Abstract

Stable route-tracking synchronization is experimentally demonstrated in two semiconductor lasers with delayed optoelectronic feedback. When the two lasers are stably synchronized, the receiver laser is observed to track the route to chaotic pulsing of the transmitter laser. The stability of the route-tracking synchronization is examined by calculation of the transverse Lyapunov exponents of the coupled system.

© 2001 Optical Society of America

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References

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  1. G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 2547 (1998).
    [CrossRef]
  2. J. P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80, 2249 (1998).
    [CrossRef]
  3. S. Sivaprakasam and K. A. Shore, Opt. Lett. 24, 466 (1999).
    [CrossRef]
  4. Y. Takiguchi, H. Fujino, and J. Ohtsubo, Opt. Lett. 24, 1570 (1999).
    [CrossRef]
  5. S. Tang and J. M. Liu, IEEE J. Quantum Electron. 37, 329 (2001).
    [CrossRef]
  6. S. Tang and J. M. Liu, Opt. Lett. 26, 596 (2001).
    [CrossRef]
  7. L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
    [CrossRef]

2001 (2)

S. Tang and J. M. Liu, IEEE J. Quantum Electron. 37, 329 (2001).
[CrossRef]

S. Tang and J. M. Liu, Opt. Lett. 26, 596 (2001).
[CrossRef]

1999 (2)

1998 (2)

G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 2547 (1998).
[CrossRef]

J. P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80, 2249 (1998).
[CrossRef]

1997 (1)

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
[CrossRef]

Carroll, T. L.

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
[CrossRef]

Fujino, H.

Goedgebuer, J. P.

J. P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80, 2249 (1998).
[CrossRef]

Johnson, G. A.

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
[CrossRef]

Larger, L.

J. P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80, 2249 (1998).
[CrossRef]

Liu, J. M.

S. Tang and J. M. Liu, IEEE J. Quantum Electron. 37, 329 (2001).
[CrossRef]

S. Tang and J. M. Liu, Opt. Lett. 26, 596 (2001).
[CrossRef]

Mar, D. J.

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
[CrossRef]

Ohtsubo, J.

Pecora, L. M.

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
[CrossRef]

Porte, H.

J. P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80, 2249 (1998).
[CrossRef]

Roy, R.

G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 2547 (1998).
[CrossRef]

Shore, K. A.

Sivaprakasam, S.

Takiguchi, Y.

Tang, S.

S. Tang and J. M. Liu, Opt. Lett. 26, 596 (2001).
[CrossRef]

S. Tang and J. M. Liu, IEEE J. Quantum Electron. 37, 329 (2001).
[CrossRef]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 2547 (1998).
[CrossRef]

Chaos (1)

L. M. Pecora, T. L. Carroll, G. A. Johnson, and D. J. Mar, Chaos 7, 520 (1997).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Tang and J. M. Liu, IEEE J. Quantum Electron. 37, 329 (2001).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (2)

G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 2547 (1998).
[CrossRef]

J. P. Goedgebuer, L. Larger, and H. Porte, Phys. Rev. Lett. 80, 2249 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup for route-tracking synchronization. LDs, laser diodes; PDs, photodetectors; As, amplifiers. Delay times are adjusted by the positions of the prisms.

Fig. 2
Fig. 2

Time series and correlation plots of synchronization at three different pulsing states under c=1: (a) regular pulsing, τT7.47 ns; (b) two-frequency quasi-periodic pulsing, τT7.09 ns; (c) chaotic pulsing, τT6.92 ns. In (a)–(c) the top trace is for the transmitter and the bottom trace is for the receiver. Tx, output of the transmitter; Rx, output of the receiver.

Fig. 3
Fig. 3

Phase portraits of peak intensity of synchronization at different pulsing states as in Fig.  2. Pn, series of peak intensities.

Fig. 4
Fig. 4

Conditions for stable route-tracking synchronization. (a) Bifurcation diagram of the extrema of peak series. A, regular pulsing; B, two-frequency quasi-periodic pulsing; C, three-frequency quasi-periodic pulsing; D, chaotic pulsing. (b) Largest average TLE of the coupled system for the same dynamic states as in (a) under different coupling strengths, c=0.1,0.6,1.

Equations (7)

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dSTdt=-γcST+ΓgST+2S0STFsT,
dNTdt=Jed1+ξyTt-τT-γsNT-gST,
yTt=-tdηfTt-ηSTη/S0,
dSRdt=-γcSR+ΓgSR+2S0SRFsR,
dNRdt=Jed1+cξyTRt-τT+1-cξyRt-τR-γsNR-gSR,
yTRt=-tdηfTRt-ηSTη/S0,
yRt=-tdηfRt-ηSRη/S0,

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