Abstract

A synchronously pumped modulational-instability ring laser with a nonlinear dispersive fiber can be operated in both the anomalous and the normal dispersion regimes. We obtain simple analytical expressions for the sideband gain in the cavity by using an average pulse formalism. The numerical simulations indicate that stable stationary trains of pulses may be formed in the cavity. This is independent of the sign of the dispersion.

© 1992 Optical Society of America

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References

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  1. A. Hasegawa, W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
    [CrossRef]
  2. G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
    [CrossRef] [PubMed]
  3. S. Wabnitz, Phys. Rev. A 38, 2018 (1988); S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989); G. Cappellini, S. Trillo, Opt. Lett. 16, 895 (1991).
    [CrossRef] [PubMed]
  4. K. J. Blow, D. Wood, J. Opt. Soc. Am. B 5, 629 (1988).
    [CrossRef]
  5. E. P. Ippen, H. A. Haus, L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
    [CrossRef]
  6. M. Nakazawa, K. Susuki, H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Susuki, H. Kubota, H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
    [CrossRef]
  7. A. Hasegawa, Y. Kodama, Opt. Lett. 7, 285 (1982).
    [CrossRef] [PubMed]
  8. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  9. L. A. Lugiato, C. Oldano, Phys. Rev. A 37, 3896 (1988).
    [CrossRef] [PubMed]
  10. S. Trillo, S. Wabnitz, Opt. Lett. 16, 986 (1991).
    [CrossRef] [PubMed]
  11. A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
    [CrossRef]

1991

1990

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
[CrossRef]

1989

E. P. Ippen, H. A. Haus, L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
[CrossRef]

M. Nakazawa, K. Susuki, H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Susuki, H. Kubota, H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

1988

L. A. Lugiato, C. Oldano, Phys. Rev. A 37, 3896 (1988).
[CrossRef] [PubMed]

K. J. Blow, D. Wood, J. Opt. Soc. Am. B 5, 629 (1988).
[CrossRef]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988); S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989); G. Cappellini, S. Trillo, Opt. Lett. 16, 895 (1991).
[CrossRef] [PubMed]

1987

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

1982

1980

A. Hasegawa, W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

Bishop, A.

A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
[CrossRef]

Blow, K. J.

Brinkman, W. F.

A. Hasegawa, W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

Forest, G.

A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
[CrossRef]

Hasegawa, A.

Haus, H. A.

E. P. Ippen, H. A. Haus, L. Y. Liu, J. Opt. Soc. Am. B 6, 1736 (1989).
[CrossRef]

M. Nakazawa, K. Susuki, H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Susuki, H. Kubota, H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

Ippen, E. P.

Kodama, Y.

Liu, L. Y.

Lugiato, L. A.

L. A. Lugiato, C. Oldano, Phys. Rev. A 37, 3896 (1988).
[CrossRef] [PubMed]

McLaughlin, D.

A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Susuki, H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Susuki, H. Kubota, H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

Oldano, C.

L. A. Lugiato, C. Oldano, Phys. Rev. A 37, 3896 (1988).
[CrossRef] [PubMed]

Overman, E.

A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
[CrossRef]

Susuki, K.

M. Nakazawa, K. Susuki, H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Susuki, H. Kubota, H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

Trillo, S.

Wabnitz, S.

S. Trillo, S. Wabnitz, Opt. Lett. 16, 986 (1991).
[CrossRef] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988); S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989); G. Cappellini, S. Trillo, Opt. Lett. 16, 895 (1991).
[CrossRef] [PubMed]

Wood, D.

IEEE J. Quantum Electron.

A. Hasegawa, W. F. Brinkman, IEEE J. Quantum Electron. QE-16, 694 (1980).
[CrossRef]

M. Nakazawa, K. Susuki, H. A. Haus, IEEE J. Quantum Electron. 25, 2036 (1989); M. Nakazawa, K. Susuki, H. Kubota, H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Lett. A

A. Bishop, G. Forest, D. McLaughlin, E. Overman, Phys. Lett. A 144, 17 (1990).
[CrossRef]

Phys. Rev. A

S. Wabnitz, Phys. Rev. A 38, 2018 (1988); S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989); G. Cappellini, S. Trillo, Opt. Lett. 16, 895 (1991).
[CrossRef] [PubMed]

L. A. Lugiato, C. Oldano, Phys. Rev. A 37, 3896 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Normalized MI gain λ(Ω)/θ versus frequency Ω/(θ)1/2 with YP/θ = 2 (curve a), Y = 2.5 (curve b), and Y = 3 (curve c). For η = 1, the curves correspond to Δ ≡ δ/θ = 6 (curve a), Δ = 7.5 (curve b), and Δ = 8 (curve c). For η = −1, one obtains Δ = 2 (curve a), Δ = 2.5 (curve b), and Δ = 4 (curve c).

Fig. 2
Fig. 2

Evolution of an initially weakly modulated continuous wave in the cavity with T = 0.39, P = 4.7, and δ = 29. The time unit is the input modulation period Tm = 2πm.

Fig. 3
Fig. 3

Pulse-train generation represented by a trajectory in the phase plane (η cos ϕ, η sin ϕ).

Equations (7)

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U n + 1 ( ξ = 0 ) = T V + R exp ( - i Δ ϕ ) G [ U n ( ξ = 0 ) ] ,
i U n ξ - η 2 2 U n τ 2 + U n 2 U n = 0.
i U ξ - η 2 2 U τ 2 + U 2 U = ( δ - i θ ) U + i κ V ,
U ( ξ , τ ) = A 0 + A - 1 ( ξ ) exp ( i Ω τ ) + A 1 ( ξ ) exp ( - i Ω τ ) ,
λ ( Ω ) = - θ ± [ 4 ( δ - η Ω 2 / 2 ) P - ( δ - η Ω 2 / 2 ) 2 - 3 P 2 ] 1 / 2 .
Ω m = [ 2 η ( δ - 2 P ) ] 1 / 2 ,
d a - 1 d ξ = i A 0 2 a + 1 * exp ( - i Δ k ξ ) , d a + 1 * d ξ = - i ( A 0 * ) 2 a - 1 exp ( i Δ k ξ ) .

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