Abstract

Using a stability analysis based on the Lyapunov method, we study pulse dropout in an actively mode-locked fiber laser. The analysis gives a limit on the maximum pulse duration and the minimum laser power that are needed for stable operation without pulse dropout. The stability of pulse trains was studied analytically and validated numerically for different pulse shapes.

© 2000 Optical Society of America

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References

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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]
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    [CrossRef]
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    [CrossRef]

1997 (1)

1996 (3)

1995 (2)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

F. X. Kärtner, D. Kopf, and U. Keller, J. Opt. Soc. Am. B 12, 486 (1995).
[CrossRef]

1994 (1)

1992 (1)

1985 (1)

1975 (1)

H. A. Haus, IEEE J. Quantum Electron. 11, 323 (1975).
[CrossRef]

Carruthers, T. F.

T. F. Carruthers and I. N. Duling, Opt. Lett. 23, 1927 (1996).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Pulse dropout in harmonically modelocked lasers,” submitted to IEEE Photon. Technol. Lett.

Chen, C. J.

Doran, N. J.

Duling, I. N.

T. F. Carruthers and I. N. Duling, Opt. Lett. 23, 1927 (1996).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Pulse dropout in harmonically modelocked lasers,” submitted to IEEE Photon. Technol. Lett.

Fork, R. L.

Forysiak, W.

Golovchenko, E. A.

Gordon, J. P.

Grigoryan, V. S.

Haus, H. A.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus and A. Mecozzi, Opt. Lett. 17, 1500 (1992).
[CrossRef]

H. A. Haus, IEEE J. Quantum Electron. 11, 323 (1975).
[CrossRef]

Horowitz, M.

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Pulse dropout in harmonically modelocked lasers,” submitted to IEEE Photon. Technol. Lett.

Ippen, E. P.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Kärtner, F. X.

Keller, U.

Knox, F. M.

Kopf, D.

Li, W.

J.-J. E. Slotine and W. Li, Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 53–57.

Martinez, D. E.

Mecozzi, A.

Menyuk, C. R.

V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk, and A. N. Pilipetskii, Opt. Lett. 22, 1609 (1997).
[CrossRef]

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 19, 198 (1994).
[CrossRef]

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Pulse dropout in harmonically modelocked lasers,” submitted to IEEE Photon. Technol. Lett.

Minorsky, N.

N. Minorsky, Nonlinear Oscillation (Van Nostrand, New York, 1987).

Nakazawa, N.

N. Nakazawa, K. Tamura, and E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

Nelson, L. E.

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Pilipetskii, A. N.

Slotine, J.-J. E.

J.-J. E. Slotine and W. Li, Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 53–57.

Smith, N. J.

Tamura, K.

N. Nakazawa, K. Tamura, and E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

Wai, P. K. A.

Yoshida, E.

N. Nakazawa, K. Tamura, and E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

Yu, T.

Electron. Lett. (1)

N. Nakazawa, K. Tamura, and E. Yoshida, Electron. Lett. 32, 461 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

H. A. Haus, K. Tamura, L. E. Nelson, and E. P. Ippen, IEEE J. Quantum Electron. 31, 591 (1995).
[CrossRef]

H. A. Haus, IEEE J. Quantum Electron. 11, 323 (1975).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (5)

Other (3)

M. Horowitz, C. R. Menyuk, T. F. Carruthers, and I. N. Duling, “Pulse dropout in harmonically modelocked lasers,” submitted to IEEE Photon. Technol. Lett.

J.-J. E. Slotine and W. Li, Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, N.J., 1991), pp. 53–57.

N. Minorsky, Nonlinear Oscillation (Van Nostrand, New York, 1987).

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Figures (1)

Fig. 1
Fig. 1

Cavity loss depending on the pulse duration, Fτ, versus the FWHM of pulse duration, τ, obtained from the numerical model (solid curve), from soliton perturbation theory (dashed–dotted curve), and from Eq. (3) for a hyperbolic-secant pulse (dashed curve) and a Gaussian pulse (dotted curve).

Equations (4)

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ΔWΔT=1TRi=1nTi-1W1TRFWW,
dWzdz=2g01+Wz/TPs1-ω2ωg2τ2Wz.
τ<τmax=2Gω2x2Mωm2ωg21/4.
Pmin=sech-12-1/2EDπγnlωm3/28Mωg2x2Gω21/4.

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