, F. Marino, R. Toral, and S. Balle, “Mechanism of Anticipating Synchronization in Excitable Systems,” Phys. Rev. Lett. 93, 114102-1–114102-4 ( 2004).

J. M. Buldú, T. Heil, I. Fischer, M. C. Torrent, and J. Garcia-Ojalvo, “Episodic Synchronization via Dynamic Injection,” Phys. Rev. Lett. 96, 024102-1–024102-4 ( 2006)
[Crossref]

I. Kanter, N. Gross, E. Klein, E. Kopelowitz, P. Yoskovits, L. Khaykovich, W. Kinzel, and M Rosenbluh, “Synchronization of mutually coupled chaotic lasers in the presence of a shutter,” Phys. Rev. Lett. 98, 154101-1–154101-4 ( 2007).
[Crossref]

T. Sugawara, M. Tachikawa, T. Tsukamoto, and T. Y. Shimizu, “Observation of Synchronization in Laser Chaos,” Phys. Rev. Lett. 72, 3502–3505 ( 1994).
[Crossref] [PubMed]

R. Roy and K. S. Thornburg, “Experimental Synchronization of Chaotic Lasers,” Phys. Rev. Lett. 72, 2009–2012 ( 1994).
[Crossref] [PubMed]

PNAS- Proceedings of the National Academy of Sciences of the USA (1)

R. Vicente, L. L Gollo, C. R. Mirasso, I. Fisher, and Gordon Pipa, “Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays,” PNAS- Proceedings of the National Academy of Sciences of the USA 105, 17157–17162 ( 2008).
[Crossref]

Quant. Semiclass. Opt. (1)

G. H. M. van Tartwijk and D. Lenstra, “Semiconductor lasers with optical injection and feedback,” Quant. Semiclass. Opt. 7, 87–143 ( 1995).
[Crossref]

Source: Phys. Rev. A (1)

P. Rees, P. S. Spencer, I. Pierce, S. Sivaprakasam, and K. A. Shore “Anticipated chaos in a non symmetric coupled external-cavity-laser system” Source: Phys. Rev. A 68, 033818-1–033818-7 ( 2003).

Other (1)

A. Pikovsky, M. Rosenblum, and J. Kurths, “Synchronization: A Universal Concept in Nonlinear Sciences,” (Cambridge Nonlinear Science Series, 2003)

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Figures (7)

Fig. 1.
Fig. 1. Experimental setup for the synchronization of Low Frequency Fluctuations in optically coupled laser.

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Fig. 2.
Fig. 2. Segment of experimental time series of the power of (a) laser 1 and (b) laser 2, showing the low frequency synchronism and including the interchange of time delay between the lasers. τF =10 ns and τC =10 ns.

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Fig. 3.
Fig. 3. Typical segment of the numerical time series of (a) laser 1 and (b) laser 2 LFF power drops under synchronized condition. Notice that the first drops are isochronous while time leadership was interchanged between drops two and three. τF =10 ns and τC =10.05 ns.

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Fig. 4.
Fig. 4. Histograms of the time delays between LFF pulses of the two synchronized lasers with τF =10 ns and τC =10 ns(a) experimental, (b) numerical calculated with no optical detuning and equal parameters and (c) numerical with laser 2 and 1 having currents 1.014 and 1.013 above threshold, respectively.

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Fig. 5.
Fig. 5. Histograms from experimental (a) and numerical (b) series for the time delays between LFF drops of the two synchronized lasers: τF =10 ns and τC =15 ns. These delay values do not allow isochrone events, according to Eq. 1

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Fig. 6.
Fig. 6. Histograms of the numerical delay times between synchronized LFF drops of the lasers with τF =10 ns and τC =15 ns and showing the effect of asymmetric conditions in the pump currents. In (a). Ji =1.013 for the two lasers and in (b) J 1=1.025 and J 2=1.013, making Laser 1 the time leader.

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Fig. 7.
Fig. 7. Histograms of the numerical delay times between synchronized LFF drops of the lasers with τF =10 ns and τC =15 ns and Ji =1.013, showing the effect of optical frequency detuning. Above, with Ω/2π=-1 GHz, laser 1 had higher frequency and was time leader in the LFF synchronized drops. Below, the optical frequency was higher for laser 2, which became time leader. See text for explanation on the difference between the two histograms

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Equations (5)

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

Δ T i = m i ∙ τ C − n i ∙ τ F
dE i ( t ) dt = ( 1 + iα ) 2 [ G ( N i ) − 1 τ p ] E i ( t ) + κ E i ( t − τ F ) exp ( iϕ i )
+ γE j ≠ i ( t − τ C ) exp ( − i Ω j ) ( t − τ C )
dN i ( t ) dt = J i − N i ( t ) τ s − G ( N i ) ∣ E i ( t ) ∣ 2 ,
G ( N i ) = G 0 ( N i − N 0 ) 1 + ε ∣ E i ( t ) ∣ 2

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