Abstract

The nonlinear dynamics of a four-mirror Kerr-lens mode-locked laser is investigated. It is shown that the mode-locking regime contains the windows of nonregular behavior. Theoretical predictions are confirmed by numerical experiments based on the fluctuation model.

© 1997 Optical Society of America

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References

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  1. V. Magni, G. Cerullo, S. De Silvestri, and A. Monguzzi, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lensmode locking,” J. Opt. Soc. Am. B 12, 476 (1995).
    [CrossRef]
  2. J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radiallyvarying gain,” J. Opt. Soc. Am. B 11, 498 (1994).
    [CrossRef]
  3. M. Ramaswamy and J. G. Fujimoto, “Compact dispersion-compensating geometry for Kerr-lens mode-lockedfemtosecond lasers,” Opt. Lett. 19, 1756 (1994).
    [CrossRef]
  4. G. Cerullo, S. De Silvestri, V. Magni, and L. Pallaro, “Resonators for Kerr-lens mode-locked femtosecond Ti:sapphire lasers,” Opt. Lett. 19, 807 (1994).
    [CrossRef] [PubMed]
  5. V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
    [CrossRef]
  6. V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “General approach to mode-locking mechanism analysis for cw solid-statelasers with nonlinear Fabry–Perot interferometer,” Opt. Quantum Electron. 25, 770 (1995).
    [CrossRef]
  7. G. Sucha, S. R. Bolton, S. Weiss, and D. S. Chemla, “Period doubling and quasi-periodicity in additive-pulse mode-lockedlasers,” Opt. Lett. 20, 1794 (1996).
    [CrossRef]

1996 (1)

1995 (3)

1994 (3)

Bolton, S. R.

Cerullo, G.

Chemla, D. S.

De Silvestri, S.

Fujimoto, J. G.

Herrmann, J.

Kalashnikov, V. L.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “General approach to mode-locking mechanism analysis for cw solid-statelasers with nonlinear Fabry–Perot interferometer,” Opt. Quantum Electron. 25, 770 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

Kalosha, V. P.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “General approach to mode-locking mechanism analysis for cw solid-statelasers with nonlinear Fabry–Perot interferometer,” Opt. Quantum Electron. 25, 770 (1995).
[CrossRef]

Magni, V.

Mikhailov, V. P.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “General approach to mode-locking mechanism analysis for cw solid-statelasers with nonlinear Fabry–Perot interferometer,” Opt. Quantum Electron. 25, 770 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

Monguzzi, A.

Pallaro, L.

Poloyko, I. G.

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “General approach to mode-locking mechanism analysis for cw solid-statelasers with nonlinear Fabry–Perot interferometer,” Opt. Quantum Electron. 25, 770 (1995).
[CrossRef]

V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror-cavity solid-state lasers by Kerrself-focusing,” J. Opt. Soc. Am. B 12, 462 (1995).
[CrossRef]

Ramaswamy, M.

Sucha, G.

Weiss, S.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the laser under consideration: M1M4, mirrors; A, aperture; z0, nonlinear crystal with length z0.

Fig. 2
Fig. 2

(a) Bifurcation diagram computed for the pulse peak intensity versus pump intensity. The vertical scale for the right-hand part of the plot is 2.5 times greater than for the left-hand part. The lower curve is a Lyapunov exponent. f1=f2=5 cm, L1=60 cm, L2=114 cm, L3=10.45 cm, b1=5 cm, d=1 cm is the distance from the end mirror, z0=0.75 cm, D=1 mm, σ=10-5, Tcav=6 ns, and gm=1.5. (b) Poincaré sections in (gain–intensity) coordinate plane Ip=0.007 (case A), Ip=0.0072 (case B), Ip=0.0078 (case C), and Ip=0.008 (case D).

Fig. 3
Fig. 3

Bifurcation diagram computed for the pulse peak intensity versus the position of active medium b1. The vertical scale for the right-hand part of the plot is 40 times greater than for the left-hand part. Ip=0.008. Other parameters are as in Fig. 1.

Fig. 4
Fig. 4

Ultrashort-pulse peak intensity versus transit number (fluctuation model): a, Ip=0.0013; b, Ip=0.003; c, Ip=0.005; d, Ip =0.012; b1=5.537 cm. Other parameters are as in Fig. 1.

Fig. 5
Fig. 5

a, Pulse autocorrelation function averaged over 3500 cavity transits for the cases of Figs. 4c (curve 1), 4b (curve 2), and 4d (curve 3). Spectral function P(ω) of the dependence of the pulse peak intensity on cavity transit for the cases of b, Fig. 4b and c, Fig. 4d.

Fig. 6
Fig. 6

Bifurcation diagram computed for the pulse peak intensity versus pump intensity. The pump beam size in the active rod is a, wp=; b, 60 µm; c, 26 µm; and d, 20 µm. f1=f2=5 cm, L1=54 cm, L2=109 cm, L3=11.01 cm, and b1=5.26 cm. Other parameters are as in Fig. 1.

Equations (7)

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z+i 12k0Δ+iβ1|E|2E(r, z)=0,
ρ=[(C1z0+C2)2+C3]/C1,
R=ρ/(C1z0+C2),
Iζ=gI,
dgdi=(gm-g)Ip-σgI,
P(ω)=1Nj=1NIj2πiωj2.
ρ=ρ0[1+g(ρ0/ρp)2].

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