Abstract

We studied the dynamic behavior of laser-diode-pumped nonidentical thin-slice solid-state lasers, coupled face to face, with orthogonally polarized emissions. When such an incoherent mutual optical coupling was introduced, the coupled lasers exhibited slow fluctuations of transverse-mode patterns, and isolated lasers exhibited stable transversemode-patterns. When one laser exhibited nonorthogonal multi-transverse-mode operations without coupling, simultaneous random bursts of chaotic relaxation oscillations took place in both lasers over time with coupling. A plausible physical interpretation is proposed in terms of the simultaneous excitation of chaotic relaxation oscillations in both lasers through resonances that stem from interference-induced modulation of one laser at a swept beat frequency of the fluctuating nonorthogonal mode pair. Observed instabilities were well reproduced by numerical simulation of the model equation.

© 2005 Optical Society of America

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  1. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (2002).
    [Crossref]
  2. A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
    [Crossref]
  3. T. Heil, I. Fisher, W. Elsasser, J. Mullet, and C. Mirasso, “Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers,” Phys. Rev. Lett. 86, 795–798 (2001).
    [Crossref] [PubMed]
  4. J. K. White, M. Matus, and J. V. Moloney, “Achronal generalized synchronization in mutually coupled semiconductor lasers,” Phys. Rev. E 65, 036229 (2002).
    [Crossref]
  5. J. Javaloyes, P. Mandel, and D. Pieroux, “Dynamical properties of lasers coupled face to face,” Phys. Rev. E 67, 036201 (2003).
    [Crossref]
  6. K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
    [Crossref]
  7. M. H. Ulrich, L. Maraschi, and C. M. Urry, “Variability of active galactic nuclei,” Ann. Rev. Astron. Astrophys. 35, 445–502 (1997).
    [Crossref]
  8. R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
    [Crossref]
  9. F. C. Hoppenstead and E. M. Izhikevich, Weakly Connected Neural Networks (Springer, New York1997).
    [Crossref]
  10. K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
    [Crossref] [PubMed]
  11. K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
    [Crossref]
  12. 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]
  13. P. G. Drazin, Nonlinear Systems, Cambridge Texts in Applied Mathematics (Cambridge U. Press, Cambridge, UK, 1992).
  14. J. C. Celet, D. Dangoisse, and P. Glorieux, “Slowly passing through resonance strongly depends on noise,” Phys. Rev. Lett. 81, 975–978 (1998).
    [Crossref]
  15. D. J. DeShazer, B. P. Tighe, J. Kurths, and R. Roy , “Experimental observation of noise-induced synchronization of bursting dynamical systems,” D. J. DeShazer, B. P. Tighe, J. Kurths, and R. Roy, IEEE J.. Sel. Top. Quantum Electron.10, 906–910 (2004).
    [Crossref]

2003 (2)

J. Javaloyes, P. Mandel, and D. Pieroux, “Dynamical properties of lasers coupled face to face,” Phys. Rev. E 67, 036201 (2003).
[Crossref]

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

2002 (3)

K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
[Crossref] [PubMed]

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (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 (2)

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

K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
[Crossref]

1998 (2)

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

J. C. Celet, D. Dangoisse, and P. Glorieux, “Slowly passing through resonance strongly depends on noise,” Phys. Rev. Lett. 81, 975–978 (1998).
[Crossref]

1997 (3)

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. H. Ulrich, L. Maraschi, and C. M. Urry, “Variability of active galactic nuclei,” Ann. Rev. Astron. Astrophys. 35, 445–502 (1997).
[Crossref]

A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
[Crossref]

Abarbanel, H. D. I.

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

Boccaletti, S.

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (2002).
[Crossref]

Celet, J. C.

J. C. Celet, D. Dangoisse, and P. Glorieux, “Slowly passing through resonance strongly depends on noise,” Phys. Rev. Lett. 81, 975–978 (1998).
[Crossref]

Dangoisse, D.

J. C. Celet, D. Dangoisse, and P. Glorieux, “Slowly passing through resonance strongly depends on noise,” Phys. Rev. Lett. 81, 975–978 (1998).
[Crossref]

DeShazer, D. J.

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

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

Drazin, P. G.

P. G. Drazin, Nonlinear Systems, Cambridge Texts in Applied Mathematics (Cambridge U. Press, Cambridge, UK, 1992).

Elsasser, W.

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

Elson, R. C.

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

Eurnex, T.

A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
[Crossref]

Fisher, I.

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

Gavrielides, A.

A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
[Crossref]

Glorieux, P.

J. C. Celet, D. Dangoisse, and P. Glorieux, “Slowly passing through resonance strongly depends on noise,” Phys. Rev. Lett. 81, 975–978 (1998).
[Crossref]

Heil, T.

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

Hohl, A.

A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
[Crossref]

Hoppenstead, F. C.

F. C. Hoppenstead and E. M. Izhikevich, Weakly Connected Neural Networks (Springer, New York1997).
[Crossref]

Huerta, R.

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

Izhikevich, E. M.

F. C. Hoppenstead and E. M. Izhikevich, Weakly Connected Neural Networks (Springer, New York1997).
[Crossref]

Javaloyes, J.

J. Javaloyes, P. Mandel, and D. Pieroux, “Dynamical properties of lasers coupled face to face,” Phys. Rev. E 67, 036201 (2003).
[Crossref]

Ko, J.Y.

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
[Crossref] [PubMed]

K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
[Crossref]

Kovanis, V.

A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
[Crossref]

Kurths, J.

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (2002).
[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]

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

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

Lim, T.S.

K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
[Crossref] [PubMed]

Makino, H.

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
[Crossref] [PubMed]

Mandel, P.

J. Javaloyes, P. Mandel, and D. Pieroux, “Dynamical properties of lasers coupled face to face,” Phys. Rev. E 67, 036201 (2003).
[Crossref]

Maraschi, L.

M. H. Ulrich, L. Maraschi, and C. M. Urry, “Variability of active galactic nuclei,” Ann. Rev. Astron. Astrophys. 35, 445–502 (1997).
[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]

Mirasso, C.

T. Heil, I. Fisher, W. Elsasser, J. Mullet, and C. 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]

Mullet, J.

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

Ohki, K.

K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
[Crossref]

Ohtomo, T.

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
[Crossref]

Okamoto, A.

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

Osipov, G.

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (2002).
[Crossref]

Otsuka, K.

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
[Crossref] [PubMed]

K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
[Crossref]

Pieroux, D.

J. Javaloyes, P. Mandel, and D. Pieroux, “Dynamical properties of lasers coupled face to face,” Phys. Rev. E 67, 036201 (2003).
[Crossref]

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]

Rabinovich, M. I.

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[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]

Roy, R.

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

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

Rulkov, N. F.

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

Selverston, A. I.

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

Tighe, B. P.

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

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

Ulrich, M. H.

M. H. Ulrich, L. Maraschi, and C. M. Urry, “Variability of active galactic nuclei,” Ann. Rev. Astron. Astrophys. 35, 445–502 (1997).
[Crossref]

Urry, C. M.

M. H. Ulrich, L. Maraschi, and C. M. Urry, “Variability of active galactic nuclei,” Ann. Rev. Astron. Astrophys. 35, 445–502 (1997).
[Crossref]

Valladares, D. L.

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (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]

Zhou, C. S.

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (2002).
[Crossref]

Ann. Rev. Astron. Astrophys. (1)

M. H. Ulrich, L. Maraschi, and C. M. Urry, “Variability of active galactic nuclei,” Ann. Rev. Astron. Astrophys. 35, 445–502 (1997).
[Crossref]

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

K. Otsuka, J.Y. Ko, H. Makino, T. Ohtomo, and A. Okamoto,“Transverse effects in a microchip laser with asymmetric emd-pumping: modal interference and dynamic instability,” J. Opt. Quantum Semiclass. Opt. 5, R137–R145 (2003).
[Crossref]

Phys. Reports (1)

S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Phys. Reports 366, 1–101 (2002).
[Crossref]

Phys. Rev. E (3)

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

J. Javaloyes, P. Mandel, and D. Pieroux, “Dynamical properties of lasers coupled face to face,” Phys. Rev. E 67, 036201 (2003).
[Crossref]

K. Otsuka, J.Y. Ko, T. Ohtomo, and K. Ohki, “Information circulation in a two-mode solid-state laser with optical feedback,” Phys. Rev. E 64, 056239 (2001).
[Crossref]

Phys. Rev. Lett. (6)

A. Hohl, A. Gavrielides, T. Eurnex, and V. Kovanis, “Localized synchronization in two coupled nonidentical semiconductor lasers,” Phys. Rev. Lett. 78, 4745–4748 (1997).
[Crossref]

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

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel, “Synchronous behavior of two coupled biological neurons,” Phys. Rev. Lett. 81, 5692–5695 (1998).
[Crossref]

J. C. Celet, D. Dangoisse, and P. Glorieux, “Slowly passing through resonance strongly depends on noise,” Phys. Rev. Lett. 81, 975–978 (1998).
[Crossref]

K. Otsuka, J.Y. Ko, T.S. Lim, and H. Makino, “Modal interference and dynamical instability in a solid-state slice laser with asymmetric end-pumping,” Phys. Rev. Lett. 89, 083903 (2002).
[Crossref] [PubMed]

Other (3)

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

F. C. Hoppenstead and E. M. Izhikevich, Weakly Connected Neural Networks (Springer, New York1997).
[Crossref]

P. G. Drazin, Nonlinear Systems, Cambridge Texts in Applied Mathematics (Cambridge U. Press, Cambridge, UK, 1992).

Supplementary Material (4)

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Figures (14)

Fig. 1.
Fig. 1.

Experimental setup of two LNP lasers incoherently coupled face-to-face. LD, laser diode; AP, anamorphic prism pair; OL, microscope objective lens; WM, multiwavelength meter; PD, photodiode; SF, scanning Fabry-Perot interferometer; DO, digital oscilloscope; P, polarizer. Far-field patterns of two lasers in the absence of coupling are shown. The associated movie file, indicating stable patterns over times, has a size of 1.43 Mbytes for laser A and 1.42 Mbytes for laser B, respectively.

Fig. 2.
Fig. 2.

Global optical spectra of two lasers measured by a multiwavelength meter. Polarization directions of the two lasers are orthogonal.

Fig. 3.
Fig. 3.

Detailed oscillation spectra of two lasers measured by scanning Fabry-Perot interferometers with 6-MHz resolution.

Fig. 4.
Fig. 4.

Scanning Fabry-Perot traces when the burst synchronization was the result of tuning the pump power of laser B.

Fig. 5.
Fig. 5.

Snapshots of far-field patterns in lasers coupled face to face. (a) Laser A; the associated movie file has a size of 1.33 Mbytes. (b) Laser B; the associated movie file has a size of 1.94 Mbytes. A stable pattern without spot dancing was observed in each laser when the other laser was turned off.

Fig. 6.
Fig. 6.

Global view of burst synchronization. (a) Long-term time series indicating synchronized bursting dynamics. (b) Magnified view of burst synchronization. (c) JTFA of (b). Pump powers 120 mW (laser A), 100 mW (laser B).

Fig. 7.
Fig. 7.

(a) Detailed waveforms of burst synchronization. (b) Magnified views of region B.

Fig. 8.
Fig. 8.

Correlation plots of wave forms in regions A, B, and C in Fig. 7(a). Left, amplitude; right, phase.

Fig. 9.
Fig. 9.

JTFA patterns of time series shown in Fig. 7(a).

Fig. 10.
Fig. 10.

Detailed oscillation spectra of the two lasers when the pump power was slightly increased.

Fig.11.
Fig.11.

Last modulations without bursting observed in the optical spectra shown in Fig. 10.(a) Long-term evolution of waveforms. Magnified views are shown in the insets. (b) JTFA patterns of (a).

Fig. 12.
Fig. 12.

Numerical results indicating burst synchronization. The normalized beat frequency f B/κ in laser B was swept as shown in the upper figure. As for parameters, see the text. Normalized intensities of lasers A and B are given by E 1 2 + E 2 2 and E 3 2 + E 4 2 , respectively.

Fig. 13.
Fig. 13.

Numerical result indicating fast modulation without bursting. (a) Numerical time series. (b) JTFA patterns of (a).

Fig. 14.
Fig. 14.

Level of burst synchronization. (a) Experimental time series. (b) Symbolic time series. (c) Evolution of the local level of burst synchronization.

Equations (10)

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d N 1 d t = [ w 1 1 N 1 ( 1 + 2 N 1 ) ( E 1 2 + β E 2 2 + γ E 3 2 + γ E 4 2 ) ] K ,
d N 2 d t = [ w 2 1 N 2 ( 1 + 2 N 2 ) ( E 2 2 + β E 1 2 + γ E 3 2 + γ E 4 2 ) ] K ,
d N 3 d t = [ w 3 1 N 3 ( 1 + 2 N 3 ) ( E 3 2 + β E 4 2 + γ E 1 2 + γ E 2 2 ) ] K ,
d N 4 d t = [ w 4 1 N 4 ( 1 + 2 N 4 ) ( E 4 2 + β E 3 2 + γ E 1 2 + γ E 2 2 ) ] K ,
d E 1 d t = N 1 E 1 ,
d E 2 d t = N 2 E 2 ,
d E 3 d t = N 3 E 3 + g 3 , 4 E 3 E 4 cos ϕ 3 , 4 ,
d E 4 d t = N 4 E 4 + g 3 , 4 E 4 E 3 cos ϕ 3 , 4 ,
d ϕ 3 , 4 d t = Δ Ω 3 , 4 ( t ) + D ξ ( t ) ,
M = ( 1 N ) [ Σ ( S A ( i ) S A ) ( S B ( i ) S B ) ] σ ( S A ) σ ( S B ) ,

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