Abstract

We present what is to our knowledge the first full spatial plus temporal model of a self-mode-locked titanium-doped sapphire laser. The self-consistent evolution of the pulse toward steady state imposes strong space–time focusing in the crystal, where both the space and time foci are located. This combined focusing significantly improves the discrimination properties of the nonlinear resonator for shorter pulses and reduces the transient stage of pulse formation. Our theoretical results are in very good agreement with experiment.

© 1995 Optical Society of America

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References

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1995 (2)

1994 (3)

1993 (2)

1992 (2)

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

G. W. Pearson, C. Radzewicz, J. S. Krasinski, Opt. Commun. 94, 221 (1992).
[CrossRef]

1991 (4)

1984 (1)

’tHooft, G. W.

Brabec, T.

Christov, I. P.

Cunningham, J. E.

Dunlop, A. M.

Feugnet, G.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feugnet, in Digest of Conference on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), p. 120.

Firth, W. J.

Fork, R. L.

Fujimoto, J. G.

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

Goldblatt, N.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feugnet, in Digest of Conference on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), p. 120.

Gordon, J. P.

Haus, H. A.

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

Heatley, D. R.

Huang, C. P.

Ippen, E. P.

E. P. Ippen, Appl. Phys. B 58, 159 (1994).
[CrossRef]

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

Kapteyn, H. C.

Kean, P. N.

Keller, U.

Knox, W. H.

Krasinski, J. S.

G. W. Pearson, C. Radzewicz, J. S. Krasinski, Opt. Commun. 94, 221 (1992).
[CrossRef]

Krausz, F.

Lenzner, M.

Martinez, O. E.

Murnane, M. M.

Negus, D. K.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feugnet, in Digest of Conference on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), p. 120.

Pearson, G. W.

G. W. Pearson, C. Radzewicz, J. S. Krasinski, Opt. Commun. 94, 221 (1992).
[CrossRef]

Piché, M.

Radzewicz, C.

G. W. Pearson, C. Radzewicz, J. S. Krasinski, Opt. Commun. 94, 221 (1992).
[CrossRef]

Salin, F.

Sibbett, W.

Sipocs, R.

Spence, D. E.

Spielmann, C.

Spinelli, L.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feugnet, in Digest of Conference on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), p. 120.

Stingl, A.

Taft, G.

Zhou, J.

Zhou, J. P.

Appl. Phys. B (1)

E. P. Ippen, Appl. Phys. B 58, 159 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

Opt. Commun. (2)

G. W. Pearson, C. Radzewicz, J. S. Krasinski, Opt. Commun. 94, 221 (1992).
[CrossRef]

M. Piché, Opt. Commun. 86, 156 (1991).
[CrossRef]

Opt. Lett. (10)

Other (1)

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feugnet, in Digest of Conference on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), p. 120.

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Figures (4)

Fig. 1
Fig. 1

Schematic of the resonator. M1, M4, flat mirrors; M2, M3, curved mirrors with a focal length f = 5 cm; C, laser crystal; D, dispersion control. The distances are l1 = 58.8 cm, l2 = 4.96 cm, l3 = 0.23 cm, l4 = 4.93 cm, and l5 = 101 cm.

Fig. 2
Fig. 2

(a) Stability and mode size of the linear resonator shown in Fig. 1 as a function of the offset of mirror M3 with respect to the confocal position for the case of a Gaussian spatial gain with radius 14 μm. (b) Transmission of the nonlinear resonator for an optimally chirped 20-fs pulse (solid curve) and for an unchirped pulse (dashed curve). The horizontal axis represents the peak intensity in the crystal.

Fig. 3
Fig. 3

Evolution of (a) the spectrum and (b) the pulse duration at the output coupler (M1) versus the number of round trips in the SML laser. The single-pass gain is 1.06.

Fig. 4
Fig. 4

(a) Relative position of the space and time foci in the crystal in steady state, (b) peak intensity versus the distance into the crystal.

Equations (2)

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E i + 1 ( r , t ) = R 0.5 T l T r E i ( r , t ) ,
T r = F D F f C F f F ,

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