Abstract

We experimentally investigate phase synchronization between two electronically coupled diode laser pumped Nd:YAG lasers. As the coupling strength increases, the phase of the two chaotic laser outputs develops from a nonsynchronous state to a phase synchronous one through a phase jump state. We find that there are 2π phase jumps and a π/2 phase shift between the two laser outputs unlike in optically coupled Nd:YAG lasers. To clarify the transition to phase synchronization with a π/2 phase shift, we analyze the phenomenon of phase synchronization by using a phase portrait, phase difference dynamics, and frequency variation depending on the coupling strength and obtain the scaling rule of the average phase locking time in the intermittent phase jump state.

© 2006 Optical Society of America

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  1. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladres, and C. S. Zhou, “The synchronization of chaotic systems, ” Phys. Rep. 366, 1 (2002).
    [Crossref]
  2. D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
    [Crossref]
  3. C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
    [Crossref] [PubMed]
  4. K. Miyakawa and H. Isikawa, “Noise-enchanced phase locking in a chemical oscillator system,” Phys. Rev. E 65, 056206 (2002).
    [Crossref]
  5. István Z. Kiss, Qing Lv, and John L. Hudson, “Synchronization of non-phase-coherent chaotic electrochemical oscillations,” Phys. Rev. E 71, 035201(R) (2005).
    [Crossref]
  6. C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
    [Crossref]
  7. P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
    [Crossref]
  8. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett. 76, 1804 (1996).
    [Crossref] [PubMed]
  9. A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
    [Crossref]
  10. E. Rosa, E. Ott, and M. H. Hess, “Transition to Phase Synchronization of Chaos,” Phys. Rev. Lett. 80, 1642 (1998).
    [Crossref]
  11. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From Phase to Lag Synchronization in Coupled Chaotic Oscillators,” Phys. Rev. Lett. 78, 4193 (1997).
    [Crossref]
  12. W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
    [Crossref]
  13. D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
    [Crossref]
  14. S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
    [Crossref] [PubMed]
  15. R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
    [Crossref]
  16. S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
    [Crossref]
  17. K. V. Volodchenko, V. N. Ivanov, S. H. Gong, M. Choi, Y. J. Park, and C. M. Kim, “Phase synchronization in coupled Nd:YAG lasers,” Opt. Lett. 26, 1406 (2001).
    [Crossref]
  18. M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013 (2003).
    [Crossref] [PubMed]
  19. Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
    [Crossref]
  20. F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Mégret, and M. Blondel, “Secure communication scheme using chaotic laser diodes subject to incoherent optical feedback and incoherent optical injection,” Opt. Lett. 26, 1486 (2001).
    [Crossref]
  21. T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
    [Crossref]
  22. I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
    [Crossref]
  23. C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
    [Crossref]

2005 (1)

István Z. Kiss, Qing Lv, and John L. Hudson, “Synchronization of non-phase-coherent chaotic electrochemical oscillations,” Phys. Rev. E 71, 035201(R) (2005).
[Crossref]

2003 (7)

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
[Crossref]

S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
[Crossref]

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[Crossref]

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013 (2003).
[Crossref] [PubMed]

2002 (3)

S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
[Crossref] [PubMed]

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

K. Miyakawa and H. Isikawa, “Noise-enchanced phase locking in a chemical oscillator system,” Phys. Rev. E 65, 056206 (2002).
[Crossref]

2001 (3)

2000 (3)

I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
[Crossref]

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
[Crossref]

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

1998 (3)

C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
[Crossref]

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

E. Rosa, E. Ott, and M. H. Hess, “Transition to Phase Synchronization of Chaos,” Phys. Rev. Lett. 80, 1642 (1998).
[Crossref]

1997 (2)

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From Phase to Lag Synchronization in Coupled Chaotic Oscillators,” Phys. Rev. Lett. 78, 4193 (1997).
[Crossref]

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[Crossref]

1996 (1)

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett. 76, 1804 (1996).
[Crossref] [PubMed]

Abel, H.

C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
[Crossref]

Aida, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[Crossref]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
[Crossref]

Allaria, E.

S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
[Crossref] [PubMed]

Arecchi, F. T.

S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
[Crossref] [PubMed]

Barbay, S.

S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
[Crossref]

Blondel, M.

Boccaletti, S.

S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
[Crossref] [PubMed]

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

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
[Crossref]

Chen, H. F.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
[Crossref]

Choi, M.

Davis, P.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[Crossref]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
[Crossref]

Deparis, O.

DeShazer, D.

R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
[Crossref]

Freund, H.-J.

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

Giacomelli, G.

S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
[Crossref]

Gong, S. H.

Heil, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[Crossref]

Hess, M. H.

E. Rosa, E. Ott, and M. H. Hess, “Transition to Phase Synchronization of Chaos,” Phys. Rev. Lett. 80, 1642 (1998).
[Crossref]

Hudson, John L.

István Z. Kiss, Qing Lv, and John L. Hudson, “Synchronization of non-phase-coherent chaotic electrochemical oscillations,” Phys. Rev. E 71, 035201(R) (2005).
[Crossref]

Hwang, D. U.

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

Isikawa, H.

K. Miyakawa and H. Isikawa, “Noise-enchanced phase locking in a chemical oscillator system,” Phys. Rev. E 65, 056206 (2002).
[Crossref]

Ivanov, V. N.

Kim, C. M.

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013 (2003).
[Crossref] [PubMed]

K. V. Volodchenko, V. N. Ivanov, S. H. Gong, M. Choi, Y. J. Park, and C. M. Kim, “Phase synchronization in coupled Nd:YAG lasers,” Opt. Lett. 26, 1406 (2001).
[Crossref]

I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
[Crossref]

Kim, G. U.

Kim, I.

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
[Crossref]

Kiss, István Z.

István Z. Kiss, Qing Lv, and John L. Hudson, “Synchronization of non-phase-coherent chaotic electrochemical oscillations,” Phys. Rev. E 71, 035201(R) (2005).
[Crossref]

Kurths, J.

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

C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
[Crossref]

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From Phase to Lag Synchronization in Coupled Chaotic Oscillators,” Phys. Rev. Lett. 78, 4193 (1997).
[Crossref]

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett. 76, 1804 (1996).
[Crossref] [PubMed]

Kwon, T. Y.

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

Kye, W. H.

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013 (2003).
[Crossref] [PubMed]

I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
[Crossref]

Lee, D. S.

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

Lee, E. K.

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

Lepri, S.

S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
[Crossref]

Liu, J. M.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
[Crossref]

Liu, Y.

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
[Crossref]

Locquet, A.

Lv, Qing

István Z. Kiss, Qing Lv, and John L. Hudson, “Synchronization of non-phase-coherent chaotic electrochemical oscillations,” Phys. Rev. E 71, 035201(R) (2005).
[Crossref]

Mancini, H.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
[Crossref]

Maza, D.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
[Crossref]

McAllister, R.

R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
[Crossref]

Mégret, P.

Meucci, R.

R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
[Crossref]

S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
[Crossref] [PubMed]

Miyakawa, K.

K. Miyakawa and H. Isikawa, “Noise-enchanced phase locking in a chemical oscillator system,” Phys. Rev. E 65, 056206 (2002).
[Crossref]

Monti, M.

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

Osipov, G.

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

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[Crossref]

Ott, E.

E. Rosa, E. Ott, and M. H. Hess, “Transition to Phase Synchronization of Chaos,” Phys. Rev. Lett. 80, 1642 (1998).
[Crossref]

Pardo, W. B.

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

Park, Y. J.

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013 (2003).
[Crossref] [PubMed]

K. V. Volodchenko, V. N. Ivanov, S. H. Gong, M. Choi, Y. J. Park, and C. M. Kim, “Phase synchronization in coupled Nd:YAG lasers,” Opt. Lett. 26, 1406 (2001).
[Crossref]

I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
[Crossref]

Pieroux, D.

Pikovsky, A.

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[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 (1997).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett. 76, 1804 (1996).
[Crossref] [PubMed]

Rim, S.

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

M. Choi, K. V. Volodchenko, S. Rim, W. H. Kye, C. M. Kim, Y. J. Park, and G. U. Kim, “Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers,” Opt. Lett. 28, 1013 (2003).
[Crossref] [PubMed]

Rogister, F.

Rosa, E.

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

E. Rosa, E. Ott, and M. H. Hess, “Transition to Phase Synchronization of Chaos,” Phys. Rev. Lett. 80, 1642 (1998).
[Crossref]

Rosenblum, M.

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[Crossref]

Rosenblum, M. G.

C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
[Crossref]

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From Phase to Lag Synchronization in Coupled Chaotic Oscillators,” Phys. Rev. Lett. 78, 4193 (1997).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett. 76, 1804 (1996).
[Crossref] [PubMed]

Roy, R.

R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
[Crossref]

Schnitzler, A.

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

Sciamanna, M.

Shäfer, C.

C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
[Crossref]

Tass, P.

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

Ticos, C. M.

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

Uchida, A.

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[Crossref]

Valladres, D. L.

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

Vallone, A.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
[Crossref]

Volkmann, J.

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

Volodchenko, K. V.

Walkenstein, J. A.

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

Weule, J

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

Zaks, M.

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[Crossref]

Zavatta, A.

S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
[Crossref]

Zhou, C. S.

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

Nature (1)

C. Shäfer, M. G. Rosenblum, J. Kurths, and H. Abel, “Heartbeat synchronized with ventilation,” Nature 392, 239 (1998).
[Crossref]

Opt. Lett. (3)

Phys. Lett. A (1)

C. M. Kim, W. H. Kye, S. Rim, D. U. Hwang, I. Kim, Y. J. Park, and E. K. Lee, “Origin of the Transition inside the Desynchronization State in Coupled Chaotic Oscillators,” Phys. Lett. A 313, 62 (2003).
[Crossref]

Phys. Rep. (1)

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

Phys. Rev. A (2)

T. Heil, A. Uchida, P. Davis, and T. Aida, “TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback,” Phys. Rev. A 68, 033811 (2003).
[Crossref]

Y. Liu, H. F. Chen, J. M. Liu, P. Davis, and T. Aida, “Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection,” Phys. Rev. A 63, 031802(R) (2001).
[Crossref]

Phys. Rev. E (7)

I. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, “Phase synchronization with Type-II Intermittency in Chaotic Oscillators,” Phys. Rev. E 62, 8826 (2000).
[Crossref]

W. H. Kye, D. S. Lee, S. Rim, C. M. Kim, and Y. J. Park, “Periodic phase synchronization in coupled chaotic oscillators,” Phys. Rev. E 68, 025201(R) (2003).
[Crossref]

D. S. Lee, W. H. Kye, S. Rim, T. Y. Kwon, and C. M. Kim, “Generalized phase synchronization in unidirectionally coupled chaotic oscillators,” Phys. Rev. E 67, 045201(R) (2003).
[Crossref]

R. McAllister, R. Meucci, D. DeShazer, and R. Roy, “Competition between two frequencies for phase synchronization of a chaotic laser,” Phys. Rev. E 67, 015202(R) (2003).
[Crossref]

S. Barbay, G. Giacomelli, S. Lepri, and A. Zavatta, “Experimental study of noise-induced phase synchronization in vertical-cavity lasers,” Phys. Rev. E 68, 020101(R) (2003).
[Crossref]

K. Miyakawa and H. Isikawa, “Noise-enchanced phase locking in a chemical oscillator system,” Phys. Rev. E 65, 056206 (2002).
[Crossref]

István Z. Kiss, Qing Lv, and John L. Hudson, “Synchronization of non-phase-coherent chaotic electrochemical oscillations,” Phys. Rev. E 71, 035201(R) (2005).
[Crossref]

Phys. Rev. Lett. (8)

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, “Experimental Phase Synchronization of a Chaotic Convective Flow,” Phys. Rev. Lett. 85, 5567 (2000).
[Crossref]

C. M. Ticos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, “Experimental Real-Time Phase Synchronization of a Paced Chaotic Plasma Discharge,”Phys. Rev. Lett. 85, 2929 (2000).
[Crossref] [PubMed]

P. Tass, M. G. Rosenblum, J Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H.-J. Freund, “Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography,” Phys. Rev. Lett. 81, 3291 (1998).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett. 76, 1804 (1996).
[Crossref] [PubMed]

A. Pikovsky, G. Osipov, M. Rosenblum, M. Zaks, and J. Kurths, “Attractor-Repeller Collision and Eyelet Intermittency at the Transition to Phase Synchronization,” Phys. Rev. Lett. 79, 47 (1997).
[Crossref]

E. Rosa, E. Ott, and M. H. Hess, “Transition to Phase Synchronization of Chaos,” Phys. Rev. Lett. 80, 1642 (1998).
[Crossref]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From Phase to Lag Synchronization in Coupled Chaotic Oscillators,” Phys. Rev. Lett. 78, 4193 (1997).
[Crossref]

S. Boccaletti, E. Allaria, R. Meucci, and F. T. Arecchi, “Experimental Characterization of the Transition to Phase Synchronization of Chaotic CO2 Laser Systems,” Phys. Rev. Lett. 89, 194101 (2002).
[Crossref] [PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup in the coupled diode laser pumped Nd:YAG lasers. LD, PD, and PM are the diode laser, the Si P-I-N photo diode, and the potentio-meter, respectively.

Fig. 2.
Fig. 2.

(Color online). Temporal behaviors of the two laser outputs. Coupling strength (a) ε= 0.000, (b) ε= 0.428, and (c) ε= 0.468.

Fig. 3.
Fig. 3.

Power spectra of the two laser outputs. (a) and (b) are the spectra of laser 1 and 2 at coupling strength ε= 0.000, (c) and (d) at ε= 0.436, and (e) and (f) at ε= 0.468. This shows that ε= 0.000, (c) and (d) at ε= 0.436, and (e) and (f) at ε= 0.468. This shows that, in the synchronous state, their center frequencies coincide with each other.

Fig. 4.
Fig. 4.

Phase portraits of the two laser outputs. (a) uncoupled lasers at ε= 0.000, (b) phase synchronization state at ε= 0.468. Units are arbitrary.

Fig. 5.
Fig. 5.

Phase difference of the two laser outputs when (a) ε = 0.456, (b) ε = 0.460, (c) ε = 0.464, and (d) ε = 0.468.

Fig. 6.
Fig. 6.

Scaling behavior of average phase locking time depending on the coupling strength. The strait line implies that the experimental result is well matched to the scaling of eyelet intermittency.

Equations (1)

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ϕ i ( t ) = 2 π t ( I i ) t ( I n i ) t ( I n + 1 i ) t ( I n i ) + 2 πn ,

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