Abstract

Nonstationary pulse regimes associated with self-modulation of a Kerr-lens mode-locked Ti:sapphire laser have been studied experimentally and theoretically. Such laser regimes occur at an intracavity group delay dispersion that is smaller than or larger than what is required for stable mode locking and exhibit modulation in pulse amplitude and spectra at frequencies of several hundred kilohertz. Stabilization of such modulations, leading to an increase in the pulse peak power by a factor of 10, were accomplished by weak modulation of the pump laser with the self-modulation frequency. The main experimental observations can be explained with a round-trip model of the femtosecond laser, taking into account gain saturation, Kerr lensing, and second- and third-order dispersion.

© 2000 Optical Society of America

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  1. E. W. Castner, J. J. Korpershoek, and D. A. Wiersma, “Experimental and theoretical analysis of linear femtosecond dye lasers,” Opt. Commun. 78, 90–99 (1990).
    [CrossRef]
  2. T. Tsang, “Observation of high-order solitons from a mode-locked Ti:sapphire laser,” Opt. Lett. 18, 293–295 (1993).
    [CrossRef] [PubMed]
  3. F. W. Wise, I. A. Walmsley, and C. L. Tang, “Simultaneous formation of solitons and dispersive waves in a femtosecond dye ring laser,” Opt. Lett. 13, 129–131 (1988).
    [CrossRef]
  4. V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
    [CrossRef] [PubMed]
  5. Q. R. Xing, W. L. Zhang, and K. M. Yoo, “Self-Q-switched self-modelocked Ti:sapphire laser,” Opt. Commun. 119, 113–116 (1995).
    [CrossRef]
  6. A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
    [CrossRef]
  7. D. Cote and H. M. van Driel, “Period doubling of a femtosecond Ti:sapphire laser by total mode locking,” Opt. Lett. 23, 715–717 (1998).
    [CrossRef]
  8. S. R. Bolton, R. A. Jenks, C. N. Elkinton, and G. Sucha, “Pulse-resolved measurements of subharmonic oscillations in a Kerr-lens mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 16, 339–344 (1999).
    [CrossRef]
  9. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996).
  10. H. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
    [CrossRef]
  11. D. Kühlke, W. Rudolph, and B. Wilhelmi, “Calculation of the colliding pulse mode-locking in CW dye ring lasers,” IEEE J. Quantum Electron. QE-19, 526–533 (1983).
    [CrossRef]
  12. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
    [CrossRef]
  13. T. Brabec, Ch. Spielmann, P. F. Curley, and F. Krausz, “Kerr lens mode locking,” Opt. Lett. 17, 1292–1294 (1992).
    [CrossRef] [PubMed]
  14. J. L. A. Chilla and O. E. Martinez, “Spatial-temporal analysis of the self-mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 10, 638–643 (1993).
    [CrossRef]
  15. V. Magni, G. Cerullo, S. de Silvestri, and A. Monguzzi, “Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking,” J. Opt. Soc. Am. B 12, 476–485 (1995).
    [CrossRef]
  16. V. P. Kalosha, M. Müller, J. Herrmann, and G. Gatz, “Spatiotemporal model of femtosecond pulse generation in Kerr-lens mode-locked solid-state lasers,” J. Opt. Soc. Am. B 15, 535–550 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode locking with saturable absorbers: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
    [CrossRef]
  20. J. Herrmann, “Theory of Kerr-lens mode locking: role of self-focusing and radially varying gain,” J. Opt. Soc. Am. B 11, 498–512 (1994).
    [CrossRef]
  21. A. M. Sergeev, E. V. Vanin, and F. W. Wise, “Stability of passively modelocked lasers with fast saturable absorbers,” Opt. Commun. 140, 61–64 (1997).
    [CrossRef]
  22. V. L. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “New principle of formation of ultrashort pulses in solid-state lasers with self-phase-modulation and gain saturation,” Quantum Electron. 26, 236–242 (1996).
    [CrossRef]

1999 (1)

1998 (2)

1997 (3)

V. L. Kalashnikov, I. G. Poloyko, V. P. Mikhailov, and D. von der Linde, “Regular, quasi-periodic, and chaotic behavior in continuous-wave solid-state Kerr-lens mode-locked lasers,” J. Opt. Soc. Am. B 14, 2691–2695 (1997).
[CrossRef]

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

A. M. Sergeev, E. V. Vanin, and F. W. Wise, “Stability of passively modelocked lasers with fast saturable absorbers,” Opt. Commun. 140, 61–64 (1997).
[CrossRef]

1996 (2)

V. L. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “New principle of formation of ultrashort pulses in solid-state lasers with self-phase-modulation and gain saturation,” Quantum Electron. 26, 236–242 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode locking with saturable absorbers: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[CrossRef]

1995 (3)

1994 (1)

1993 (2)

1992 (2)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

T. Brabec, Ch. Spielmann, P. F. Curley, and F. Krausz, “Kerr lens mode locking,” Opt. Lett. 17, 1292–1294 (1992).
[CrossRef] [PubMed]

1990 (1)

E. W. Castner, J. J. Korpershoek, and D. A. Wiersma, “Experimental and theoretical analysis of linear femtosecond dye lasers,” Opt. Commun. 78, 90–99 (1990).
[CrossRef]

1989 (1)

V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
[CrossRef] [PubMed]

1988 (1)

1983 (1)

D. Kühlke, W. Rudolph, and B. Wilhelmi, “Calculation of the colliding pulse mode-locking in CW dye ring lasers,” IEEE J. Quantum Electron. QE-19, 526–533 (1983).
[CrossRef]

1975 (1)

H. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
[CrossRef]

Baltuska, A.

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

Bolton, S. R.

Brabec, T.

Castner, E. W.

E. W. Castner, J. J. Korpershoek, and D. A. Wiersma, “Experimental and theoretical analysis of linear femtosecond dye lasers,” Opt. Commun. 78, 90–99 (1990).
[CrossRef]

Cerullo, G.

Chilla, J. L. A.

Cote, D.

Curley, P. F.

de Silvestri, S.

Demchuk, M. I.

Eichler, H. J.

Elkinton, C. N.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

Gatz, G.

Haus, H.

H. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
[CrossRef]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

Herrmann, J.

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

Jenks, R. A.

Jung, I. D.

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode locking with saturable absorbers: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[CrossRef]

Kalashnikov, V. L.

Kalosha, V. P.

Kärtner, F. X.

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode locking with saturable absorbers: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[CrossRef]

Keller, U.

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode locking with saturable absorbers: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[CrossRef]

Koltchanov, I. G.

Korpershoek, J. J.

E. W. Castner, J. J. Korpershoek, and D. A. Wiersma, “Experimental and theoretical analysis of linear femtosecond dye lasers,” Opt. Commun. 78, 90–99 (1990).
[CrossRef]

Krausz, F.

Kühlke, D.

D. Kühlke, W. Rudolph, and B. Wilhelmi, “Calculation of the colliding pulse mode-locking in CW dye ring lasers,” IEEE J. Quantum Electron. QE-19, 526–533 (1983).
[CrossRef]

Magni, V.

Martinez, O. E.

Mikhailov, V. P.

Monguzzi, A.

Müller, M.

Petrov, V.

V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
[CrossRef] [PubMed]

Poloyko, I. G.

Pshenichnikov, M. S.

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

Rudolph, W.

V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
[CrossRef] [PubMed]

D. Kühlke, W. Rudolph, and B. Wilhelmi, “Calculation of the colliding pulse mode-locking in CW dye ring lasers,” IEEE J. Quantum Electron. QE-19, 526–533 (1983).
[CrossRef]

Sergeev, A. M.

A. M. Sergeev, E. V. Vanin, and F. W. Wise, “Stability of passively modelocked lasers with fast saturable absorbers,” Opt. Commun. 140, 61–64 (1997).
[CrossRef]

Spielmann, Ch.

Stamm, U.

V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
[CrossRef] [PubMed]

Sucha, G.

Szipöcs, R.

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

Tang, C. L.

Tsang, T.

van Driel, H. M.

Vanin, E. V.

A. M. Sergeev, E. V. Vanin, and F. W. Wise, “Stability of passively modelocked lasers with fast saturable absorbers,” Opt. Commun. 140, 61–64 (1997).
[CrossRef]

von der Linde, D.

Walmsley, I. A.

Wei, Z.

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

Wiersma, D. A.

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

E. W. Castner, J. J. Korpershoek, and D. A. Wiersma, “Experimental and theoretical analysis of linear femtosecond dye lasers,” Opt. Commun. 78, 90–99 (1990).
[CrossRef]

Wilhelmi, B.

V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
[CrossRef] [PubMed]

D. Kühlke, W. Rudolph, and B. Wilhelmi, “Calculation of the colliding pulse mode-locking in CW dye ring lasers,” IEEE J. Quantum Electron. QE-19, 526–533 (1983).
[CrossRef]

Wise, F. W.

A. M. Sergeev, E. V. Vanin, and F. W. Wise, “Stability of passively modelocked lasers with fast saturable absorbers,” Opt. Commun. 140, 61–64 (1997).
[CrossRef]

F. W. Wise, I. A. Walmsley, and C. L. Tang, “Simultaneous formation of solitons and dispersive waves in a femtosecond dye ring laser,” Opt. Lett. 13, 129–131 (1988).
[CrossRef]

Xing, Q. R.

Q. R. Xing, W. L. Zhang, and K. M. Yoo, “Self-Q-switched self-modelocked Ti:sapphire laser,” Opt. Commun. 119, 113–116 (1995).
[CrossRef]

Yoo, K. M.

Q. R. Xing, W. L. Zhang, and K. M. Yoo, “Self-Q-switched self-modelocked Ti:sapphire laser,” Opt. Commun. 119, 113–116 (1995).
[CrossRef]

Zhang, W. L.

Q. R. Xing, W. L. Zhang, and K. M. Yoo, “Self-Q-switched self-modelocked Ti:sapphire laser,” Opt. Commun. 119, 113–116 (1995).
[CrossRef]

Appl. Phys. B (1)

A. Baltuska, Z. Wei, M. S. Pshenichnikov, D. A. Wiersma, and R. Szipöcs, “All solid-state cavity dumped sub-5-fs laser,” Appl. Phys. B 65, 175–188 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Kühlke, W. Rudolph, and B. Wilhelmi, “Calculation of the colliding pulse mode-locking in CW dye ring lasers,” IEEE J. Quantum Electron. QE-19, 526–533 (1983).
[CrossRef]

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode locking with saturable absorbers: theory and experiments,” IEEE J. Sel. Top. Quantum Electron. 2, 540–556 (1996).
[CrossRef]

J. Appl. Phys. (1)

H. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
[CrossRef]

J. Opt. Soc. Am. B (7)

Opt. Commun. (3)

A. M. Sergeev, E. V. Vanin, and F. W. Wise, “Stability of passively modelocked lasers with fast saturable absorbers,” Opt. Commun. 140, 61–64 (1997).
[CrossRef]

E. W. Castner, J. J. Korpershoek, and D. A. Wiersma, “Experimental and theoretical analysis of linear femtosecond dye lasers,” Opt. Commun. 78, 90–99 (1990).
[CrossRef]

Q. R. Xing, W. L. Zhang, and K. M. Yoo, “Self-Q-switched self-modelocked Ti:sapphire laser,” Opt. Commun. 119, 113–116 (1995).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

V. Petrov, W. Rudolph, U. Stamm, and B. Wilhelmi, “Limits of ultrashort pulse generation in cw modelocked dye lasers,” Phys. Rev. A 40, 1474–1483 (1989).
[CrossRef] [PubMed]

Quantum Electron. (1)

V. L. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, “New principle of formation of ultrashort pulses in solid-state lasers with self-phase-modulation and gain saturation,” Quantum Electron. 26, 236–242 (1996).
[CrossRef]

Other (1)

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1996).

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Figures (9)

Fig. 1
Fig. 1

(a) Pulse train from a mode-locked Ti:sapphire laser in self-Q-switched regime A (upper curve) and the acousto-optic (A-O) driver signal used when the pump laser was modulated. On the time scale shown here there was no observable difference between the Ti:sapphire laser pulse train with the modulated and the unmodulated pump laser. (b) Laser spectrum observed during regime A. The fluctuations in the pulse train resulted from an inadequate sampling rate of the digital oscilloscope (512 sampling points during the 17-µs time window).

Fig. 2
Fig. 2

Temporal position of the various spectral components relative to the peak of the Q-switched envelope (bottom curve).

Fig. 3
Fig. 3

(a) Pulse train and (b) spectrum observed in regime B.

Fig. 4
Fig. 4

Temporal behavior of spectral components at 810 and 827 nm in regime B and the mode-locked pulse train (bottom curve).

Fig. 5
Fig. 5

Steady-state pulse duration (a) and chirp (b) versus the normalized SPM coefficient β0 for a normalized GDD coefficient of d=0 (curve 1) and d=-10 (curve 2). The other laser parameters are σ0=1,l=0.05, αm=0.5, U=4×10-4, L=0.3 cm, λ=800 nm, and Tcav=10 ns. The hatched regions describe various nonstationary pulse regimes (see text).

Fig. 6
Fig. 6

Steady-state pulse duration (a) and chirp (b) versus the normalized GDD coefficient d for β0=1 and σ0=10 (curve 1), σ0=1 (curve 2), σ0=0.1 (curve 3). The other parameters are the same as in Fig. 5.

Fig. 7
Fig. 7

Normalized pulse intensity |a0|2 (log scale) versus global time T. The laser parameters for the different curves are chosen as follows: Curve a: U=4×10-4, β0=0, d=0;σ0=1. Curve b: U=5×10-4, β0=0, d=-10; σ0=1. Curve c: U=4×10-4, β0=1, d=0;σ0=1. Curve d: U=6×10-4, β0=1, d=-20;σ0=0.1.

Fig. 8
Fig. 8

Pulse chirp ψ (a) and normalized frequency shift ω (b) versus global time T for the laser parameters used in Fig. 7, curve d, and d3=-30.

Fig. 9
Fig. 9

Calculated pulse spectrum at different times near the peak of the Q-switched pulse for the parameters of Fig. 8.

Equations (16)

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a(k, t)k=α-l+(1+id) 2t2+(σ-iβ)|a|2a(k, t).
(dα/dt)=σ14(αm-α)Ip/hνp-σ32α|a|2/hν-α/T31.
α=α exp-2τ|a|2tp-TcavT31-U+αmU(U+Tcav/T31)1-exp-TcavT31-U,
a(k, t)=a0 sech1+iψ(t/tp)exp(iϕk),
tp=tp+4-7dψ-3ψ2+(ϕψ-2σa02-ψβa02)tp22tp2,
ψ=(1-2σa02)ψ+(ϕ-βa02)ψ2+ϕ-3βa02-5d+3ψ+5dψ2+3ψ3tp2,
a0=a01+dψ-1+(α-l-σa02)tp2tp2.
ϕ=βa02+d+ψtp2.
a(k, t)=a0 sech1+iψ[(t-ϑk)/tp]×exp{i[ϕk+ω(t-ϑk)]},
-ω(21d3ψ+ϑψtp2)-dψω2tp2-d3ω3ψtp2,
ω[3ϑ+θψ2-(25+9ψ2)d3/tp2]
-ω2(6d-5ψ-dψ2+ϕtp2-σa02tp2)
-ω3(10d3-d3ψ2+ϑtp2)-dω4tp2-d3ω5tp2,
3d3ωψ-ω2tp2,
ϑ=ω(2-4dψ+2d2ψ2)+ω2d3(9dψ2-ψ)+9ω3d32ψ2-8d3ψ(α-l+σa02)-ψ+dψ2+3d3ωψ2,
ω=ω+8d3ψ-tp2(2ω+ϑψ-2dωψ-3d3ψω2)tp4,

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