Abstract

The mode locking dynamics of a diode-pumped thin-disk laser oscillator with an active multipass cell operated in ambient atmosphere was studied numerically. The numerical results are compared to experimental results of a passively mode-locked thin-disk Yb:YAG laser with several megahertz repetition rate, sub-picosecond pulse duration, and >10μJ pulse energy. The numerical simulations prove that the soliton area theorem predicts a correct pulse duration when considering an average pulse energy inside the oscillator. Furthermore, they show a variation in the full width at half-maximum pulse length for the pulse that propagates within the oscillator. This oscillation shows a behavior that is contrary to a change in the pulse length given by the soliton area theorem when considering the real pulse energies at respective points in the resonator. The “breathing” is caused by the strong influence of the self-phase modulation of the ambient atmosphere and large amounts of dispersion resulting in a deviation from the sech2 pulse shape and a chirped pulse.

© 2009 Optical Society of America

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References

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  1. B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
    [CrossRef]
  2. F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red-green-blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29, 1921-1923 (2004).
    [CrossRef] [PubMed]
  3. L. Shah, M. E. Fermann, J. W. Dawson, and C. P. J. Barty, “Micromachining with a 50 W, 50 μJ, subpicosecond fiber laser system,” Opt. Express 14, 12546-12551 (2006).
    [CrossRef] [PubMed]
  4. M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
    [CrossRef]
  5. S. V. Marchese, C. R. Baer, A. G. Engqvist, S. Hashimoto, D. J. Maas, M. Golling, T. Südmeyer, and U. Keller, “Femtosecond thin-disk laser oscillator with pulse energy beyond the 10-microjoule level,” Opt. Express 16, 6397-6407 (2008).
    [CrossRef] [PubMed]
  6. T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2, 599-604 (2008).
    [CrossRef]
  7. F. Röser, D. Schimpf, B. Ortac, K. Rademaker, J. Limpert, and A. Tünnermann, “90 W average power 100 μJ energy femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32, 2230-2232 (2007).
    [CrossRef] [PubMed]
  8. S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
    [CrossRef]
  9. S. Dewald, T. Lang, C. D. Schröter, R. Moshammer, J. Ullrich, M. Siegel, and U. Morgner, “Ionization of noble gases with pulses directly from a laser oscillator,” Opt. Lett. 31, 2072-2074 (2006).
    [CrossRef] [PubMed]
  10. A. Killi, A. Steinmann, J. Dörring, U. Morgner, M. J. Lederer, D. Kopf, and C. Fallnich, “High-peak-power pulses from a cavity-dumped Yb:KY(WO4)2 oscillator,” Opt. Lett. 30, 1891-1893 (2005).
    [CrossRef] [PubMed]
  11. G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. J. Lederer, and U. Morgner, “Passively mode-locked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion,” Opt. Express 15, 16017-16021 (2007).
    [CrossRef] [PubMed]
  12. A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
    [CrossRef]
  13. E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, C. Hönninger, M. Kumkar, and U. Keller, “60 W average power in 810 fs pulses from a thin-disk Yb:YAG laser,” Opt. Lett. 28, 367-369 (2003).
    [CrossRef] [PubMed]
  14. J. Neuhaus, J. Kleinbauer, A. Killi, S. Weiler, D. H. Sutter, and T. Dekorsy, “Passively mode-locked Yb:YAG thin-disk laser with pulse energies exceeding 13 μJ by use of an active multipass geometry,” Opt. Lett. 33, 726-729 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975).
    [CrossRef]
  20. G. Agrawal, Nonlinear Fiber Optics (Academic, 2001), Vol. 3.
  21. W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487-2490 (1965).
    [CrossRef]
  22. F. X. Kärtner, I. D. Jung, and U. Keller, “Soliton mode-locking with saturable absorbers,” IEEE J. Sel. Top. Quantum Electron. 2, 540-556 (1996).
    [CrossRef]
  23. F. Brunner, T. Südmeyer, E. Innerhofer, F. Mourier-Genoud, R. Paschotta, V. E. Kisel, V. G. Shcherbitsky, J. Gao, K. Contag, A. Giesen, and U. Keller, “240 fs pulses with 22 W average power from a mode-locked thin-disk Yb:KYW laser,” Opt. Lett. 27, 1162-1164 (2002).
    [CrossRef]

2009 (1)

2008 (5)

2007 (2)

2006 (2)

2005 (2)

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

A. Killi, A. Steinmann, J. Dörring, U. Morgner, M. J. Lederer, D. Kopf, and C. Fallnich, “High-peak-power pulses from a cavity-dumped Yb:KY(WO4)2 oscillator,” Opt. Lett. 30, 1891-1893 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

2002 (1)

2000 (1)

H. A. Haus, “Mode locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

1996 (2)

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

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

1994 (1)

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

1975 (1)

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975).
[CrossRef]

1965 (1)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487-2490 (1965).
[CrossRef]

Abdelalim, M. A.

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic, 2001), Vol. 3.

Anis, H.

Apolonski, A.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Arisholm, G.

Aschwanden, A.

Baer, C. R.

Baer, C. R. E.

T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2, 599-604 (2008).
[CrossRef]

Barty, C. P. J.

Bauer, D.

Brauch, U.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

Brunner, F.

Chichkov, B. N.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Contag, K.

Dawson, J. W.

Dekorsy, T.

Dewald, S.

Dombi, P.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Dörring, J.

Emons, M.

Engqvist, A. G.

Fallnich, C.

Fermann, M. E.

Fernandez, A.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Gao, J.

Giesen, A.

Gingras, G.

T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2, 599-604 (2008).
[CrossRef]

Golling, M.

Graf, R.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Guina, M.

Häring, R.

Hashimoto, S.

S. V. Marchese, C. R. Baer, A. G. Engqvist, S. Hashimoto, D. J. Maas, M. Golling, T. Südmeyer, and U. Keller, “Femtosecond thin-disk laser oscillator with pulse energy beyond the 10-microjoule level,” Opt. Express 16, 6397-6407 (2008).
[CrossRef] [PubMed]

T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2, 599-604 (2008).
[CrossRef]

Haus, H. A.

H. A. Haus, “Mode locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975).
[CrossRef]

Hebling, J.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Hoffmann, M. C.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Hönninger, C.

Hügel, H.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

Hwang, H.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Innerhofer, E.

Ito, H.

Jung, I. D.

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

Keller, U.

Khalil, D. A.

Killi, A.

Kisel, V. E.

Kitamura, K.

Kleinbauer, J.

Kopf, D.

Krausz, F.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Kumkar, M.

Kurimura, S.

Lang, T.

Lederer, M. J.

Limpert, J.

Logvin, Y.

Maas, D. J.

Marchese, S. V.

Momma, C.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Morgner, U.

Moshammer, R.

Mourier-Genoud, F.

Naumov, S.

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Nelson, K. A.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Neuhaus, J.

Nolte, S.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Opower, H.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

Ortac, B.

Palmer, G.

Paschotta, R.

Prall, B. S.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Rademaker, K.

Rigrod, W. W.

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487-2490 (1965).
[CrossRef]

Röser, F.

Schimpf, D.

Schröter, C. D.

Schultze, M.

Shah, L.

Shcherbitsky, V. G.

Siegel, M.

Sosnowski, T.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Steinmann, A.

Südmeyer, T.

Sutter, D. H.

Tünnermann, A.

F. Röser, D. Schimpf, B. Ortac, K. Rademaker, J. Limpert, and A. Tünnermann, “90 W average power 100 μJ energy femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32, 2230-2232 (2007).
[CrossRef] [PubMed]

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Ullrich, J.

Usami, T.

von Alvensleben, F.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Voss, A.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

Weiler, S.

Wittig, K.

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

Witzel, B.

T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2, 599-604 (2008).
[CrossRef]

Yeh, K. -L.

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

Zhang, J.

Appl. Phys. A (1)

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109-115 (1996).
[CrossRef]

Appl. Phys. B (1)

A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, and H. Opower, “Scalable concept for diode-pumped high-power solid-state lasers,” Appl. Phys. B 58, 365-372 (1994).
[CrossRef]

Appl. Phys. Lett. (1)

M. C. Hoffmann, K.-L. Yeh, H. Hwang, T. Sosnowski, B. S. Prall, J. Hebling, and K. A. Nelson, “Fiber laser pumped high average power single-cycle terahertz pulse source,” Appl. Phys. Lett. 93, 141107 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE J. Quantum Electron. 11, 736-746 (1975).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

H. A. Haus, “Mode locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

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

J. Appl. Phys. (1)

W. W. Rigrod, “Saturation effects in high-gain lasers,” J. Appl. Phys. 36, 2487-2490 (1965).
[CrossRef]

Nat. Photonics (1)

T. Südmeyer, S. V. Marchese, S. Hashimoto, C. R. E. Baer, G. Gingras, B. Witzel, and U. Keller, “Femtosecond laser oscillators for high-field science,” Nat. Photonics 2, 599-604 (2008).
[CrossRef]

New J. Phys. (1)

S. Naumov, A. Fernandez, R. Graf, P. Dombi, F. Krausz, and A. Apolonski, “Approaching the microjoule frontier with femtosecond laser oscillators,” New J. Phys. 7, 216-227 (2005).
[CrossRef]

Opt. Express (6)

Opt. Lett. (7)

F. Brunner, T. Südmeyer, E. Innerhofer, F. Mourier-Genoud, R. Paschotta, V. E. Kisel, V. G. Shcherbitsky, J. Gao, K. Contag, A. Giesen, and U. Keller, “240 fs pulses with 22 W average power from a mode-locked thin-disk Yb:KYW laser,” Opt. Lett. 27, 1162-1164 (2002).
[CrossRef]

E. Innerhofer, T. Südmeyer, F. Brunner, R. Häring, A. Aschwanden, R. Paschotta, C. Hönninger, M. Kumkar, and U. Keller, “60 W average power in 810 fs pulses from a thin-disk Yb:YAG laser,” Opt. Lett. 28, 367-369 (2003).
[CrossRef] [PubMed]

J. Neuhaus, J. Kleinbauer, A. Killi, S. Weiler, D. H. Sutter, and T. Dekorsy, “Passively mode-locked Yb:YAG thin-disk laser with pulse energies exceeding 13 μJ by use of an active multipass geometry,” Opt. Lett. 33, 726-729 (2008).
[CrossRef] [PubMed]

F. Brunner, E. Innerhofer, S. V. Marchese, T. Südmeyer, R. Paschotta, T. Usami, H. Ito, S. Kurimura, K. Kitamura, G. Arisholm, and U. Keller, “Powerful red-green-blue laser source pumped with a mode-locked thin disk laser,” Opt. Lett. 29, 1921-1923 (2004).
[CrossRef] [PubMed]

S. Dewald, T. Lang, C. D. Schröter, R. Moshammer, J. Ullrich, M. Siegel, and U. Morgner, “Ionization of noble gases with pulses directly from a laser oscillator,” Opt. Lett. 31, 2072-2074 (2006).
[CrossRef] [PubMed]

A. Killi, A. Steinmann, J. Dörring, U. Morgner, M. J. Lederer, D. Kopf, and C. Fallnich, “High-peak-power pulses from a cavity-dumped Yb:KY(WO4)2 oscillator,” Opt. Lett. 30, 1891-1893 (2005).
[CrossRef] [PubMed]

F. Röser, D. Schimpf, B. Ortac, K. Rademaker, J. Limpert, and A. Tünnermann, “90 W average power 100 μJ energy femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32, 2230-2232 (2007).
[CrossRef] [PubMed]

Other (1)

G. Agrawal, Nonlinear Fiber Optics (Academic, 2001), Vol. 3.

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Figures (7)

Fig. 1
Fig. 1

Schematic design of an AMC cavity, as it was simulated here and was used in the experiments demonstrated in [15]. Most of the mirrors were highly dispersive mirrors. For starting and stabilizing the mode locking, mirror M13 was replaced with a SESAM. Whereas here only four passes through the AMC are shown, up to 13 passes have been realized.

Fig. 2
Fig. 2

Schematic of the numerical simulation, demonstrating the repetitive action of the various operators within the AMC as given by Eq. (1). Any additional SPM or GDD is included in the symbol labeled “add. phase change.”

Fig. 3
Fig. 3

Simulated laser efficiency for a TD laser, comprising an AMC while operating in CW mode. The figure shows the laser behavior for 1–15 passes through the AMC, thereby shifting the peak efficiency further to the right.

Fig. 4
Fig. 4

(a) Pulse duration over OC rate as given by numerical simulations for 11 passes through the AMC, showing the applicability of the soliton area theorem at an OC rate of 0%. For large OC rates, however, the modified version of the soliton area theorem as given by Eq. (8) must be used. (b) Spectra for various OC rates starting at 64% and ending at 0% OC rate. For non-vanishing OC rates Kelly sidebands appear.

Fig. 5
Fig. 5

(a) FWHM pulse length as determined by the numerical simulation and the soliton area theorem. Every symbol (dot or triangle) corresponds to the soliton just before passage over the TD or through the output coupler. (b) FWHM pulse length as determined by the numerical simulation on a larger scale, together with a pulse energy increase inside the resonator. Dashed arrows mark a change in chirp, whereas larger colored circles refer to positions during a round trip which are discussed in the text and the following figures.

Fig. 6
Fig. 6

(a) B-integral and GDD for each section in between two passes through the gain medium of the AMC laser. The large colored circles are highlighting five specific points that are mentioned in detail in the text. (b) Group delay of the pulse at all five marked positions shown in corresponding colors.

Fig. 7
Fig. 7

Residual of the temporal shape of the pulse while propagating within the oscillator compared to an ideal sech 2 pulse shape. The residuals at all five previously mentioned points are also shown in the diagram on the right side (b) with the specified positions resembling the correspondingly marked positions in (a). At some positions within the resonator, the pulse shows stronger wings and a more distinct peak compared to an ideal sech 2 shape.

Tables (3)

Tables Icon

Table 1 Parameters Used for the Numerical Simulations of the Experiments (Upper Part) and Respective Results (Lower Part)

Tables Icon

Table 2 Parameters Used for the Numerical Simulations of Various OC Rates (Upper Part) with Respective Results (Lower Part)

Tables Icon

Table 3 Parameters Used for the Numerical Simulations of a Larger Gain Bandwidth (Upper Part) with Respective Results (Lower Part)

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

v ( t + T R ) = O ̂ i v ( t ) .
O ̂ gain ( t ) = g ( ω , t ) N 2 t 2 ,
O ̂ loss ( t ) = 1 l ( t ) ,
O ̂ GDD ( t ) = i D 2 2 t 2 ,
O ̂ SPM ( t ) = exp ( i γ SPM | v | 2 ) ,
g ( ω , t ) = g ( T ) 1 + ( ω ω g Δ ω g ) 2 ,
g ( T ) T = g ( T ) g 0 τ eff | v | 2 E sat , g g ( T ) ,
l ( t ) t = l ( t ) l 0 τ l | v ( t ) | 2 E sat , l l ( t ) ,
β ( I ( P ) , I ( L ) ) = I ( L ) h ν ( L ) σ a b s ( L ) + I ( P ) h ν ( P ) σ a b s ( P ) I ( L ) h ν ( L ) { σ a b s ( L ) + σ e m ( L ) } + I ( P ) h ν ( P ) { σ a b s ( P ) + σ e m ( P ) } + 1 / τ f ,
I ( L / P ) = i N ( L / P ) I i ( L / P ) ,
τ P 1.76 2 | β 2 | γ SPM E P , int ,
τ P 1.76 2 | β 2 | ln ( 1 OC ) γ SPM E P , ext .

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