Abstract

Self-starting of passively mode-locked lasers with fast saturable absorption is studied. Our basic assumption is that the lasers will self-start when cw operation is unstable and mode-locked operation is stable. We start with a standard model, closely related to the Ginzburg–Landau equation, that is valid when the change in the time variation of the laser light during one round trip through the laser is small, and we determine the parameter regime in which cw mode operation becomes unstable. Coupled with previous results on the stability of mode-locked operation, these results allow us to determine when a laser will self-start. We apply our theory to figure-eight lasers with external gain.

© 1995 Optical Society of America

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References

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  1. H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
    [CrossRef]
  2. H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
    [CrossRef]
  3. E. P. Ippen, L. Y. Liu, H. A. Haus, Opt. Lett. 15, 183 (1990).
    [CrossRef] [PubMed]
  4. F. Krausz, T. Brabec, Ch. Speilmann, Opt. Lett. 16, 235 (1991).
    [CrossRef] [PubMed]
  5. H. A. Haus, E. P. Ippen, Opt. Lett. 16, 1331 (1991).
    [CrossRef] [PubMed]
  6. C.-J. Chen, “Theoretical study of passively modelocked lasers with fast saturable absorbers,” Ph.D. dissertation (Department of Electrical Engineering, University of Maryland, College Park, Md., 1993).
  7. C.-J. Chen, P. K. A. Wai, C. R. Menyuk, Opt. Lett. 19, 198 (1994).
    [CrossRef] [PubMed]
  8. I. N. Duling, Electron. Lett. 27, 544 (1991); D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, M. W. Phillips, Electron. Lett. 27, 542 (1991); N. Pandit, D. V. Noske, S. M. J. Kelley, J. R. Taylor, Electron. Lett. 28, 455 (1992); M. Nakazawa, E. Yoshida, Y. Kimura, Appl. Phys. Lett. 59, 2073 (1991).
    [CrossRef]
  9. S. Wu, J. Strait, R. L. Fork, T. F. Morse, Opt. Lett. 17, 1444 (1993).
    [CrossRef]
  10. J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schultz, Opt. Lett. 15, 1300 (1990).
    [CrossRef] [PubMed]

1994 (1)

1993 (1)

1992 (1)

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

1991 (3)

F. Krausz, T. Brabec, Ch. Speilmann, Opt. Lett. 16, 235 (1991).
[CrossRef] [PubMed]

H. A. Haus, E. P. Ippen, Opt. Lett. 16, 1331 (1991).
[CrossRef] [PubMed]

I. N. Duling, Electron. Lett. 27, 544 (1991); D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, M. W. Phillips, Electron. Lett. 27, 542 (1991); N. Pandit, D. V. Noske, S. M. J. Kelley, J. R. Taylor, Electron. Lett. 28, 455 (1992); M. Nakazawa, E. Yoshida, Y. Kimura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

1990 (2)

1975 (1)

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Brabec, T.

Chen, C.-J.

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

C.-J. Chen, “Theoretical study of passively modelocked lasers with fast saturable absorbers,” Ph.D. dissertation (Department of Electrical Engineering, University of Maryland, College Park, Md., 1993).

Duling, I. N.

I. N. Duling, Electron. Lett. 27, 544 (1991); D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, M. W. Phillips, Electron. Lett. 27, 542 (1991); N. Pandit, D. V. Noske, S. M. J. Kelley, J. R. Taylor, Electron. Lett. 28, 455 (1992); M. Nakazawa, E. Yoshida, Y. Kimura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

Fork, R. L.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schultz, Opt. Lett. 15, 1300 (1990).
[CrossRef] [PubMed]

Goodberlet, J.

Haus, H. A.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

H. A. Haus, E. P. Ippen, Opt. Lett. 16, 1331 (1991).
[CrossRef] [PubMed]

E. P. Ippen, L. Y. Liu, H. A. Haus, Opt. Lett. 15, 183 (1990).
[CrossRef] [PubMed]

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Ippen, E. P.

Krausz, F.

Liu, L. Y.

Menyuk, C. R.

Morse, T. F.

Schultz, P. A.

Speilmann, Ch.

Strait, J.

Wai, P. K. A.

Wang, J.

Wu, S.

Electron. Lett. (1)

I. N. Duling, Electron. Lett. 27, 544 (1991); D. J. Richardson, R. I. Laming, D. N. Payne, V. Matsas, M. W. Phillips, Electron. Lett. 27, 542 (1991); N. Pandit, D. V. Noske, S. M. J. Kelley, J. R. Taylor, Electron. Lett. 28, 455 (1992); M. Nakazawa, E. Yoshida, Y. Kimura, Appl. Phys. Lett. 59, 2073 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, J. G. Fujimoto, E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[CrossRef]

J. Appl. Phys. (1)

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Opt. Lett. (6)

Other (1)

C.-J. Chen, “Theoretical study of passively modelocked lasers with fast saturable absorbers,” Ph.D. dissertation (Department of Electrical Engineering, University of Maryland, College Park, Md., 1993).

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Figures (2)

Fig. 1
Fig. 1

Eigenvalue λ on the complex plane. The solid curve corresponds to the positive branch of Eq. (7), whereas the dashed curve corresponds to the negative branch. (a) Non-self-starting case. Parameter values are Psat = 1 mW, B = 0.3 ps2, D = 0.045 ps2, Γ = 0.001 W−1, K = 0.008 W−1, T0 = 1000 ps, g0 = 3, and l = 0.05. These parameters correspond to a dye laser with a weak saturable absorber. (b) Self-starting case. Parameter values are Psat = 10 mW, B = 0.3 ps2, D = 0.045 ps2, Γ = 0.1 W−1, K = 0.008 W−1, T0 = 108 ps, g0 = 3, and l = 0.2. These parameters correspond to a figure-eight laser.

Fig. 2
Fig. 2

Self-starting region in the g0l plane. The small-signal power gain is exp(2g0). The parameter values are T0 = 106 ps, Psat = 1 mW, B = 0.3 ps, D = 0.045 ps2, Γ = 0.001 W−1, and K = 0.008 W−1.

Equations (8)

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U z = ( g - l + i θ ) U + ( B + i D ) 2 U t 2 + ( Γ + i K ) U 2 U ,
d g d t = - g - g 0 T 0 - U ( t ) 2 T 0 P sat g ,
g 0 1 + U c 2 / P sat = l - Γ U c 2 ,
P c = θ + K U c 2 .
u ˜ z = δ g U c + ( B + i D ) 2 u ˜ t 2 + ( Γ + i K ) U c 2 ( u ˜ + u ˜ * ) ,
δ g = c T c - t ( u ˜ + u ˜ * ) exp ( - t - t T c ) d t ,
λ ( A 1 A 2 ) = [ ( M 1 M 2 M 2 * M 1 * ) - U c c 1 + i ω T c ( 1 1 1 1 ) ] ( A 1 A 2 ) ,
λ = Γ U c 2 - B ω 2 - U c c 1 + i ω T c ± [ ( U c c 1 + i ω T c - Γ U c 2 ) 2 - D 2 ω 4 + 2 D K U c 2 ω 2 ] 1 / 2 .

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