Abstract

The use of a saturable absorber as a passive mode locker in a solid-state laser can introduce a tendency for Q-switched mode-locked operation. We have investigated the transition between the regimes of cw mode locking and Q-switched mode locking. Experimental data from Nd:YLF lasers in the picosecond domain and soliton mode-locked Nd:glass lasers in the femtosecond domain, both passively mode locked with semiconductor saturable absorber mirrors, were compared with predictions from an analytical model. The observed stability limits for the picosecond lasers agree well with a previously described model, while for soliton mode-locked femtosecond lasers we have developed an extended theory that takes into account nonlinear soliton-shaping effects and gain filtering.

© 1999 Optical Society of America

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    [CrossRef]
  6. A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self mode-locking of lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174–176 (1966).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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1998

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

C. Hönninger, F. Morier-Genoud, M. Moser, U. Keller, L. R. Brovelli, and C. Harder, “Efficient and tunable diode-pumped femtosecond Yb:glass lasers,” Opt. Lett. 23, 126–128 (1998).
[CrossRef]

F. X. Kärtner, J. Aus der Au, and U. Keller, “Modelocking with slow and fast saturable absorbers—what’s the difference?” IEEE J. Sel. Topics Quantum Electron. 4, 159–168 (1998).
[CrossRef]

1997

1996

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton modelocking with saturable absorbers,” IEEE J. Sel. Topics Quantum Electron. 2, 540–556 (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. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

S. Gray and A. B. Grudinin, “Soliton fiber laser with a hybrid saturable absorber,” Opt. Lett. 21, 207–209 (1996).
[CrossRef] [PubMed]

1995

D. Kopf, F. X. Kärtner, K. J. Weingarten, and U. Keller, “Diode-pumped mode-locked Nd:glass lasers with an antiresonant Fabry–Perot saturable absorber,” Opt. Lett. 20, 1169–1171 (1995).
[CrossRef] [PubMed]

B. Braun, K. J. Weingarten, F. X. Kärtner, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part I. Experiments,” Appl. Phys. B: Photophys. Laser Chem. 61, 429–437 (1995).
[CrossRef]

F. X. Kärtner, B. Braun, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part II. Theory,” Appl. Phys. B: Photophys. Laser Chem. 61, 569–579 (1995).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. 34, 2024–2036 (1995).
[CrossRef]

F. X. Kärtner and U. Keller, “Stabilization of soliton-like pulses with a slow saturable absorber,” Opt. Lett. 20, 16–18 (1995).
[CrossRef]

L. R. Brovelli, U. Keller, and T. H. Chiu, “Design and operation of antiresonant Fabry–Perot saturable semiconductor absorbers for mode-locked solid-state lasers,” J. Opt. Soc. Am. B 12, 311–322 (1995).
[CrossRef]

1992

1984

1977

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[CrossRef]

1976

H. A. Haus, “Parameter ranges for cw passive modelocking,” IEEE J. Quantum Electron. 12, 169–176 (1976).
[CrossRef]

1966

A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self mode-locking of lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174–176 (1966).
[CrossRef]

1965

H. W. Mocker and R. J. Collins, “Mode competition and self-locking effects in a Q-switched ruby laser,” Appl. Phys. Lett. 7, 270–273 (1965).
[CrossRef]

1963

L. M. Frantz and J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346–2349 (1963).
[CrossRef]

Asom, M. T.

Aus der Au, J.

F. X. Kärtner, J. Aus der Au, and U. Keller, “Modelocking with slow and fast saturable absorbers—what’s the difference?” IEEE J. Sel. Topics Quantum Electron. 4, 159–168 (1998).
[CrossRef]

J. Aus der Au, D. Kopf, F. Morier-Genoud, M. Moser, and U. Keller, “60-fs pulses from a diode-pumped Nd:glass laser,” Opt. Lett. 22, 307–309 (1997).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Bille, J. F.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

Boyd, G. D.

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. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

B. Braun, K. J. Weingarten, F. X. Kärtner, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part I. Experiments,” Appl. Phys. B: Photophys. Laser Chem. 61, 429–437 (1995).
[CrossRef]

F. X. Kärtner, B. Braun, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part II. Theory,” Appl. Phys. B: Photophys. Laser Chem. 61, 569–579 (1995).
[CrossRef]

Brovelli, L. R.

Calasso, I.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. 34, 2024–2036 (1995).
[CrossRef]

Chichkov, B. N.

Chiu, T. H.

Collins, R. J.

H. W. Mocker and R. J. Collins, “Mode competition and self-locking effects in a Q-switched ruby laser,” Appl. Phys. Lett. 7, 270–273 (1965).
[CrossRef]

DeMaria, A. J.

A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self mode-locking of lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174–176 (1966).
[CrossRef]

Ferguson, J. F.

Fischer, J. P.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

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. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Fork, R. L.

Frantz, L. M.

L. M. Frantz and J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346–2349 (1963).
[CrossRef]

Glass, A. J.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[CrossRef]

Gordon, J. P.

Götz, M. H.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

Gray, S.

Grudinin, A. B.

Harder, C.

Haus, H. A.

H. A. Haus, “Parameter ranges for cw passive modelocking,” IEEE J. Quantum Electron. 12, 169–176 (1976).
[CrossRef]

Heynau, H.

A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self mode-locking of lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174–176 (1966).
[CrossRef]

Hönninger, C.

C. Hönninger, F. Morier-Genoud, M. Moser, U. Keller, L. R. Brovelli, and C. Harder, “Efficient and tunable diode-pumped femtosecond Yb:glass lasers,” Opt. Lett. 23, 126–128 (1998).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Horvarth, C.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

Jacobs, H.

Juhasz, T.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

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. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

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

Kamp, M.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. 34, 2024–2036 (1995).
[CrossRef]

Kärtner, F. X.

F. X. Kärtner, J. Aus der Au, and U. Keller, “Modelocking with slow and fast saturable absorbers—what’s the difference?” IEEE J. Sel. Topics Quantum Electron. 4, 159–168 (1998).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

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

F. X. Kärtner and U. Keller, “Stabilization of soliton-like pulses with a slow saturable absorber,” Opt. Lett. 20, 16–18 (1995).
[CrossRef]

F. X. Kärtner, B. Braun, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part II. Theory,” Appl. Phys. B: Photophys. Laser Chem. 61, 569–579 (1995).
[CrossRef]

B. Braun, K. J. Weingarten, F. X. Kärtner, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part I. Experiments,” Appl. Phys. B: Photophys. Laser Chem. 61, 429–437 (1995).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. 34, 2024–2036 (1995).
[CrossRef]

D. Kopf, F. X. Kärtner, K. J. Weingarten, and U. Keller, “Diode-pumped mode-locked Nd:glass lasers with an antiresonant Fabry–Perot saturable absorber,” Opt. Lett. 20, 1169–1171 (1995).
[CrossRef] [PubMed]

Keller, U.

C. Hönninger, F. Morier-Genoud, M. Moser, U. Keller, L. R. Brovelli, and C. Harder, “Efficient and tunable diode-pumped femtosecond Yb:glass lasers,” Opt. Lett. 23, 126–128 (1998).
[CrossRef]

F. X. Kärtner, J. Aus der Au, and U. Keller, “Modelocking with slow and fast saturable absorbers—what’s the difference?” IEEE J. Sel. Topics Quantum Electron. 4, 159–168 (1998).
[CrossRef]

J. Aus der Au, D. Kopf, F. Morier-Genoud, M. Moser, and U. Keller, “60-fs pulses from a diode-pumped Nd:glass laser,” Opt. Lett. 22, 307–309 (1997).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton modelocking with saturable absorbers,” IEEE J. Sel. Topics Quantum Electron. 2, 540–556 (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. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. 34, 2024–2036 (1995).
[CrossRef]

F. X. Kärtner and U. Keller, “Stabilization of soliton-like pulses with a slow saturable absorber,” Opt. Lett. 20, 16–18 (1995).
[CrossRef]

B. Braun, K. J. Weingarten, F. X. Kärtner, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part I. Experiments,” Appl. Phys. B: Photophys. Laser Chem. 61, 429–437 (1995).
[CrossRef]

F. X. Kärtner, B. Braun, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part II. Theory,” Appl. Phys. B: Photophys. Laser Chem. 61, 569–579 (1995).
[CrossRef]

L. R. Brovelli, U. Keller, and T. H. Chiu, “Design and operation of antiresonant Fabry–Perot saturable semiconductor absorbers for mode-locked solid-state lasers,” J. Opt. Soc. Am. B 12, 311–322 (1995).
[CrossRef]

D. Kopf, F. X. Kärtner, K. J. Weingarten, and U. Keller, “Diode-pumped mode-locked Nd:glass lasers with an antiresonant Fabry–Perot saturable absorber,” Opt. Lett. 20, 1169–1171 (1995).
[CrossRef] [PubMed]

U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, “Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry–Perot saturable absorber,” Opt. Lett. 17, 505–507 (1992).
[CrossRef] [PubMed]

Kopf, D.

J. Aus der Au, D. Kopf, F. Morier-Genoud, M. Moser, and U. Keller, “60-fs pulses from a diode-pumped Nd:glass laser,” Opt. Lett. 22, 307–309 (1997).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, “Control of solid-state laser dynamics by semiconductor devices,” Opt. Eng. 34, 2024–2036 (1995).
[CrossRef]

D. Kopf, F. X. Kärtner, K. J. Weingarten, and U. Keller, “Diode-pumped mode-locked Nd:glass lasers with an antiresonant Fabry–Perot saturable absorber,” Opt. Lett. 20, 1169–1171 (1995).
[CrossRef] [PubMed]

Loesel, F. H.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

Martinez, O. E.

Matuschek, N.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Milam, D.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[CrossRef]

Miller, D. A. B.

Mocker, H. W.

H. W. Mocker and R. J. Collins, “Mode competition and self-locking effects in a Q-switched ruby laser,” Appl. Phys. Lett. 7, 270–273 (1965).
[CrossRef]

Momma, C.

Morier-Genoud, F.

Moser, M.

Noack, F.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

Nodvik, J. S.

L. M. Frantz and J. S. Nodvik, “Theory of pulse propagation in a laser amplifier,” J. Appl. Phys. 34, 2346–2349 (1963).
[CrossRef]

Nolte, S.

Stetser, D. A.

A. J. DeMaria, D. A. Stetser, and H. Heynau, “Self mode-locking of lasers with saturable absorbers,” Appl. Phys. Lett. 8, 174–176 (1966).
[CrossRef]

Suhm, N.

F. H. Loesel, J. P. Fischer, M. H. Götz, C. Horvarth, T. Juhasz, F. Noack, N. Suhm, and J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B: Photophys. Laser Chem. 66, 121–128 (1998).

Tünnermann, A.

Weber, M. J.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[CrossRef]

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. Aus der Au, “Semiconductor saturable absorber mirrors (SESAMs) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Topics Quantum Electron. 2, 435–453 (1996).
[CrossRef]

B. Braun, K. J. Weingarten, F. X. Kärtner, and U. Keller, “Continuous-wave mode-locked solid-state lasers with enhanced spatial hole-burning. Part I. Experiments,” Appl. Phys. B: Photophys. Laser Chem. 61, 429–437 (1995).
[CrossRef]

D. Kopf, F. X. Kärtner, K. J. Weingarten, and U. Keller, “Diode-pumped mode-locked Nd:glass lasers with an antiresonant Fabry–Perot saturable absorber,” Opt. Lett. 20, 1169–1171 (1995).
[CrossRef] [PubMed]

Wellegehausen, B.

Welling, H.

Appl. Phys. B: Photophys. Laser Chem.

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Figures (10)

Fig. 1
Fig. 1

Instantaneous and average laser power versus time for (a) a stable cw mode-locked laser and for (b) a mode-locked laser exhibiting large Q-switching instabilities. The average laser power (thick line) is the same for both lasers.

Fig. 2
Fig. 2

Measured data (filled points) and fitted (solid) curve according to Eq. (8) for the nonlinear reflectivity R(FP,A) at 1047 nm of a SESAM as a function of the pulse energy fluence FP,A=EP/Aeff,A. The SESAM parameters are ΔR=1.7%, Fsat,A=60 µJ/cm2, Rns=98.7%, and ΔRns=1.3%.

Fig. 3
Fig. 3

Nd:YLF laser cavity setups. The parameters for (a) the delta cavity were M1=M2=15-cm radius of curvature (ROC), L1=7.6 cm, L2=7.9 cm, L3=35 cm, L4=45 cm. We used 10-cm-, 15-cm-, and 30-cm-ROC mirrors as M3, with corresponding lengths (in cm) L5=4.9, 7.3, 14.3. We used 0.5%, 1.5%, and 5% output coupling (OC). For the experiment with the higher repetition rate of 197 MHz, M2 was a 10-cm-ROC mirror and M3 a 20-cm-ROC mirror. The lengths were L1=7.5 cm, L2=5.4 cm, L3=22 cm, L4=30 cm, and L5=10.6 cm, and the output coupling was 1%. In (b) the V-cavity laser setup we used 50-cm-, 80-cm-, and 50-cm-ROC mirrors for M1, M2, and M3. The arm lengths were L1=30.2 cm, L2=59.5 cm, L3=113 cm, L4=90 cm, and L5=11.5 cm. We used a 3% output coupler.

Fig. 4
Fig. 4

Schematic structure of the SESAM’s. The bottom AlAs/GaAs Bragg mirror is grown by metal-organic chemical-vapor deposition (MOCVD). For the absorber structures we used low-temperature molecular-beam epitaxial or MOCVD growth. The absorber structures consisted of 15- and 25-nm-thick single quantum wells or double quantum wells of 10-nm thickness separated by a 10-nm-thick transparent GaAs spacer layer.

Fig. 5
Fig. 5

Measured impulse response of the same SESAM with the use of different excitation pulse durations (100 fs and 4 ps). The fast intraband thermalization (≈200-fs recovery time) is no longer visible with the 4-ps excitation pulse. The slow recovery time is 4 ps.

Fig. 6
Fig. 6

Microwave spectrum analyzer signal for (a) cw mode locking (cw ML) and for (b) QML of a Nd:YLF laser. The side peaks are due to (a) weak relaxation oscillations and to (b) the large Q-switching modulation, respectively.

Fig. 7
Fig. 7

Experimental determination of the Q-switching stability limit of cw mode locking. The measured suppression of the laser relaxation oscillation peak below the carrier (right-hand ordinate) is displayed versus the pulse energy. The experimentally determined stability limit (≈31 nJ) agrees with the EP,c=29 nJ calculated from Eq. (16), which is indicated by the vertical line between 10-8 and 10-7. For EP<EP,c we observe QML; for EP>EP,c, cw mode locking. On the left-hand ordinate we show the nonlinear reflectivity of the SESAM.

Fig. 8
Fig. 8

Results from all the experiments performed to verify relations (13) and (16) for picosecond lasers. The critical pulse energy is shown versus the QML parameter Esat,LEsat,AΔR. The solid curve shows the theoretical expectation of the critical pulse energy EP,c according to Eq. (16). For higher pulse energies with EP>EP,c, the laser operates cw mode locked; below the solid curve with EP<EP,c it runs Q-switched mode locked. The markers represent the measured values of EP,c for the different experimental setups and saturable absorbers (compare the markers with the symbols listed in Table 3).

Fig. 9
Fig. 9

Nd:glass laser cavity setup. The gain medium is a 4-mm-thick 4% Nd-doped phosphate glass (Schott LG760). The mirrors M1 and M2 had a 15-cm ROC, and the lengths were L1=7.6 cm, L2=7.5 cm, L3=100 cm, and L4=75 cm. We used 15-cm- and 20-cm-ROC mirrors as M3, with corresponding lengths L5=7.4 cm and L5=9.8 cm. The output coupling was 1.5%. The prism separation was Lpr=31 cm.

Fig. 10
Fig. 10

Q-switching stability limit of cw mode locking for the soliton mode-locked Nd:glass laser. The GDD was approximately -2350 fs2 per round trip. The dashed curve represents the critical pulse energy EP,c according to Eq. (16); the solid curve takes soliton shaping into account [relation (27)]. Above the curves with EP>EP,c the laser operation is cw mode locked, below those with EP<EP,c, Q-switched mode locked.

Tables (3)

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Table 1 Laser Material Parametersa

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Table 2 Resonator Parameters for the Different Nd:YLF Laser Setups Calculated by the ABCD Matrix Formalism

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Table 3 Measured SESAM Parametersa

Equations (30)

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dPdt=g-l-qP(EP)TRP,
dgdt=-g-g0τL-PEsat,Lg,
dqdt=-q-q0τA-PEsat,Aq,
qP(EP)=q0Fsat,AAeff,AEP1-exp-EPFsat,AAeff,A.
TRdEPdt=[g-l-qP(EP)]EP,
dgdt=-g-g0τL-EPEsat,LTRg.
EPdqPdEPE¯P<TRτLr=TRτL+EPEsat,L
R(EP)=Rnsln1+exp(-ΔR)expEPEsat,A-1EP/Esat,A,
R(EP)=Rns1-ΔRFsat,AAeff,AEP×1-exp-EPFsat,AAeff,A.
R(EP)exp[-qP(EP)]1-qP(EP).
EP dR(EP)dEPE¯P<TRτLr=TRτL+EPEsat,L.
R(EP)1-ΔRFsat,AAeff,AEPor
R(FP,A)1-ΔRFsat,AFP,A,
EP2>Esat,LEsat,AΔR,
FP,A2>Fsat,LFsat,AΔRAeff,LAeff,A,
P2>Fsat,LFsat,AΔRAeff,LAeff,A1TR2.
EP,c(Esat,LEsat,AΔR)1/2=(Fsat,LAeff,LFsat,AAeff,AΔR)1/2.
geffg(ν)I(ν)dνI(ν)dν.
geff(EP)=g1+Δν(EP)Δνg21/2.
TRdEPdt=[geff(EP)-l-qP(EP)]EP,
dgdt=-g-g0τL-EPEsat,LTRgeff(EP).
EPdgeff(EP)dEP-dqP(EP)dEPE¯P<TRτL+EPEsat,Lgeffg.
geffg-dgeffdEPE¯PEP2>Esat,LEsat,AΔR.
(1+f2)-1/2+Esat,Lgf(1+f2)-3/2dfdEPEP2
>Esat,LEsat,AΔR.
τP=1.76D2λ0Aeff,L4πn2LK1EP
f=4πn2LKD2Aeff,Lλ0Δνg0.3151.76EP,
dfdEP=4πn2LKD2Aeff,Lλ0Δνg0.3151.76K.
Esat,LgK2EP3+EP2>Esat,LEsat,AΔR.
NEP2>Esat,LEsat,AΔR

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