Abstract

The polarization dynamics of a unidirectional erbium-doped fiber ring laser has been observed for individual round trips in the cavity. A rich variety of dynamic states, including square-wave pulses and irregular temporal patterns, was observed as operating parameters were changed. A model with coupled delay and differential equations is used to interpret the dynamics.

© 1996 Optical Society of America

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References

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  1. S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992); E. Lacot, F. Stoeckel, M. Chenevier, Phys. Rev. A 49, 3997 (1994).
    [CrossRef] [PubMed]
  2. F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
    [CrossRef] [PubMed]
  3. B. Meziane, F. Sanchez, G. Stephan, P. L. Francois, Opt. Lett. 19, 1970 (1994).
    [CrossRef] [PubMed]
  4. F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
    [CrossRef]
  5. K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); K. Ikeda, K. Kondo, O. Akimoto, Phys. Rev. Lett. 49, 1467 (1982).
    [CrossRef]
  6. W. H. Loh, C. L. Tang, IEEE J. Quantum Electron. 27, 389 (1991); Opt. Commun. 85, 283 (1991).
    [CrossRef]
  7. S. H. Strogatz, I. Stewart, Sci. Am. 269, 102 (1993); S. H. Strogatz, R. E. Mirollo, J. Stat. Phys. 63, 613 (1991); S. Watanabe, S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
    [CrossRef] [PubMed]

1995

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

1994

1993

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef] [PubMed]

S. H. Strogatz, I. Stewart, Sci. Am. 269, 102 (1993); S. H. Strogatz, R. E. Mirollo, J. Stat. Phys. 63, 613 (1991); S. Watanabe, S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
[CrossRef] [PubMed]

1992

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992); E. Lacot, F. Stoeckel, M. Chenevier, Phys. Rev. A 49, 3997 (1994).
[CrossRef] [PubMed]

1991

W. H. Loh, C. L. Tang, IEEE J. Quantum Electron. 27, 389 (1991); Opt. Commun. 85, 283 (1991).
[CrossRef]

1979

K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); K. Ikeda, K. Kondo, O. Akimoto, Phys. Rev. Lett. 49, 1467 (1982).
[CrossRef]

Bielawski, S.

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992); E. Lacot, F. Stoeckel, M. Chenevier, Phys. Rev. A 49, 3997 (1994).
[CrossRef] [PubMed]

Derozier, D.

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992); E. Lacot, F. Stoeckel, M. Chenevier, Phys. Rev. A 49, 3997 (1994).
[CrossRef] [PubMed]

Francois, P. L.

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

B. Meziane, F. Sanchez, G. Stephan, P. L. Francois, Opt. Lett. 19, 1970 (1994).
[CrossRef] [PubMed]

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef] [PubMed]

Glorieux, P.

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992); E. Lacot, F. Stoeckel, M. Chenevier, Phys. Rev. A 49, 3997 (1994).
[CrossRef] [PubMed]

Ikeda, K.

K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); K. Ikeda, K. Kondo, O. Akimoto, Phys. Rev. Lett. 49, 1467 (1982).
[CrossRef]

Le Boudec, P.

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef] [PubMed]

Le Flohic, M.

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

Loh, W. H.

W. H. Loh, C. L. Tang, IEEE J. Quantum Electron. 27, 389 (1991); Opt. Commun. 85, 283 (1991).
[CrossRef]

Meziane, B.

Sanchez, F.

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

B. Meziane, F. Sanchez, G. Stephan, P. L. Francois, Opt. Lett. 19, 1970 (1994).
[CrossRef] [PubMed]

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef] [PubMed]

Stephan, G.

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

B. Meziane, F. Sanchez, G. Stephan, P. L. Francois, Opt. Lett. 19, 1970 (1994).
[CrossRef] [PubMed]

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef] [PubMed]

Stewart, I.

S. H. Strogatz, I. Stewart, Sci. Am. 269, 102 (1993); S. H. Strogatz, R. E. Mirollo, J. Stat. Phys. 63, 613 (1991); S. Watanabe, S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
[CrossRef] [PubMed]

Strogatz, S. H.

S. H. Strogatz, I. Stewart, Sci. Am. 269, 102 (1993); S. H. Strogatz, R. E. Mirollo, J. Stat. Phys. 63, 613 (1991); S. Watanabe, S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
[CrossRef] [PubMed]

Tang, C. L.

W. H. Loh, C. L. Tang, IEEE J. Quantum Electron. 27, 389 (1991); Opt. Commun. 85, 283 (1991).
[CrossRef]

IEEE J. Quantum Electron.

F. Sanchez, M. Le Flohic, G. Stephan, P. Le Boudec, P. L. Francois, IEEE J. Quantum Electron. 31, 481 (1995).
[CrossRef]

W. H. Loh, C. L. Tang, IEEE J. Quantum Electron. 27, 389 (1991); Opt. Commun. 85, 283 (1991).
[CrossRef]

Opt. Commun.

K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); K. Ikeda, K. Kondo, O. Akimoto, Phys. Rev. Lett. 49, 1467 (1982).
[CrossRef]

Opt. Lett.

Phys. Rev. A

S. Bielawski, D. Derozier, P. Glorieux, Phys. Rev. A 46, 2811 (1992); E. Lacot, F. Stoeckel, M. Chenevier, Phys. Rev. A 49, 3997 (1994).
[CrossRef] [PubMed]

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993); P. Le Boudec, M. Le Flohic, P. L. Francois, F. Sanchez, G. Stephan, Opt. Quantum Electron. 25, 359 (1993).
[CrossRef] [PubMed]

Sci. Am.

S. H. Strogatz, I. Stewart, Sci. Am. 269, 102 (1993); S. H. Strogatz, R. E. Mirollo, J. Stat. Phys. 63, 613 (1991); S. Watanabe, S. H. Strogatz, Phys. Rev. Lett. 70, 2391 (1993).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Experimental arrangement: Ar+-ion laser, λp = 514.5 nm; 514.4–1550 nm wavelength division multiplexer optical coupler; Faraday optical isolator (not shown); 97/3 coupling ratio output coupler; neutral density (ND) filter with 10% transmission at 1.55 μm; λ/2 wave plate at 1.55 μm; DET's, fast-response InGaAs/p–i–n photodetectors.

Fig. 2
Fig. 2

Experimentally measured polarization resolved traces of (a) self-pulsing at the cavity round-trip time in the x-polarization direction from an EDFRL with 10% output coupling, (b) irregular trace in the y-polarization direction. The EDFRL was pumped four times threshold. (c), (d) Antiphase square pulses in the x- and y-polarization directions, respectively, from an EDFRL with 3% output coupling. The EDFRL was pumped at 3.3 times threshold.

Fig. 3
Fig. 3

Numerical simulations of time traces showing self-pulsing at the cavity round-trip time in (a) the x-polarization direction, (b) the y-polarization direction, (c), (d) Antiphase square-wave pulses in the x-and y-polarization directions corresponding to those of Figs. 2(c)−2(d). Parameters for (a) and (b): ϕA = 0.027, ϕP = π − 0.175, β = 1.5 × 10−3, and Δλ = 0.125 fm. Parameters for (c) and (d): ϕA = 0.027, ϕP = π − 0.015, β = 10−2, and Δλ = 4.09 fm. The pump rate is 3.2 times threshold.

Tables (1)

Tables Icon

Table 1 Parameter Values Used in the Numerical Simulations

Equations (3)

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S 1 ( t ) = R 1 2 2 ( S 1 ( t τ R ) exp { 2 A 1 [ W ( t ) ] } ( 1 + cos ϕ ) + S 2 ( t τ R ) exp { 2 A 2 [ W ( t ) ] } ( 1 cos ϕ ) 2 [ S 1 ( t τ R ) S 2 ( t τ R ) ] 1 / 2 × exp { A 1 [ W ( t ) ] + A 2 [ W ( t ) ] } × sin { κ [ W ( t ) ] } sin ϕ ) ,
S 2 ( t ) = R 2 2 2 ( S 1 ( t τ R ) exp { 2 A 1 [ W ( t ) ] } ( 1 cos ϕ ) + S 2 ( t τ R ) exp { 2 A 2 [ W ( t ) ] } ( 1 + cos ϕ ) + 2 [ S 1 ( t τ R ) S 2 ( t τ R ) ] 1 / 2 × exp { A 1 [ W ( t ) ] + A 2 [ W ( t ) ] } × sin { κ [ W ( t ) ] } sin ϕ ) ,
d W ( t ) d t = P γ [ W T + W ( t ) ] S 1 ( t τ R ) × ( exp { a 1 [ W ( t ) N 0 L ] } 1 ) S 2 ( t τ R ) ( exp { a 2 [ W ( t ) N 0 L ] } 1 ) ,

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