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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References

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    [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]
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    [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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [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)

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

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]

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, 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, Jr., 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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