Abstract

Numerical analysis of fast saturable absorber mode-locked Yb3+-doped solid state lasers is reported. The analysis includes a special case in which the spectral bandwidth of the short pulse is larger than the fluorescence bandwidth of the gain material. The relationship between the available shortest pulse duration and modulation depth for a standard bulk and thin disk laser geometries with several gain materials are shown. The characteristic phenomena observed in our previous Kerr-lens mode-locked laser experiments were reproduced in the simulation.

© 2015 Optical Society of America

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References

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  1. U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
    [Crossref]
  2. A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007).
    [Crossref]
  3. W. F. Krupke, “Ytterbium solid-state lasers: the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
    [Crossref]
  4. C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010).
    [Crossref] [PubMed]
  5. C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. E. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, “275 W average output power from a femtosecond thin disk oscillator operated in a vacuum environment,” Opt. Express 20(21), 23535–23541 (2012).
    [Crossref] [PubMed]
  6. Y. Zaouter, J. Didierjean, F. Balembois, G. L. Leclin, F. Druon, P. Georges, J. Petit, P. Goldner, and B. Viana, “47-fs diode-pumped Yb3+:CaGdAlO4 laser,” Opt. Lett. 31(1), 119–121 (2006).
    [Crossref] [PubMed]
  7. C. J. Saraceno, O. H. Heckl, C. R. E. Baer, M. Golling, T. Südmeyer, K. Beil, C. Kränkel, K. Petermann, G. Huber, and U. Keller, “SESAMs for high-power femtosecond modelocking: power scaling of an Yb:LuScO₃ thin disk laser to 23 W and 235 fs,” Opt. Express 19(21), 20288–20300 (2011).
    [Crossref] [PubMed]
  8. C. J. Saraceno, O. H. Heckl, C. R. E. Baer, C. Schriber, M. Golling, K. Beil, C. Kränkel, T. Südmeyer, G. Huber, and U. Keller, “Sub-100 fs from a SESAM modelocked thin disk laser,” Appl. Phys. B 106(3), 559–562 (2012).
    [Crossref]
  9. M. Tokurakawa, A. Shirakawa, K. Ueda, R. Peters, S. T. Fredrich-Thornton, K. Petermann, and G. Huber, “Ultrashort pulse generation from diode pumped mode-locked Yb3+:sesquioxide single crystal lasers,” Opt. Express 19(4), 2904–2909 (2011).
    [Crossref] [PubMed]
  10. S. Uemura and K. Torizuka, “Sub-40-fs Pulses from a diode-pumped Kerr-Lens mode-locked Yb-doped yttrium aluminum garnet laser,” Jpn. J. Appl. Phys. 50(1R), 010201 (2011).
    [Crossref]
  11. O. Pronin, J. Brons, C. Grasse, V. Pervak, G. Boehm, M.-C. Amann, V. L. Kalashnikov, A. Apolonski, and F. Krausz, “High-power 200 fs Kerr-lens mode-locked Yb:YAG thin-disk oscillator,” Opt. Lett. 36(24), 4746–4748 (2011).
    [Crossref] [PubMed]
  12. J. Brons, V. Pervak, E. Fedulova, D. Bauer, D. Sutter, V. Kalashnikov, A. Apolonskiy, O. Pronin, and F. Krausz, “Energy scaling of Kerr-lens mode-locked thin-disk oscillators,” Opt. Lett. 39(22), 6442–6445 (2014).
    [Crossref] [PubMed]
  13. Agrawal, Govind P. Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).
  14. 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(10), 2086–2096 (1991).
    [Crossref]
  15. T. Brabec, C. Spielmann, and E. Krausz, “Mode locking in solitary lasers,” Opt. Lett. 16(24), 1961–1963 (1991).
    [Crossref] [PubMed]
  16. H. A. Haus, “Parameter ranges for CW passive mode locking,” IEEE J. Quantum Electron. 12(3), 169–176 (1976).
    [Crossref]
  17. F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998).
    [Crossref]
  18. M. J. Lederer, B. Luther-Davies, H. H. Tan, C. Jagadish, N. N. Akhmediev, and J. M. Soto-Crespo, “Multipulse operation of a Ti:sapphire laser mode locked by ion-implanted semiconductor saturable-absorber mirror,” J. Opt. Soc. Am. B 16(6), 895–904 (1999).
    [Crossref]
  19. J. Neuhaus, D. Bauer, J. Kleinbauer, A. Killi, D. H. Sutter, and T. Dekorsy, “Numerical analysis of a sub-picosecond thin-disk laser oscillator with active multipass geometry showing a variation of pulse duration within one round trip,” J. Opt. Soc. Am. B 27(1), 65–71 (2010).
    [Crossref]
  20. R. Paschotta and U. Keller, “Passive mode locking with slow saturable Absorbers,” Appl. Phys. B 73(7), 653–662 (2001).
    [Crossref]
  21. 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(1), 46–56 (1999).
    [Crossref]
  22. S. Matsubara, H. Hitotsuya, M. Takama, M. Inoue, T. Yamaguchi, K. Hirata, Y. Ishida, and S. Kawato, “Generation of 65-fs ultrashort pulses at 1030-nm center wavelength directly from Kerr-lens mode-locked Yb:YAG laser,” in Conference on Lasers and Electro-Optics (OSA, 2010), paper CTuV2.
    [Crossref]
  23. R. Ell, U. Morgner, F. X. Kãârtner, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, M. J. Lederer, A. Boiko, and B. Luther-Davies, “Generation of 5-fs pulses and octave-spanning spectra directly from a Ti:sapphire laser,” Opt. Lett. 26(6), 373–375 (2001).
    [Crossref] [PubMed]
  24. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, M. Noriyuki, T. I. Yanagitani, and A. A. Kaminskii, “Diode-pumped ultrashort-pulse generation based on Yb3+:Sc2O3 and Yb3+:Y2O3 ceramic multi-gain-media oscillator,” Opt. Express 17, 3353–3361 (2009).
  25. M. Tokurakawa, A. Shirakawa, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, K. Beil, C. Kränkel, and G. Huber, “Continuous wave and mode-locked Yb3+:Y2O3 ceramic thin disk laser,” Opt. Express 20(10), 10847–10852 (2012).
    [Crossref] [PubMed]

2014 (1)

2012 (3)

2011 (4)

2010 (2)

2009 (1)

2007 (1)

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007).
[Crossref]

2006 (1)

2001 (2)

2000 (1)

W. F. Krupke, “Ytterbium solid-state lasers: the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

1999 (2)

1998 (1)

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998).
[Crossref]

1996 (1)

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

1991 (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(10), 2086–2096 (1991).
[Crossref]

T. Brabec, C. Spielmann, and E. Krausz, “Mode locking in solitary lasers,” Opt. Lett. 16(24), 1961–1963 (1991).
[Crossref] [PubMed]

1976 (1)

H. A. Haus, “Parameter ranges for CW passive mode locking,” IEEE J. Quantum Electron. 12(3), 169–176 (1976).
[Crossref]

Akhmediev, N. N.

Amann, M.-C.

Angelow, G.

Apolonski, A.

Apolonskiy, A.

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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Baer, C. R. E.

Balembois, F.

Bauer, D.

Beil, K.

Boehm, G.

Boiko, A.

Brabec, T.

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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Brons, J.

Dekorsy, T.

der Au, J. A.

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998).
[Crossref]

Didierjean, J.

Druon, F.

Ell, R.

Emaury, F.

Fedulova, E.

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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Fredrich-Thornton, S. T.

Fujimoto, J. G.

Georges, P.

Giesen, A.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007).
[Crossref]

Goldner, P.

Golling, M.

Grasse, C.

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(10), 2086–2096 (1991).
[Crossref]

H. A. Haus, “Parameter ranges for CW passive mode locking,” IEEE J. Quantum Electron. 12(3), 169–176 (1976).
[Crossref]

Heckl, O. H.

Hoffmann, M.

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(1), 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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Huber, G.

Ippen, E. P.

Jagadish, C.

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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Kãârtner, F. X.

Kalashnikov, V.

Kalashnikov, V. L.

Kaminskii, A. A.

Kärtner, F. X.

U. Keller, K. J. Weingarten, F. X. Kärtner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Hönninger, N. Matuschek, and J. A. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Keller, U.

C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. E. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, “275 W average output power from a femtosecond thin disk oscillator operated in a vacuum environment,” Opt. Express 20(21), 23535–23541 (2012).
[Crossref] [PubMed]

C. J. Saraceno, O. H. Heckl, C. R. E. Baer, C. Schriber, M. Golling, K. Beil, C. Kränkel, T. Südmeyer, G. Huber, and U. Keller, “Sub-100 fs from a SESAM modelocked thin disk laser,” Appl. Phys. B 106(3), 559–562 (2012).
[Crossref]

C. J. Saraceno, O. H. Heckl, C. R. E. Baer, M. Golling, T. Südmeyer, K. Beil, C. Kränkel, K. Petermann, G. Huber, and U. Keller, “SESAMs for high-power femtosecond modelocking: power scaling of an Yb:LuScO₃ thin disk laser to 23 W and 235 fs,” Opt. Express 19(21), 20288–20300 (2011).
[Crossref] [PubMed]

C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010).
[Crossref] [PubMed]

R. Paschotta and U. Keller, “Passive mode locking with slow saturable Absorbers,” Appl. Phys. B 73(7), 653–662 (2001).
[Crossref]

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(1), 46–56 (1999).
[Crossref]

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 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. A. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Killi, A.

Kleinbauer, J.

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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Kränkel, C.

Krausz, E.

Krausz, F.

Krupke, W. F.

W. F. Krupke, “Ytterbium solid-state lasers: the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

Kurtner, F. X.

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 159–168 (1998).
[Crossref]

Leclin, G. L.

Lederer, M. J.

Luther-Davies, B.

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. A. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Morgner, U.

Morier-Genoud, F.

Moser, M.

Neuhaus, J.

Noriyuki, M.

Paschotta, R.

Pervak, V.

Petermann, K.

Peters, R.

Petit, J.

Pronin, O.

Saraceno, C. J.

Scheuer, V.

Schriber, C.

C. J. Saraceno, F. Emaury, O. H. Heckl, C. R. E. Baer, M. Hoffmann, C. Schriber, M. Golling, T. Südmeyer, and U. Keller, “275 W average output power from a femtosecond thin disk oscillator operated in a vacuum environment,” Opt. Express 20(21), 23535–23541 (2012).
[Crossref] [PubMed]

C. J. Saraceno, O. H. Heckl, C. R. E. Baer, C. Schriber, M. Golling, K. Beil, C. Kränkel, T. Südmeyer, G. Huber, and U. Keller, “Sub-100 fs from a SESAM modelocked thin disk laser,” Appl. Phys. B 106(3), 559–562 (2012).
[Crossref]

Shirakawa, A.

Soto-Crespo, J. M.

Speiser, J.

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007).
[Crossref]

Spielmann, C.

Südmeyer, T.

Sutter, D.

Sutter, D. H.

Tan, H. H.

Tokurakawa, M.

Torizuka, K.

S. Uemura and K. Torizuka, “Sub-40-fs Pulses from a diode-pumped Kerr-Lens mode-locked Yb-doped yttrium aluminum garnet laser,” Jpn. J. Appl. Phys. 50(1R), 010201 (2011).
[Crossref]

Tschudi, T.

Ueda, K.

Uemura, S.

S. Uemura and K. Torizuka, “Sub-40-fs Pulses from a diode-pumped Kerr-Lens mode-locked Yb-doped yttrium aluminum garnet laser,” Jpn. J. Appl. Phys. 50(1R), 010201 (2011).
[Crossref]

Viana, B.

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. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

Yagi, H.

Yanagitani, T.

Yanagitani, T. I.

Zaouter, Y.

Appl. Phys. B (2)

C. J. Saraceno, O. H. Heckl, C. R. E. Baer, C. Schriber, M. Golling, K. Beil, C. Kränkel, T. Südmeyer, G. Huber, and U. Keller, “Sub-100 fs from a SESAM modelocked thin disk laser,” Appl. Phys. B 106(3), 559–562 (2012).
[Crossref]

R. Paschotta and U. Keller, “Passive mode locking with slow saturable Absorbers,” Appl. Phys. B 73(7), 653–662 (2001).
[Crossref]

IEEE J. Quantum Electron. (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(10), 2086–2096 (1991).
[Crossref]

H. A. Haus, “Parameter ranges for CW passive mode locking,” IEEE J. Quantum Electron. 12(3), 169–176 (1976).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (4)

F. X. Kurtner, J. A. der Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers-what’s the difference?” IEEE J. Sel. Top. Quantum Electron. 4(2), 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. A. Au, “Semiconductor Saturable Absorber Mirrors (SESAM’s) for Femtosecond to Nanosecond Pulse Generation in Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 2(3), 435–453 (1996).
[Crossref]

A. Giesen and J. Speiser, “Fifteen years of work on thin-disk lasers: results and scaling laws,” IEEE J. Sel. Top. Quantum Electron. 13(3), 598–609 (2007).
[Crossref]

W. F. Krupke, “Ytterbium solid-state lasers: the first decade,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1287–1296 (2000).
[Crossref]

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

S. Uemura and K. Torizuka, “Sub-40-fs Pulses from a diode-pumped Kerr-Lens mode-locked Yb-doped yttrium aluminum garnet laser,” Jpn. J. Appl. Phys. 50(1R), 010201 (2011).
[Crossref]

Opt. Express (5)

Opt. Lett. (6)

Other (2)

Agrawal, Govind P. Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

S. Matsubara, H. Hitotsuya, M. Takama, M. Inoue, T. Yamaguchi, K. Hirata, Y. Ishida, and S. Kawato, “Generation of 65-fs ultrashort pulses at 1030-nm center wavelength directly from Kerr-lens mode-locked Yb:YAG laser,” in Conference on Lasers and Electro-Optics (OSA, 2010), paper CTuV2.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Model cavity
Fig. 2
Fig. 2 (a) Relationship between temporal laser intensity and temporal saturable loss. (b) Residual saturable loss in single and double pulse operation mode is shown.
Fig. 3
Fig. 3 (a) The gain curve (blue) and the absorption curve (green) are shown. (b) The temporal profile (c) and spectral profile of the initial state of the simulation.
Fig. 4
Fig. 4 Evolution of (a) temporal shape and (b) spectral shape with cavity round trips. Deeper sides show terminal steady states.
Fig. 5
Fig. 5 (a) Spectrum of pulses with CW component (green curve) and gain curve of Yb3+:Lu2O3. (b) Center wavelength as a function of pulse duration.
Fig. 6
Fig. 6 Available shortest pulse duration of Yb3+:Lu2O3 mode-locked laser as a function of modulation depth. Simulation results (circle, square, and triangle points) and its fitting curve are shown.
Fig. 7
Fig. 7 (a) Gain curve of the Yb3+:Lu2O3/Yb3+:Sc2O3 combined active gain medium. (b) Available shortest pulse durations as a function of the modulation depths. Simulation results of Yb:YAG,Yb3+:Lu2O3 and Yb3+:Lu2O3/Yb3+:Sc2O3 combined active gain medium (circle, square, and triangle points) and their fitting curves are shown.
Fig. 8
Fig. 8 Available shortest pulse durations as a function of the modulation depths (circle and square points) of Yb3+:Y2O3 thin-disk mode-locked laser are shown. The fitting curves are also shown.
Fig. 9
Fig. 9 (a) The temporal profile and (b) spectral profile of the initial state. (c) Transition from single pulse operation to double pulse operation.

Tables (1)

Tables Icon

Table 1 Used parameters in the simulations.

Equations (9)

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Tr  t a( T,t )=[ ( L 0 +jX )+g( 1+ 1 Ω g 2 d 2 d t 2 )+jD d 2 d t 2 +( γjδ ) | a | 2 ]a( T,t )
a n+1 ( t )= T ^ a n ( t )
T ^ = e jX e jδ   1γ ( t )   e g( ω ) 2 e jD( ω ) e jδ 1 γ( t )    e jD( ω ) e g( ω ) 2 1 L 0 a n  ( t )
γ(t)=ΔL(1 I(t) I sa )         for  I(t)<  I sa ,          for  I(t) I sa  
d N u ( x ) dt = N u ( x ) [ σ e ( λ )+ σ a ( λ )]( λ,x ) /c +N σ a ( λ )( λ,x ) /c +Rp N u ( x ) τ
dI( x ) dt = N u ( x ) [ σ e ( λ )+ σ a ( λ ) ]( λ,x )N σ a ( λ )( λ,x )L( x ) I( λ,x )dλ
g( λ )= g 0 ( λ ) 1+ I( λ )/ I s ( λ )dλ   N abs ( λ )
I s ( λ )= /c τ[ σ e ( λ )+ σ a ( λ )]
g 0 ( λ )=τ[ σ e ( λ )+ σ a ( λ )]( Rp+N σ a ( λ )I ( λ ) /c dλ )

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