Abstract

We study soliton generation, based on self-consistent field theory, in cw solid-state lasers with semiconductor saturable absorbers. Various soliton destabilizations, i.e., the switch from femtosecond to picosecond generation (picosecond collapse), an automodulation regime, breakdown of soliton generation, and hysteresis behavior, are predicted. It is shown that the third-order dispersion reduces the region in which the solitons exist and causes pulse oscillation and a strong frequency shift.

© 2000 Optical Society of America

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  1. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, and U. Keller, “Semiconductor saturable-absorber mirrors assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633 (1999).
    [CrossRef]
  2. H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2095 (1995).
    [CrossRef]
  3. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
    [CrossRef]
  4. F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–555 (1996).
    [CrossRef]
  5. 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]
  6. V. L. Kalashnikov, I. G. Poloyko, V. P. Mikhailov, and D. von der Linde, “Regular, quasi-periodic and chaotic behavior in cw solid-state Kerr-lens mode-locked lasers,” J. Opt. Soc. Am. B 14, 2691–2695 (1997).
    [CrossRef]
  7. C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
    [CrossRef]
  8. V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, and V. P. Mikhailov, “Ultrashort pulse generation in cw solid-state laser with semiconductor saturable absorber in the presence of the absorption linewidth enhancement,” Opt. Commun. 159, 237–242 (1999).
    [CrossRef]
  9. 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]

1999

1997

1996

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–555 (1996).
[CrossRef]

1995

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2095 (1995).
[CrossRef]

Bolton, S. R.

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

der Au, J. A.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

Elkinton, C. N.

Fluck, R.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

Fujimoto, J. G.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2095 (1995).
[CrossRef]

Gallmann, L.

Haus, H.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2095 (1995).
[CrossRef]

Hönninger, C.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

Ippen, E. P.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2095 (1995).
[CrossRef]

Jenks, R. A.

Jung, I. D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–555 (1996).
[CrossRef]

Kalashnikov, V. L.

V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, and V. P. Mikhailov, “Ultrashort pulse generation in cw solid-state laser with semiconductor saturable absorber in the presence of the absorption linewidth enhancement,” Opt. Commun. 159, 237–242 (1999).
[CrossRef]

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

Kärtner, F. X.

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–555 (1996).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

Keller, U.

C. Hönninger, R. Paschotta, F. Morier-Genoud, M. Moser, and U. Keller, “Q-switching stability limits of continuous-wave passive mode locking,” J. Opt. Soc. Am. B 16, 46–56 (1999).
[CrossRef]

D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, and U. Keller, “Semiconductor saturable-absorber mirrors assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633 (1999).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–555 (1996).
[CrossRef]

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

Krimer, D. O.

V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, and V. P. Mikhailov, “Ultrashort pulse generation in cw solid-state laser with semiconductor saturable absorber in the presence of the absorption linewidth enhancement,” Opt. Commun. 159, 237–242 (1999).
[CrossRef]

Matuschek, N.

D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, and U. Keller, “Semiconductor saturable-absorber mirrors assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633 (1999).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

Mikhailov, V. P.

V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, and V. P. Mikhailov, “Ultrashort pulse generation in cw solid-state laser with semiconductor saturable absorber in the presence of the absorption linewidth enhancement,” Opt. Commun. 159, 237–242 (1999).
[CrossRef]

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

Morier-Genoud, F.

Moser, M.

Paschotta, R.

Poloyko, I. G.

V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, and V. P. Mikhailov, “Ultrashort pulse generation in cw solid-state laser with semiconductor saturable absorber in the presence of the absorption linewidth enhancement,” Opt. Commun. 159, 237–242 (1999).
[CrossRef]

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

Steinmeyer, G.

Sucha, G.

Sutter, D. H.

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.

Weingarten, K. J.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[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]

IEEE J. Quantum Electron.

H. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2095 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. der Au, “Semiconductor saturable absorbers mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–451 (1996).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540–555 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, and V. P. Mikhailov, “Ultrashort pulse generation in cw solid-state laser with semiconductor saturable absorber in the presence of the absorption linewidth enhancement,” Opt. Commun. 159, 237–242 (1999).
[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]

Opt. Lett.

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Figures (6)

Fig. 1
Fig. 1

Pulse width tp versus GVD coefficient k2 (time is normalized to ta). Region A, picosecond generation; region B, auto-oscillation regime for parameters of curve 3. P=5×10-4, αm=0.5, ta=2.5 fs, Tg=3 µs, Tcav=10 ns, l=0.01, γ=0.05, k3=0. β=1, 0.001; 2, 0.01; 3, 0.05; 4, 0.1.

Fig. 2
Fig. 2

Chirp Ψ versus GVD coefficient k2. The parameters correspond to those of Fig. 1. Curves 3 and 4 exist for k2-3 and k2=-1, respectively.

Fig. 3
Fig. 3

Peak intensity I normalized to Esta-1 versus round-trip number z. k2=-20, k3=0, P=5×10-4, β=0.05.

Fig. 4
Fig. 4

Pulse width tp versus pump intensity P (time is normalized to ta). Arrow l, switch between ps and fs generation for the regime depicted by triangles. Trajectory 2 (and corresponding arrow 2), variation of the pump for the previously formed pulse (i.e., for the pulse that is formed at P=10-4). k2=-10, k3=0, β=0.1; other parameters correspond to those of Fig. 1.

Fig. 5
Fig. 5

Pulse width tp versus GVD coefficient k2. Parameters correspond to those of curve 2 of Fig. 1.

Fig. 6
Fig. 6

Frequency shift ω versus GVD coefficient k2. Parameters correspond to those of curve 3 of Fig. 1. k3=1, 0; 2, -5; 3, -10; 4, 10. The left-most region B (depicted in solid gray) corresponds to all presented parameters.

Equations (9)

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a(z, t)z=α exp(-τE)-γ exp(-E)1+t+11+t-1-l+ik2 2t2+k3 3t3-iβ|a(z, t)|2a(z, t),
a(z, t)=a0 exp[iω(t-zδ)+iφz]cosh[(t-zδ)/tp]1+iΨ,
da0dz=a0α exp-τa02v+(1-ω2-v2)γ exp-a02v-l+k2Ψv2-ω2-v2-3k3ωv2Ψ,
dωdz=(Ψa02ω2+a02ω-2v2ω-2v2ωΨ2-Ψa02)γ exp-a02v-2v2ωΨ2-2v2ω-Ψa02τα exp-τa02v-3k3v4Ψ(Ψ2+1),
dvdz=12v2(a04v2+2v4Ψ2-a04+a04ω2+2a02v2-4a02ωv2Ψ-4v4)γ exp-a02v-a04τ2α2v2exp-τa02v+3k2v2Ψ+v2Ψ2-2v2-9k3ωΨv2,
dΨdz=1v2(4a02ωv2+a04Ψ+4a02ωv2Ψ2-2v4Ψ-Ψa04ω2-a04ω-2v4Ψ3)γ exp-a02v+Ψαa04τ2v2 exp-τa02v-2a02β-2v2Ψ-4k2v2Ψ2-2v2Ψ3-4k2v2+12k3ωv2(Ψ2+1),
δ=[a02(ω2+v2-1)-2v2ωΨ)]γ exp-a02v-2ωΨv2-2k2ωv2+k3v2(5v2+3ω2-3v2Ψ2)-a02τα exp-τa02v,
φ=[a02ω(ω2+v2-1)+v2Ψ(v2-2ω2)]γ×exp-a02v+k3v2ω(2v2+2ω2-3v2Ψ2)+k2v2(v2-ω2)+Ψv4+βa02v2-2ω2Ψv2-ωταa02 exp-τa02v.
dαdz=(αm-α)P-2ατa02v-αTg,

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