Abstract

We present an analysis of passively mode-locked lasers in which pulse formation is dominated by the interplay between self-phase modulation and negative dispersion in separate cavity elements. Steady-state pulse parameters and stability issues are discussed. Stability in these solitary systems relies on some passive amplitude modulation, and the ultimate system performance is found to depend sensitively on the magnitude of amplitude modulation relative to that of phase modulation.

© 1991 Optical Society of America

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References

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  1. O. E. Martinez, R. L. Fork, J. P. Gordon, J. Opt. Soc. Am. B 2, 753 (1985).
    [CrossRef]
  2. P. A. Bélanger, “Coupled-cavity mode-locking: a nonlinear model,” J. Opt. Soc. Am. B (to be published).
  3. H. A. Haus, J. G. Fujimoto, E. P. Ippen, “Structures for additive-pulse mode locking,” J. Opt. Soc. Am. B (to be published).
  4. D. E. Spence, P. N. Kean, W. Sibbett, Opt Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  5. N. Sarukura, Y. Ishida, H. Nakano, Opt. Lett. 16, 153 (1991).
    [PubMed]
  6. M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, A. J. Schmidt, Opt. Lett. 16, 502 (1991).
    [CrossRef] [PubMed]
  7. Ch. Spielmann, R. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Appl. Phys. Lett. 58, 2470 (1991).
    [CrossRef]
  8. L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP-7.
  9. Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1180 (1991).
    [CrossRef] [PubMed]
  10. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).
  11. J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
    [CrossRef]
  12. F. Krausz, T. Brabec, Ch. Spielmann, Opt. Lett. 16, 235 (1991).
    [CrossRef] [PubMed]

1991 (7)

D. E. Spence, P. N. Kean, W. Sibbett, Opt Lett. 16, 42 (1991).
[CrossRef] [PubMed]

Ch. Spielmann, R. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Appl. Phys. Lett. 58, 2470 (1991).
[CrossRef]

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

N. Sarukura, Y. Ishida, H. Nakano, Opt. Lett. 16, 153 (1991).
[PubMed]

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

M. Hofer, M. E. Fermann, F. Haberl, M. H. Ober, A. J. Schmidt, Opt. Lett. 16, 502 (1991).
[CrossRef] [PubMed]

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1180 (1991).
[CrossRef] [PubMed]

1985 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Antonetti, A.

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

Bélanger, P. A.

P. A. Bélanger, “Coupled-cavity mode-locking: a nonlinear model,” J. Opt. Soc. Am. B (to be published).

Brabec, T.

Couillaud, B.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP-7.

Fermann, M. E.

Fork, R. L.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, “Structures for additive-pulse mode locking,” J. Opt. Soc. Am. B (to be published).

Goldblatt, N.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP-7.

Gordon, J. P.

Grillon, G.

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

Haberl, F.

Haus, H. A.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, “Structures for additive-pulse mode locking,” J. Opt. Soc. Am. B (to be published).

Hofer, M.

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, “Structures for additive-pulse mode locking,” J. Opt. Soc. Am. B (to be published).

Ishida, Y.

Joffre, M.

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

Kean, P. N.

D. E. Spence, P. N. Kean, W. Sibbett, Opt Lett. 16, 42 (1991).
[CrossRef] [PubMed]

Krausz, F.

Krausz, R.

Ch. Spielmann, R. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Appl. Phys. Lett. 58, 2470 (1991).
[CrossRef]

Le Blanc, C.

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

Likforman, J. P.

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

Martinez, O. E.

Migus, A.

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

Nakano, H.

Negus, D. K.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP-7.

Ober, M. H.

Sarukura, N.

Schmidt, A. J.

Sibbett, W.

D. E. Spence, P. N. Kean, W. Sibbett, Opt Lett. 16, 42 (1991).
[CrossRef] [PubMed]

Spence, D. E.

D. E. Spence, P. N. Kean, W. Sibbett, Opt Lett. 16, 42 (1991).
[CrossRef] [PubMed]

Spielmann, Ch.

Spinelli, L.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP-7.

Wintner, E.

Ch. Spielmann, R. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Appl. Phys. Lett. 58, 2470 (1991).
[CrossRef]

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1180 (1991).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

Ch. Spielmann, R. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Appl. Phys. Lett. 58, 2470 (1991).
[CrossRef]

J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt Lett. (1)

D. E. Spence, P. N. Kean, W. Sibbett, Opt Lett. 16, 42 (1991).
[CrossRef] [PubMed]

Opt. Lett. (4)

Other (4)

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP-7.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

P. A. Bélanger, “Coupled-cavity mode-locking: a nonlinear model,” J. Opt. Soc. Am. B (to be published).

H. A. Haus, J. G. Fujimoto, E. P. Ippen, “Structures for additive-pulse mode locking,” J. Opt. Soc. Am. B (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the solitary laser.

Fig. 2
Fig. 2

Soliton and solitary pulse widths versus group-delay dispersion D for ϕ = 12.5 × 10−7 W−1, κ = 2 × 10−7 W−1, and different pulse energies W. Curves 1, 2, and 3 illustrate τ§, τ(z1), and τ(z4), respectively, for W = 138 nJ. Curves 4, 5, and 6 illustrate τs, τ(z1), and τ(z4), respectively, for W = 34.5 nJ.

Fig. 3
Fig. 3

Pulse width-bandwidth products τΔν of solitary pulses and with the chirp removed (τΔν)bl for ϕ = 12.5 × 10−7 W−1, W = 34.5 nJ, and different amplitude nonlinearities κ. Curves 1 and 2 denote τ; curves 3 and 4 denote (τΔν)bl; curves 5 and 6 denote τΔν for κ = 2 × 10−7 W−1 and κ = 4 × 10−7 W−1, respectively.

Fig. 4
Fig. 4

Boundaries of regimes of stable mode locking on the τ(D, ϕW = const.) curves for different amplitude and phase nonlinearities κ and ϕ. Curve 1, ϕW = 172.5 fs; curve 2, ϕW = 345 fs. The values of κ in units of 10−7 W−1 and the corresponding ratios κ/ϕ are as follows: a, κ = 2, κ/ϕ = 0.16; b, 1, 0.08; c, 0.5, 0.04; d, 0.25, 0.02; e, 0.125, 0.01; f, 2, 0.16; g, 1, 0.08; h, 2, 0.08; i, 0.5, 0.04; j, 1, 0.04; k, 2, 0.04; 1, 0.5, 0.02; m, 1, 0.02.

Equations (4)

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v n + 1 ( t ) = T ^ v n ( t ) ,
T ^ = e D ^ e A ^ / 2 e N ^ e A ^ / 2 ,
r = L r L s = 1 2 π ( ϕ W ) 2 D .
τ = 3.53 D ϕ W + α ϕ W ,

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