Abstract

We present experimental evidence of antiphase dynamics in self-pulsing erbium-doped fiber lasers operating simultaneously at 1.536- and 1.55-μm wavelengths. Autonomous chaos is also observed for several ranges of pumping rates. The fractal dimension of the chaotic attractor, calculated from experimental data by use of the Procaccia method, is found to depend on the pumping ratio but always remains smaller than 4.1, regardless of the chaotic regime considered.

© 1993 Optical Society of America

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  1. I. M. Jauncey, L. Reekie, R. J. Mears, C. J. Rowe, Opt. Lett. 12, 164 (1987).
    [CrossRef] [PubMed]
  2. P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
    [CrossRef]
  3. P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
    [CrossRef]
  4. F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
    [CrossRef] [PubMed]
  5. K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
    [CrossRef] [PubMed]
  6. S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992).
    [CrossRef] [PubMed]
  7. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
    [CrossRef]
  8. P. Urquhart, Proc. Inst. Electr. Eng. Part J 135, 385 (1988).
  9. See, for example, P. Bergé, Y. Pommeau, C. Vidal, Order within Chaos (Wiley, New York, 1984).
  10. P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
    [CrossRef]

1993 (4)

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

1992 (1)

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992).
[CrossRef] [PubMed]

1990 (1)

K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

1988 (1)

P. Urquhart, Proc. Inst. Electr. Eng. Part J 135, 385 (1988).

1987 (1)

1983 (1)

P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

Bayon, J.-F.

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

Bergé, P.

See, for example, P. Bergé, Y. Pommeau, C. Vidal, Order within Chaos (Wiley, New York, 1984).

Bielawski, S.

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992).
[CrossRef] [PubMed]

Bracikowski, C.

K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

Delevaque, E.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

Derozier, D.

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992).
[CrossRef] [PubMed]

François, P. L.

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

Georges, T.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

Glorieux, P.

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992).
[CrossRef] [PubMed]

Grassberger, P.

P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

James, G.

K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

Jauncey, I. M.

Lamouler, P.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

Le Boudec, P.

F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

Le Flohic, M.

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

Mears, R. J.

Monerie, M.

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

Pommeau, Y.

See, for example, P. Bergé, Y. Pommeau, C. Vidal, Order within Chaos (Wiley, New York, 1984).

Procaccia, I.

P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

Reekie, L.

Rowe, C. J.

Roy, R.

K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

Sanchez, F.

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

Stephan, G.

F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

Urquhart, P.

P. Urquhart, Proc. Inst. Electr. Eng. Part J 135, 385 (1988).

Vidal, C.

See, for example, P. Bergé, Y. Pommeau, C. Vidal, Order within Chaos (Wiley, New York, 1984).

Wiesenfeld, K.

K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (1)

E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon, IEEE Photon. Technol. Lett. 5, 73 (1993).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (2)

P. Le Boudec, M. Le Flohic, P. L. François, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef]

P. Le Boudec, F. Sanchez, P. L. François, J.-F. Bayon, E. Delevaque, G. Stephan, Opt. Quantum Electron. 25, 501 (1993).
[CrossRef]

Phys. Rev. A (2)

F. Sanchez, P. Le Boudec, P. L. François, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
[CrossRef]

K. Wiesenfeld, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef] [PubMed]

Proc. Inst. Electr. Eng. Part J (1)

P. Urquhart, Proc. Inst. Electr. Eng. Part J 135, 385 (1988).

Other (1)

See, for example, P. Bergé, Y. Pommeau, C. Vidal, Order within Chaos (Wiley, New York, 1984).

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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the experimental setup. The pump laser is injected through the microscope objective O. The laser oscillation is obtained between M1 and M2.

Fig. 2
Fig. 2

Evolution of the output average intensity of the two modes.

Fig. 3
Fig. 3

Experimental time evolution of the two modes, indicating antiphase dynamics: (a) r = 1.75, (b) r = 2, (c) r = 2.25. Note that, for increasing pumping ratios, the system exhibits periodic and chaotic windows.

Fig. 4
Fig. 4

Dynamical behavior of the laser versus r for different positions of mirror M1.

Fig. 5
Fig. 5

Low-frequency spectra corresponding to the experimental data of Fig. 3.

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