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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2009

2008

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]

2006

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. A. Rogers-Dakin, J. Garcıa-Ojalvo, D. J. DeShazer and R. Roy, "Synchronization and symmetry breaking in mutually coupled fiber lasers," Phys. Rev. E 73, 045201 (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]

2005

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

J. Mulet and C. R. Mirasso and 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]

2001

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]

1999

1997

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

G. H. M. van Tartwijk and D. Lenstra, "Semiconductor lasers with optical injection and feedback," Quant. Semiclass. Opt. 7, 87-143 (1995).
[CrossRef]

1994

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

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

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.

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. Garcıa-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.

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 and C. R. Mirasso and 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.

E. A. Rogers-Dakin, J. Garcıa-Ojalvo, D. J. DeShazer and R. Roy, "Synchronization and symmetry breaking in mutually coupled fiber lasers," Phys. Rev. E 73, 045201 (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]

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.

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]

Heil, T.

J. Mulet and C. R. Mirasso and 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]

Kanter, I.

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]

Khaykovich, L.

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]

Kinzel, W.

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]

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]

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.

Masoller, C.

C. Masoller, "Anticipation in the Synchronization of Semiconductor Lasers with Optical Feedback," Phys. Rev. Lett. 86, 2782-2785 (2001).
[CrossRef] [PubMed]

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]

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 and C. R. Mirasso and 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 and C. R. Mirasso and 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.

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]

Rios Leite, J. R.

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. Garcıa-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.

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]

Roy, R.

E. A. Rogers-Dakin, J. Garcıa-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]

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]

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]

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.

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Nature

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[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

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

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.

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.

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.

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

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.

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

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 + ) 2 [ G ( N i ) 1 τ p ] E i ( t ) + κ E i ( t τ F ) exp ( 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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