Abstract

We study the onset of synchronization in a network of N delay-coupled stochastic fiber ring lasers with respect to various parameters when the coupling power is weak. In particular, for groups of three or more ring lasers mutually coupled to a central hub laser, we demonstrate a robust tendency toward out-of-phase (achronal) synchronization between the N – 1 outer lasers and the single inner laser. In contrast to the achronal synchronization, we find the outer lasers synchronize with zero-lag (isochronal) with respect to each other, thus forming a set of N – 1 coherent fiber lasers.

© 2011 OSA

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  1. M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).
    [CrossRef]
  2. M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
    [CrossRef] [PubMed]
  3. K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
    [CrossRef]
  4. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  5. D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).
    [CrossRef]
  6. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).
    [CrossRef] [PubMed]
  7. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).
    [CrossRef]
  8. A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).
    [CrossRef] [PubMed]
  9. O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
    [CrossRef]
  10. J. Mulet, C. Mirasso, T. Heil, and I. Fischer, “Synchronication scenario of two distant mutually coupled semiconductor lasers,” J. Opt. B: Quantum Semiclass. Opt. 6, 97–105 (2004).
    [CrossRef]
  11. T. Heil, I. Fischer, W. Elsasser, J. Mulet, and C. R. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett.86, 795–798 (2001).
    [CrossRef] [PubMed]
  12. J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
    [CrossRef]
  13. Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).
    [CrossRef] [PubMed]
  14. Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).
    [CrossRef]
  15. G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).
    [CrossRef]
  16. R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).
    [CrossRef]
  17. Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).
    [CrossRef]
  18. D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
    [CrossRef]
  19. L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).
    [CrossRef]
  20. I. B. Schwartz and L. B. Shaw, “Isochronal synchronization of delay-coupled systems,” Phys. Rev. E 75, 046207 (2007).
    [CrossRef]
  21. A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
    [CrossRef] [PubMed]
  22. C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).
    [CrossRef]
  23. E. A. Rogers, “Synchronization of high dimensional dynamical systems,” Ph.D. thesis, University of Maryland College Park (2005).
  24. E. A. Rogers-Dakin, J. Garcia-Ojalvo, D. J. Deshazer, and R. Roy, “Synchronization and symmetry breaking in mutually coupled fiber lasers,” Phys. Rev. E 73, 045201 (2006).
    [CrossRef]
  25. A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).
    [CrossRef]
  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, 264101 (2010).
    [CrossRef]
  27. D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).
    [CrossRef]
  28. L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).
    [CrossRef] [PubMed]

2010 (2)

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
[CrossRef]

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

2007 (4)

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).
[CrossRef]

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

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
[CrossRef] [PubMed]

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).
[CrossRef] [PubMed]

2006 (3)

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).
[CrossRef]

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

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).
[CrossRef]

2005 (1)

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).
[CrossRef]

2004 (2)

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
[CrossRef]

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

2003 (1)

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).
[CrossRef]

2002 (2)

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).
[CrossRef]

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
[CrossRef]

2001 (1)

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

2000 (1)

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).
[CrossRef]

1999 (1)

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).
[CrossRef]

1997 (2)

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).
[CrossRef]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).
[CrossRef]

1996 (3)

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).
[CrossRef] [PubMed]

Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).
[CrossRef] [PubMed]

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).
[CrossRef] [PubMed]

1980 (1)

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

1979 (1)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

1977 (1)

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).
[CrossRef]

Bertram, M.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Buldu, J. M.

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).
[CrossRef] [PubMed]

Danckaert, J.

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
[CrossRef]

Deshazer, D. J.

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

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
[CrossRef]

Elsasser, W.

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

Ertl, G.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Fischer, I.

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
[CrossRef]

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

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

Franz, A. L.

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
[CrossRef] [PubMed]

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, 264101 (2010).
[CrossRef]

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

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).
[CrossRef]

Glass, L.

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).
[CrossRef]

Heil, T.

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

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

Huys, O. D.

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
[CrossRef]

Ikeda, K.

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Imai, Y.

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).
[CrossRef]

Imoto, T.

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).
[CrossRef]

Johnston, G. L.

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).
[CrossRef]

Kim, M.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Kobayashi, K.

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

Kocarev, L.

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).
[CrossRef] [PubMed]

Kurths, J.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).
[CrossRef]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).
[CrossRef] [PubMed]

Kurths, M.

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
[CrossRef]

Landsman, A. S.

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).
[CrossRef]

Lang, R.

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

Mackey, M.

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).
[CrossRef]

Marti, A.

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).
[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, 264101 (2010).
[CrossRef]

Massoller, C.

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).
[CrossRef]

Matus, M.

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
[CrossRef]

Mikhailov, A. S.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Mirasso, C.

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

Mirasso, C. R.

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

Moloney, J. V.

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
[CrossRef]

Mulet, J.

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

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

Murakawa, H.

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).
[CrossRef]

Parlitz, U.

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).
[CrossRef] [PubMed]

Pikovsky, A. S.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).
[CrossRef]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).
[CrossRef] [PubMed]

Pollmann, M.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Reddy, D. V. R.

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).
[CrossRef]

Rogers, E. A.

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).
[CrossRef]

E. A. Rogers, “Synchronization of high dimensional dynamical systems,” Ph.D. thesis, University of Maryland College Park (2005).

Rogers-Dakin, E. A.

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

Rosenblum, M. G.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).
[CrossRef]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).
[CrossRef] [PubMed]

Rotermund, H. H.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Roy, R.

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

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
[CrossRef] [PubMed]

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).
[CrossRef]

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

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
[CrossRef]

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).
[CrossRef]

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).
[CrossRef]

Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).
[CrossRef] [PubMed]

Sanjuan, M.

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).
[CrossRef] [PubMed]

Schwartz, I. B.

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

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
[CrossRef] [PubMed]

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).
[CrossRef]

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).
[CrossRef]

Sen, A.

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).
[CrossRef]

Shaw, L. B.

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

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
[CrossRef] [PubMed]

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (2006).
[CrossRef]

Shen, K.

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).
[CrossRef]

Tighe, B. P.

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
[CrossRef]

Tsygankov, D.

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).
[CrossRef]

Vanwiggeren, G. D.

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).
[CrossRef]

Vicente, R.

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
[CrossRef]

von Oertzen, A.

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Wagemakers, A.

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).
[CrossRef] [PubMed]

Wang, R.

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).
[CrossRef]

White, J. K.

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
[CrossRef]

Wiesenfeld, K.

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).
[CrossRef]

Williams, Q. L.

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).
[CrossRef]

Q. L. Williams and R. Roy, “Fast polarization dynamics of an erbium-doped fiber ring laser,” Opt. Lett. 21, 1478–1480 (1996).
[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, 264101 (2010).
[CrossRef]

Chaos (3)

A. Wagemakers, J. M. Buldu, and M. Sanjuan, “Isochronous synchronization in mutually couple chaotic circuits,” Chaos 17, 023128 (2007).
[CrossRef] [PubMed]

O. D. Huys, R. Vicente, J. Danckaert, and I. Fischer, “Amplitude and phase effects on the synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010).
[CrossRef]

L. B. Shaw, I. B. Schwartz, E. A. Rogers, and R. Roy, “Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers,” Chaos 16, 01511 (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. 16, 347–355 (1980).
[CrossRef]

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

D. J. DeShazer, B. P. Tighe, M. Kurths, and R. Roy, “Experimental observation of noise-induced synchronization of bursting dynamical systems,” IEEE J. Sel. Top. Quantum Electron. 10, 906–910 (2004).
[CrossRef]

Int. J. Bifurcation Chaos Appl. Sci. Eng. (1)

G. D. Vanwiggeren and R. Roy, “Chaotic communication using time-delayed optical systems,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2129–2156 (1999).
[CrossRef]

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

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

Opt. Commun. (2)

K. Ikeda, “Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system,” Opt. Commun. 30, 257–261 (1979).
[CrossRef]

Y. Imai, H. Murakawa, and T. Imoto, “Chaos synchronization characteristics in erbium-doped fiber laser systems,” Opt. Commun. 217, 415–420 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

Q. L. Williams, J. Garcia-Ojalvo, and R. Roy, “Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects,” Phys. Rev. A 55, 2376–2386 (1997).
[CrossRef]

Phys. Rev. E (6)

R. Wang and K. Shen, “Synchronization of chaotic erbium-doped fiber dual-ring lasers by using the method of another chaotic system to drive them,” Phys. Rev. E 65, 016207 (2002).
[CrossRef]

J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
[CrossRef]

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

A. S. Landsman and I. B. Schwartz, “Complete chaotic synchronization in mutually coupled time-delay systems,” Phys. Rev. E 75, 026201 (2007).
[CrossRef]

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

D. Tsygankov and K. Wiesenfeld, “Weak link synchronization,” Phys. Rev. E 73, 026222 (2006).
[CrossRef]

Phys. Rev. Lett. (7)

L. Kocarev and U. Parlitz, “Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems,” Phys. Rev. Lett. 76, 1816–1819 (1996).
[CrossRef] [PubMed]

A. L. Franz, R. Roy, L. B. Shaw, and I. B. Schwartz, “Changing dynamical complexity with time delay in coupled fiber laser oscillators,” Phys. Rev. Lett. 99, 053905 (2007).
[CrossRef] [PubMed]

C. Massoller and A. Marti, “Random delays and the sychronization of chaotic maps,” Phys. Rev. Lett. 94, 134102 (2005).
[CrossRef]

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

D. V. R. Reddy, A. Sen, and G. L. Johnston, “Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators,” Phys. Rev. Lett. 85, 3381–3384 (2000).
[CrossRef]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase synchronization of chaotic oscillators,” Phys. Rev. Lett. 76, 1804–1807 (1996).
[CrossRef] [PubMed]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From phase to lag synchronization in coupled chaotic oscillators,” Phys. Rev. Lett. 78, 4193–4196 (1997).
[CrossRef]

Science (2)

M. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science 197, 289–289 (1977).
[CrossRef]

M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic co oxidation on pt(110),” Science 292, 1357–1360 (2001).
[CrossRef] [PubMed]

Other (2)

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

E. A. Rogers, “Synchronization of high dimensional dynamical systems,” Ph.D. thesis, University of Maryland College Park (2005).

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Figures (4)

Fig. 1
Fig. 1

The cross correlation and phase coherence for N = 5 fiber ring lasers, as a function of a shift τs in the time series, for the star configuration. In this experiment, τd = 45ns, and it is clear that Cout peaks at zero while Cin peaks at τd.

Fig. 2
Fig. 2

A time history of the intensity for a numerical experiment with N = 5 and κ = .01. Here the inner “hub” laser (in blue) is shifted to the right by one delay because, in this experiment, the outer lasers are being led by the inner hub. Lasers 2–4 are shifted up or down by a small amount for illustrative purposes.

Fig. 3
Fig. 3

Here we demonstrate the growth of the cross-correlation for N = 3, N = 9 and N = 20 lasers as a function of κ. Here Cout is recorded with τs = 0 over ten cavity round trips. Note that the smallest values of κ represent a nearly uncoupled system.

Fig. 4
Fig. 4

Achronal synchronization for the weak pumping case. Here the outer lasers have q = 200 while the inner have q = 40. Here κ = .01. The inner laser here is in blue and is blown up in Figure 4b. Here Cout ∼ .901.

Tables (1)

Tables Icon

Table 1 Summary of parameters used in the laser coupling model. The detuning parameter of the outer lasers was uniform, αout = .0352, while αin = .0202 was picked for the inner laser. For simplicity, the length of the fibers (and thus the delays) were fixed for all experiments, as were the coupling strengths.

Equations (8)

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E j ( t ) = R exp [ Γ ( 1 i α j ) W j ( t ) + i Δ ϕ ] E j f d b ( t ) + ξ j ( t )
d W j d t = q 1 W j ( t ) | E j f d b ( t ) | 2 { exp [ 2 Γ W j ( t ) ] 1 } ,
E j f d b ( t ) = E j ( t τ R ) + 1 b j k = 1 N B j , k κ k E k ( t τ d ) .
B = ( 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 ) .
τ R = ( L a + L p ) n γ || / c ,
C a b = 1 σ a σ b 1 K j = 1 K [ I a ( t j τ s ) I a ] [ I b ( t j ) I b ] ,
R a b = | 1 K j = 1 K e Δ ϕ a b , j | ,
Δ ϕ a b , j = ϕ a ( t j τ s ) ϕ b ( t j )

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