Abstract

It is demonstrated that with rigorous inclusion of diffraction on an intracavity hard aperture the values of the nonlinear differential loss coefficient Γ (which characterizes the efficiency of Kerr-lens mode locking) are several times higher than in the commonly used simplified approach in which diffraction effects are neglected. Diffraction changes modal properties and causes a faster decrease of mode losses with increasing power than predicted by the traditional approach. With this correction, the discrepancy between the Kerr-lens mode-locking theory and the theoretical estimates of the self-starting condition is substantially decreased.

© 1995 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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. O. Haderka, J. Opt. Soc. Am. A 12, 340 (1995).
    [CrossRef]
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    [CrossRef]
  9. F. Krausz, T. Brabec, Ch. Spielmann, Opt. Lett. 16, 235 (1991).
    [CrossRef] [PubMed]
  10. H. A. Haus, E. P. Ippen, Opt. Lett. 16, 1331 (1991).
    [CrossRef] [PubMed]
  11. G. Cerullo, S. DeSilvestri, V. Magni, L. Pallaro, Opt. Lett. 19, 807 (1994).
    [CrossRef] [PubMed]
  12. G. Cerullo, S. DeSilvestri, V. Magni, Opt. Lett. 19, 1040 (1994).
    [CrossRef] [PubMed]
  13. V. Magni, G. Cerullo, S. DeSilvestri, Opt. Lett. 96, 348 (1993).
  14. J. L. A. Chilla, O. E. Martínez, J. Opt. Soc. Am. B 10, 638 (1993).
    [CrossRef]
  15. O. Haderka, “Diffraction theory investigation of nonlinear Z resonators for Kerr-lens mode locking,” submitted toJ. Opt. Soc. Am. B.

1995

1994

1993

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Commun. 101, 365 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Lett. 96, 348 (1993).

J. L. A. Chilla, O. E. Martínez, J. Opt. Soc. Am. B 10, 638 (1993).
[CrossRef]

1992

T. Brabec, Ch. Spielmann, P. F. Curley, F. Krausz, Opt. Lett. 17, 1292 (1992).
[CrossRef] [PubMed]

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

1991

Brabec, T.

Cerullo, G.

G. Cerullo, S. DeSilvestri, V. Magni, L. Pallaro, Opt. Lett. 19, 807 (1994).
[CrossRef] [PubMed]

G. Cerullo, S. DeSilvestri, V. Magni, Opt. Lett. 19, 1040 (1994).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Commun. 101, 365 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Lett. 96, 348 (1993).

Chilla, J. L. A.

Curley, P. F.

DeSilvestri, S.

G. Cerullo, S. DeSilvestri, V. Magni, Opt. Lett. 19, 1040 (1994).
[CrossRef] [PubMed]

G. Cerullo, S. DeSilvestri, V. Magni, L. Pallaro, Opt. Lett. 19, 807 (1994).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Lett. 96, 348 (1993).

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Commun. 101, 365 (1993).
[CrossRef]

Fujimoto, J. G.

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

Haderka, O.

O. Haderka, J. Opt. Soc. Am. A 12, 340 (1995).
[CrossRef]

O. Haderka, “Diffraction theory investigation of nonlinear Z resonators for Kerr-lens mode locking,” submitted toJ. Opt. Soc. Am. B.

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]

Herrmann, J.

Ippen, E. P.

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]

Kean, P. N.

Krausz, F.

Magni, V.

G. Cerullo, S. DeSilvestri, V. Magni, L. Pallaro, Opt. Lett. 19, 807 (1994).
[CrossRef] [PubMed]

G. Cerullo, S. DeSilvestri, V. Magni, Opt. Lett. 19, 1040 (1994).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Lett. 96, 348 (1993).

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Commun. 101, 365 (1993).
[CrossRef]

Martínez, O. E.

Pallaro, L.

Piché, M.

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

Sibbett, W.

Spence, D. E.

Spielmann, Ch.

IEEE J. Quantum Electron.

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

J. Herrmann, Opt. Commun. 98, 111 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. DeSilvestri, Opt. Commun. 101, 365 (1993).
[CrossRef]

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

Opt. Lett.

Other

O. Haderka, “Diffraction theory investigation of nonlinear Z resonators for Kerr-lens mode locking,” submitted toJ. Opt. Soc. Am. B.

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Figures (4)

Fig. 1
Fig. 1

Map of Γ for an asymmetric cavity (b/c = 2/3) without gain guiding computed by the diffraction method with the aperture radius set to 0.5 of the respective Gaussian 00-mode beam waist. The aperture is placed at mirror M1 (Fig. 2). The regions with negative Γ are shaded (see the inset legend; units are inverse watts). Data for Ti:sapphire crystal are used in the computations: L = 10 mm, n0 = 1.76, emission cross section 4 × 10−19 cm2, critical power for self-focusing 2.6 MW, upper-level lifetime 3.15 μs, saturation intensity 300 kW cm−2, and average intracavity power 5 W. Other parameters: b = 80 cm, R = 10 cm.

Fig. 2
Fig. 2

Linearized scheme of the Z-shaped resonator. Focusing mirrors M2 and M3 of radius of curvature R are represented by lenses.

Fig. 3
Fig. 3

Plot of −Γ computed by the diffraction-theory approach (symbols on solid curves, DT) and by the geometric approach [Eq. (1)] (plain solid curves, SA) for the selected value of Δd2 where −Γ reaches its maximum (see the dotted line in Fig. 1). Filled circles and squares and crosses are obtained without gain guiding (DT), open circles with gain guiding by the pump beam with saddle waist wp0 = 150 μm (DTGG). The dashed curves were obtained for soft-aperture KLM alone (GG); wp0 = 150 μm, −Γ × 102 is plotted. Other parameters as in Fig. 1.

Fig. 4
Fig. 4

Comparison of power-dependent losses of 00 mode computed by the diffraction method (without gain guiding, solid curve) and in the simplified approach [Eq. (1), dashed curve] for a selected cavity configuration (g = −0.01993, Δd2 = −3.83 mm, a = 0.6w00). Other parameters as in Fig. 1.

Equations (1)

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Γ = 4 a 2 w 2 exp ( - 2 a 2 w 2 ) Ψ .

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