Abstract

We investigate experimentally the transition to phase synchronization in coupled Nd:YAG lasers. As the coupling strength increases, the phase difference of two chaotic laser outputs develops from nonsynchronous to a phase-synchronous state via ±2π phase jumps. We analyze this transition.

© 2001 Optical Society of America

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  1. L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47, 4287 (1993).
    [CrossRef] [PubMed]
  2. J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. A 50, 1874 (1994).
  3. S. K. Han, C. Kurrer, and Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995).
    [CrossRef] [PubMed]
  4. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
    [CrossRef] [PubMed]
  5. S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
    [CrossRef]
  6. M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
    [CrossRef] [PubMed]
  7. A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
    [CrossRef]
  8. E. Rosa, E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998).
    [CrossRef]
  9. M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
    [CrossRef]
  10. I. I. Blekhman, Synchronization in Science and TechnologyNauka, Moscow, 1981; in Russian; English translation , American Institute of Mechanical Engineers, New York, 1988.
  11. K. J. Lee, Y. Kwak, and T. K. Lim, Phys. Rev. Lett. 81, 321 (1998).
    [CrossRef]
  12. W. H. Kye and C. M. Kim, Phys. Rev. E 62, 6303 (2000).
    [CrossRef]
  13. C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.
  14. I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
    [CrossRef]
  15. C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
    [CrossRef]
  16. D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
    [CrossRef]
  17. S. H. Gong and C. M. Kim, “On–off intermittency in the threshold of a cw Nd:YAG laser,” J. Opt. Soc. Am. B (to be published) .
  18. T. Yalcinkaya and Y. C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
    [CrossRef]

2001

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
[CrossRef]

2000

W. H. Kye and C. M. Kim, Phys. Rev. E 62, 6303 (2000).
[CrossRef]

I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
[CrossRef]

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
[CrossRef]

1998

E. Rosa, E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998).
[CrossRef]

K. J. Lee, Y. Kwak, and T. K. Lim, Phys. Rev. Lett. 81, 321 (1998).
[CrossRef]

1997

A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
[CrossRef]

T. Yalcinkaya and Y. C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

1996

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
[CrossRef] [PubMed]

1995

S. K. Han, C. Kurrer, and Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995).
[CrossRef] [PubMed]

1994

J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. A 50, 1874 (1994).

1993

L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

1990

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

Blekhman, I. I.

I. I. Blekhman, Synchronization in Science and TechnologyNauka, Moscow, 1981; in Russian; English translation , American Institute of Mechanical Engineers, New York, 1988.

Boccaletti, S.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
[CrossRef]

Carroll, T. L.

J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. A 50, 1874 (1994).

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

Colet, P.

L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Fabiny, L.

L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Gong, S. H.

S. H. Gong and C. M. Kim, “On–off intermittency in the threshold of a cw Nd:YAG laser,” J. Opt. Soc. Am. B (to be published) .

Han, S. K.

S. K. Han, C. Kurrer, and Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995).
[CrossRef] [PubMed]

Heagy, J. F.

J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. A 50, 1874 (1994).

Hess, M. H.

E. Rosa, E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998).
[CrossRef]

Hwang, D. U.

S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
[CrossRef]

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

Kim, C. M.

S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
[CrossRef]

I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
[CrossRef]

W. H. Kye and C. M. Kim, Phys. Rev. E 62, 6303 (2000).
[CrossRef]

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

S. H. Gong and C. M. Kim, “On–off intermittency in the threshold of a cw Nd:YAG laser,” J. Opt. Soc. Am. B (to be published) .

Kim, I.

S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
[CrossRef]

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

Kim, I. B.

I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
[CrossRef]

Kuramoto, Y.

S. K. Han, C. Kurrer, and Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995).
[CrossRef] [PubMed]

Kurrer, C.

S. K. Han, C. Kurrer, and Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995).
[CrossRef] [PubMed]

Kurths, J.

A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
[CrossRef] [PubMed]

Kwak, Y.

K. J. Lee, Y. Kwak, and T. K. Lim, Phys. Rev. Lett. 81, 321 (1998).
[CrossRef]

Kye, W. H.

W. H. Kye and C. M. Kim, Phys. Rev. E 62, 6303 (2000).
[CrossRef]

I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
[CrossRef]

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

Lai, Y. C.

T. Yalcinkaya and Y. C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
[CrossRef]

Lee, E. K.

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

Lee, K. J.

K. J. Lee, Y. Kwak, and T. K. Lim, Phys. Rev. Lett. 81, 321 (1998).
[CrossRef]

Lim, T. K.

K. J. Lee, Y. Kwak, and T. K. Lim, Phys. Rev. Lett. 81, 321 (1998).
[CrossRef]

Mancini, H.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
[CrossRef]

Maza, D.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
[CrossRef]

Monti, M.

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

Osipov, G. V.

A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
[CrossRef]

Ott, E.

E. Rosa, E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998).
[CrossRef]

Pardo, W. B.

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

Park, Y. J.

I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
[CrossRef]

Pecora, L. M.

J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. A 50, 1874 (1994).

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

Pikovsky, A.

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
[CrossRef] [PubMed]

Pikovsky, A. S.

A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
[CrossRef]

Rim, S.

S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
[CrossRef]

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

Rosa, E.

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

E. Rosa, E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998).
[CrossRef]

Rosenblum, M.

A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
[CrossRef] [PubMed]

Roy, R.

L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

Vallone, A.

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
[CrossRef]

Walkenstein, J. A.

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

Yalcinkaya, T.

T. Yalcinkaya and Y. C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
[CrossRef]

Yicos, C. M.

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

Phys. D

A. S. Pikovsky, M. Rosenblum, G. V. Osipov, and J. Kurths, Phys. D 104, 219 (1997).
[CrossRef]

Phys. Lett.

S. Rim, D. U. Hwang, I. Kim, and C. M. Kim, Phys. Lett. 85, 2304 (2000).
[CrossRef]

Phys. Rev. A

L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47, 4287 (1993).
[CrossRef] [PubMed]

J. F. Heagy, T. L. Carroll, and L. M. Pecora, Phys. Rev. A 50, 1874 (1994).

Phys. Rev. E

W. H. Kye and C. M. Kim, Phys. Rev. E 62, 6303 (2000).
[CrossRef]

I. B. Kim, C. M. Kim, W. H. Kye, and Y. J. Park, Phys. Rev. E 62, 8826 (2000).
[CrossRef]

Phys. Rev. Lett.

C. M. Yicos, E. Rosa, W. B. Pardo, J. A. Walkenstein, and M. Monti, Phys. Rev. Lett. 85, 2929 (2000).
[CrossRef]

D. Maza, A. Vallone, H. Mancini, and S. Boccaletti, Phys. Rev. Lett. 85, 5567 (2001).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996).
[CrossRef] [PubMed]

S. K. Han, C. Kurrer, and Y. Kuramoto, Phys. Rev. Lett. 75, 3190 (1995).
[CrossRef] [PubMed]

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

E. Rosa, E. Ott, and M. H. Hess, Phys. Rev. Lett. 80, 1642 (1998).
[CrossRef]

M. Rosenblum, A. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

K. J. Lee, Y. Kwak, and T. K. Lim, Phys. Rev. Lett. 81, 321 (1998).
[CrossRef]

T. Yalcinkaya and Y. C. Lai, Phys. Rev. Lett. 79, 3885 (1997).
[CrossRef]

Other

I. I. Blekhman, Synchronization in Science and TechnologyNauka, Moscow, 1981; in Russian; English translation , American Institute of Mechanical Engineers, New York, 1988.

C. M. Kim, W. H. Kye, D. U. Hwang, S. Rim, I. Kim, and E. K. Lee are preparing a manuscript called “Origin of transition to phase synchronization via phase jump,” to be submitted to Phys. Rev. E.

S. H. Gong and C. M. Kim, “On–off intermittency in the threshold of a cw Nd:YAG laser,” J. Opt. Soc. Am. B (to be published) .

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the experiment in two coupled Nd:YAG lasers.

Fig. 2
Fig. 2

Temporal behaviors of the two laser outputs depending on the coupling strength: the angles of the Glan–Thompson polarizer are (a) 90°, (b) 45°, (c) 15°, and (d) 0°.

Fig. 3
Fig. 3

Phase portraits of laser outputs: (a) phase-jump state when the angle of the Glan–Thompson polarizer is 45° and (b) PS when the angle is 15°.

Fig. 4
Fig. 4

Temporal behaviors of phase difference: (a) nonsynchronous state when the angle of the Glan–Thompson polarizer is 90°, (b) phase jump state when the angle is 45°, and (c) PS when the angle is 15°.

Fig. 5
Fig. 5

Scaling behavior of the average phase-locking time according to the coupling strength: (a) the average time l versus the coupling strength ϵ and (b) lnl versus ϵt-ϵ-1/2.

Equations (1)

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I1,2=r1,2cosθ1,2,I˙1,2=r1,2sinθ1,2,

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