Abstract

An extension of the ray-pulse matrix formalism is presented that includes self-phase-modulation, self-focusing, bandwidth limitations, and Gaussian apertures. With this more complete set of matrices it is shown how self-mode-locked lasers can be modeled and how the different pulse-shaping mechanisms interact in order to provide a stable femtosecond output.

© 1992 Optical Society of America

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References

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  1. D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  2. L. Spinelli, B. Couillaud, N. Goldblat, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.
  3. G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, E. P. Ippen, J. G. Fujimoto, Opt. Lett. 16, 1756 (1991).
    [CrossRef] [PubMed]
  4. J. P. Likforman, G. Grillon, M. Joffre, C. Le Blanc, A. Migus, A. Antonetti, Appl. Phys. Lett. 58, 2061 (1991).
    [CrossRef]
  5. Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1880 (1991).
    [CrossRef]
  6. F. Salin, J. Squier, M. Piché, Opt. Lett. 16, 1674 (1991).
    [CrossRef] [PubMed]
  7. W. Rudolph, B. Wilhelmi, Appl. Phys. B 35, 37 (1984).
    [CrossRef]
  8. H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
    [CrossRef]
  9. H. A. Haus, Y. Silberberg, IEEE J. Quantum Electron. QE-22, 325 (1986).
    [CrossRef]
  10. O. E. Martinez, R. L. Fork, J. P. Gordon, J. Opt. Soc. Am. B 2, 753 (1985).
    [CrossRef]
  11. A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
    [CrossRef]
  12. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  13. S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
    [CrossRef]

1991

1990

A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
[CrossRef]

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

1986

H. A. Haus, Y. Silberberg, IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

1985

1984

W. Rudolph, B. Wilhelmi, Appl. Phys. B 35, 37 (1984).
[CrossRef]

Antonetti, A.

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

Brabec, T.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1880 (1991).
[CrossRef]

Couillaud, B.

L. Spinelli, B. Couillaud, N. Goldblat, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Dienes, A.

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

Dijaili, S. P.

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

Fork, R. L.

Fujimoto, J. G.

Gabetta, G.

Goldblat, N.

L. Spinelli, B. Couillaud, N. Goldblat, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

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]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, E. P. Ippen, J. Opt. Soc. Am. B 8, 2068 (1991).
[CrossRef]

H. A. Haus, Y. Silberberg, IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

Huang, D.

Ippen, E. P.

Jacobson, J.

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.

Kostenbauder, A. G.

A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
[CrossRef]

Krausz, F.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1880 (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]

Negus, D. K.

L. Spinelli, B. Couillaud, N. Goldblat, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Piché, M.

Ramaswamy, M.

Rudolph, W.

W. Rudolph, B. Wilhelmi, Appl. Phys. B 35, 37 (1984).
[CrossRef]

Salin, F.

Schmidt, A. J.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1880 (1991).
[CrossRef]

Sibbett, W.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Silberberg, Y.

H. A. Haus, Y. Silberberg, IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

Smith, J. S.

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

Spence, D. E.

Spielmann, Ch.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1880 (1991).
[CrossRef]

Spinelli, L.

L. Spinelli, B. Couillaud, N. Goldblat, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Squier, J.

Wilhelmi, B.

W. Rudolph, B. Wilhelmi, Appl. Phys. B 35, 37 (1984).
[CrossRef]

Wintner, E.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A. J. Schmidt, Opt. Lett. 16, 1880 (1991).
[CrossRef]

Appl. Phys. B

W. Rudolph, B. Wilhelmi, Appl. Phys. B 35, 37 (1984).
[CrossRef]

Appl. Phys. Lett.

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

IEEE J. Quantum Electron.

H. A. Haus, Y. Silberberg, IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

A. G. Kostenbauder, IEEE J. Quantum Electron. 26, 1148 (1990).
[CrossRef]

S. P. Dijaili, A. Dienes, J. S. Smith, IEEE J. Quantum Electron. 26, 1158 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Other

L. Spinelli, B. Couillaud, N. Goldblat, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (2)

Fig. 1
Fig. 1

Schematic of the self-mode-locked Ti:sapphire laser cavity showing the different regions and the effects present in each of them. M1, M4, flat mirrors; M2, M3, 10-cm-radius mirrors; BWL, Lyot filter (bandwidth limitation); Ap, aperture; P1, P2, prisms for dispersion compensation; SPM, self-phase-modulation. Regions II and IV correspond to passages through the rod in different directions.

Fig. 2
Fig. 2

Performance of the laser for a certain cavity configuration as a function of the group-velocity dispersion (GVD) provided by the prisms. We plot the mean output power and the pulse width. Mirror M2 is 53.9 mm from the rod, and mirror M3 is 49.7 mm from the rod. The total (two passages) GVD of the rod is 2200 fs2. Mirror M1 is taken to be the output coupler, with a 5% transmission. The slit was taken with an aperture of 3 mm, and the cavity was symmetric with a round trip of 12 ns.

Equations (15)

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[ x θ t f ] out = M [ x θ t f ] in .
M = [ A B 0 0 C D 0 0 0 0 K I 0 0 J L ] ,
I = 2 π 2 ϕ ω 2 ,
[ A B C D ] = [ 1 0 - j a λ 0 2 π 1 ]
T ( x ) = exp ( - a x 2 / 2 ) .
T ( ω ) = exp ( - α ω 2 / 2 ) = exp [ j ϕ ( ω ) ] ,
I = j 2 π α .
E ( t ) = E 0 exp ( - j k r 2 / 2 q ) exp ( - j k t 2 / 2 p ) ,
1 q = n R - j n λ π σ 2 ,
1 p = 1 k 2 ϕ t 2 - j n λ π τ 2 ,
q out = A q in + B C q in + D ,
p out = K p in + I / λ λ J p in + L .
Re ( C ) = - 4 γ U l σ 4 τ ( 2 π ) 3 / 2 ,
n ( t , r ) = n 0 + γ I ( t , r ) ,
J = 4 γ U l λ σ 2 τ 3 ( 2 π ) 3 / 2 .

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