Abstract

The pulse shape and spectrum of ultrashort-pulse Ti:sapphire mode-locked lasers are explained by a model akin to dispersion-managed pulse propagation of optical communications. The pulse is characterized as a nonlinear Bloch wave in a periodic structure. The ultimate spectral width is limited by dispersion and mirror bandwidth and less strongly by gain filtering. The main role of Kerr-lens mode locking is to provide stability against noise buildup. One-dimensional computer simulations are sufficient to explain the major pulse-shaping dynamics. Results are compared with experiment.

© 1999 Optical Society of America

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References

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  1. H. A. Haus, “Theory of mode locking with a fast saturable absorber,” J. Appl. Phys. 46, 3049–3058 (1975).
    [CrossRef]
  2. O. E. Martinez, R. L. Fork, and J. P. Gordon, “Theory of passively mode-locked lasers for the case of a nonlinear complex propagation coefficient,” J. Opt. Soc. Am. B 2, 753–760 (1985).
    [CrossRef]
  3. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984).
    [CrossRef] [PubMed]
  4. J. D. Kafka, T. Bear, and D. Wiltall, “Mode-locked erbium-doped fiber laser with soliton pulse shaping,” Opt. Lett. 14, 1269–1271 (1989).
    [CrossRef] [PubMed]
  5. I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
    [CrossRef]
  6. M. T. Guy, D. U. Noske, and T. R. Taylor, “Generation of femtosecond soliton pulses by passive mode locking of an ytterbium–erbium figure-of-eight fiber laser,” Opt. Lett. 18, 1447–1449 (1993).
    [CrossRef] [PubMed]
  7. N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
    [CrossRef]
  8. D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
    [CrossRef] [PubMed]
  9. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Sub-two cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24, 411–413 (1999).
    [CrossRef]
  10. J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Pulse evolution in a broad-bandwidth Ti:sapphire laser,” Opt. Lett. 19, 1149–1151 (1994).
    [CrossRef] [PubMed]
  11. L. Xu, C. Spielmann, F. Krausz, and R. Szipöcs, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1259–1261 (1996).
    [CrossRef] [PubMed]
  12. I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
    [CrossRef] [PubMed]
  13. I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and C.-P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465–1467 (1994).
    [CrossRef] [PubMed]
  14. C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1102 (1994).
    [CrossRef]
  15. S. T. Cundiff, W. H. Knox, E. P. Ippen, and H. A. Haus, “Frequency-dependent mode size in broadband Kerr-lens mode locking,” Opt. Lett. 21, 662–664 (1996).
    [CrossRef] [PubMed]
  16. I. P. Christov, H. C. Kapteyn, M. M. Murnane, Ch.-P. Huang, and J. Zhou, “Space–time focusing of femtosecond pulses in a Ti:sapphire laser,” Opt. Lett. 20, 309–311 (1995).
    [CrossRef] [PubMed]
  17. I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Sub-10 fs operation of Kerr-lens mode-locked lasers,” Opt. Lett. 21, 1493–1495 (1996).
    [CrossRef] [PubMed]
  18. I. P. Christov and V. D. Stoev, “Kerr-lens mode-locked laser model: role of space–time effects,” J. Opt. Soc. Am. B 15, 1960–1966 (1998).
    [CrossRef]
  19. V. P. Kalosha, M. Müller, J. Herrmann, and S. Gatz, “Spatiotemporal model of femtosecond pulse generator in a Kerr-lens mode-locked solid-state laser,” J. Opt. Soc. Am. B 15, 535–550 (1998).
    [CrossRef]
  20. H. A. Haus and J. G. Fujimoto, “Structures for additive pulse mode locking,” J. Opt. Soc. Am. B 8, 2068–2076 (1991).
    [CrossRef]
  21. F. X. Kärtner, J. Aus des Au, and U. Keller, “Mode-locking with slow and fast saturable absorbers—what’s the difference?,” IEEE J. Sel. Top. Quantum Electron. 4, 159–168 (1998).
    [CrossRef]
  22. E. P. Ippen, “Principles of passive mode locking,” Appl. Phys. B 58, 159–170 (1994).
    [CrossRef]
  23. H. A. Haus and Y. Chen, “Dispersion managed solitons as nonlinear Bloch waves,” J. Opt. Soc. Am. B 16, 889–894 (June1999).
    [CrossRef]
  24. T. H. B. Nijhof, N. T. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
    [CrossRef]
  25. Y. Chen and H. A. Haus, “Dispersion-managed solitons in the net positive dispersion regime,” J. Opt. Soc. Am. B 16, 24–30 (1999).
    [CrossRef]
  26. F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Schener, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
    [CrossRef] [PubMed]
  27. N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
    [CrossRef]
  28. V. Scheuer, M. Tilsch, and T. Tschudi, “Reduction of absorption losses in ion beam spattered deposition of optical coatings for the visible and near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 445–454 (1994).
    [CrossRef]
  29. M. Tilsch, V. Schener, J. Staub, and T. Tschudi, “Direct optical monitoring instrument with a double detection system for the control of multi-layer systems from the visible to the near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 414–422 (1994).
    [CrossRef]

1999 (3)

1998 (4)

V. P. Kalosha, M. Müller, J. Herrmann, and S. Gatz, “Spatiotemporal model of femtosecond pulse generator in a Kerr-lens mode-locked solid-state laser,” J. Opt. Soc. Am. B 15, 535–550 (1998).
[CrossRef]

I. P. Christov and V. D. Stoev, “Kerr-lens mode-locked laser model: role of space–time effects,” J. Opt. Soc. Am. B 15, 1960–1966 (1998).
[CrossRef]

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

N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

1997 (3)

1996 (3)

1995 (1)

1994 (4)

1993 (1)

1992 (1)

N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
[CrossRef]

1991 (2)

1990 (1)

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

1989 (1)

1985 (1)

1984 (1)

1975 (1)

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

Aus des Au, J.

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

Bear, T.

Brabec, T.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1102 (1994).
[CrossRef]

Chen, Y.

Cho, S. H.

Christov, I. P.

Cundiff, S. T.

Curley, P. F.

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1102 (1994).
[CrossRef]

Doran, N. T.

T. H. B. Nijhof, N. T. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

Fork, R. L.

Forysiak, W.

T. H. B. Nijhof, N. T. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Fujimoto, J. G.

Gatz, S.

Geer, E. T.

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

Gordon, J. P.

Guy, M. T.

Haus, H. A.

Heine, C.

Herrmann, J.

Huang, C.-P.

Huang, Ch.-P.

Ippen, E. P.

Jung, I. D.

Kafka, J. D.

Kalosha, V. P.

Kapteyn, H. C.

Kärtner, F. X.

Kean, P. N.

Keller, U.

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

N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Schener, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[CrossRef] [PubMed]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
[CrossRef] [PubMed]

Kelly, S. M. J.

N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
[CrossRef]

Knox, F. M.

T. H. B. Nijhof, N. T. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Knox, W. H.

Krausz, F.

L. Xu, C. Spielmann, F. Krausz, and R. Szipöcs, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1259–1261 (1996).
[CrossRef] [PubMed]

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1102 (1994).
[CrossRef]

Martinez, O. E.

Matuschek, N.

Mollenauer, L. F.

Morf, R.

Morgner, U.

Morier-Genoud, F.

Müller, M.

Murnane, M. M.

Nijhof, T. H. B.

T. H. B. Nijhof, N. T. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

Noske, D. U.

Pandit, N.

N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
[CrossRef]

Schener, V.

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Schener, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[CrossRef] [PubMed]

M. Tilsch, V. Schener, J. Staub, and T. Tschudi, “Direct optical monitoring instrument with a double detection system for the control of multi-layer systems from the visible to the near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 414–422 (1994).
[CrossRef]

Scheuer, V.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
[CrossRef] [PubMed]

V. Scheuer, M. Tilsch, and T. Tschudi, “Reduction of absorption losses in ion beam spattered deposition of optical coatings for the visible and near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 445–454 (1994).
[CrossRef]

Schibli, T.

Sibbett, W.

Smith, I.

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

Spence, D. E.

Spielmann, C.

L. Xu, C. Spielmann, F. Krausz, and R. Szipöcs, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1259–1261 (1996).
[CrossRef] [PubMed]

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1102 (1994).
[CrossRef]

Staub, J.

M. Tilsch, V. Schener, J. Staub, and T. Tschudi, “Direct optical monitoring instrument with a double detection system for the control of multi-layer systems from the visible to the near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 414–422 (1994).
[CrossRef]

Stoev, V. D.

Stolen, R. H.

Sutter, D. H.

Szipöcs, R.

Taft, G.

Taylor, J. R.

N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
[CrossRef]

Taylor, T. R.

Tilsch, M.

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
[CrossRef] [PubMed]

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Schener, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[CrossRef] [PubMed]

V. Scheuer, M. Tilsch, and T. Tschudi, “Reduction of absorption losses in ion beam spattered deposition of optical coatings for the visible and near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 445–454 (1994).
[CrossRef]

M. Tilsch, V. Schener, J. Staub, and T. Tschudi, “Direct optical monitoring instrument with a double detection system for the control of multi-layer systems from the visible to the near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 414–422 (1994).
[CrossRef]

Tschudi, T.

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Schener, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[CrossRef] [PubMed]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
[CrossRef] [PubMed]

V. Scheuer, M. Tilsch, and T. Tschudi, “Reduction of absorption losses in ion beam spattered deposition of optical coatings for the visible and near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 445–454 (1994).
[CrossRef]

M. Tilsch, V. Schener, J. Staub, and T. Tschudi, “Direct optical monitoring instrument with a double detection system for the control of multi-layer systems from the visible to the near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 414–422 (1994).
[CrossRef]

Wheatley, P.

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

Wiltall, D.

Woske, D. U.

N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
[CrossRef]

Wyatt, R.

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

Xu, L.

Zhang, G.

Zhou, J.

Appl. Phys. B (1)

E. P. Ippen, “Principles of passive mode locking,” Appl. Phys. B 58, 159–170 (1994).
[CrossRef]

Electron. Lett. (3)

T. H. B. Nijhof, N. T. Doran, W. Forysiak, and F. M. Knox, “Stable soliton-like propagation in dispersion managed systems with net anomalous, zero and normal dispersion,” Electron. Lett. 23, 1726–1727 (1997).
[CrossRef]

N. Pandit, D. U. Woske, S. M. J. Kelly, and J. R. Taylor, “Characteristic instability of fiber loop soliton lasers,” Electron. Lett. 28, 455–456 (1992).
[CrossRef]

I. Smith, E. T. Geer, R. Wyatt, P. Wheatley, and N. T. Doran, “Totally integrated erbium fiber soliton laser pumped by a laser diode,” Electron. Lett. 27, 244–245 (1990).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1102 (1994).
[CrossRef]

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

N. Matuschek, F. X. Kärtner, and U. Keller, “Theory of double-chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

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

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. B (6)

Opt. Lett. (13)

F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Schener, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22, 831–833 (1997).
[CrossRef] [PubMed]

M. T. Guy, D. U. Noske, and T. R. Taylor, “Generation of femtosecond soliton pulses by passive mode locking of an ytterbium–erbium figure-of-eight fiber laser,” Opt. Lett. 18, 1447–1449 (1993).
[CrossRef] [PubMed]

S. T. Cundiff, W. H. Knox, E. P. Ippen, and H. A. Haus, “Frequency-dependent mode size in broadband Kerr-lens mode locking,” Opt. Lett. 21, 662–664 (1996).
[CrossRef] [PubMed]

I. P. Christov, H. C. Kapteyn, M. M. Murnane, Ch.-P. Huang, and J. Zhou, “Space–time focusing of femtosecond pulses in a Ti:sapphire laser,” Opt. Lett. 20, 309–311 (1995).
[CrossRef] [PubMed]

I. P. Christov, V. D. Stoev, M. M. Murnane, and H. C. Kapteyn, “Sub-10 fs operation of Kerr-lens mode-locked lasers,” Opt. Lett. 21, 1493–1495 (1996).
[CrossRef] [PubMed]

L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984).
[CrossRef] [PubMed]

J. D. Kafka, T. Bear, and D. Wiltall, “Mode-locked erbium-doped fiber laser with soliton pulse shaping,” Opt. Lett. 14, 1269–1271 (1989).
[CrossRef] [PubMed]

D. E. Spence, P. N. Kean, and W. Sibbett, “60-fsec pulse generation from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 16, 42–44 (1991).
[CrossRef] [PubMed]

U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Sub-two cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24, 411–413 (1999).
[CrossRef]

J. Zhou, G. Taft, C.-P. Huang, M. M. Murnane, H. C. Kapteyn, and I. P. Christov, “Pulse evolution in a broad-bandwidth Ti:sapphire laser,” Opt. Lett. 19, 1149–1151 (1994).
[CrossRef] [PubMed]

L. Xu, C. Spielmann, F. Krausz, and R. Szipöcs, “Ultrabroadband ring oscillator for sub-10-fs pulse generation,” Opt. Lett. 21, 1259–1261 (1996).
[CrossRef] [PubMed]

I. D. Jung, F. X. Kärtner, N. Matuschek, D. H. Sutter, F. Morier-Genoud, G. Zhang, U. Keller, V. Scheuer, M. Tilsch, and T. Tschudi, “Self-starting 6.5 fs pulses from a Ti:sapphire laser,” Opt. Lett. 22, 1009–1011 (1997).
[CrossRef] [PubMed]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. Zhou, and C.-P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465–1467 (1994).
[CrossRef] [PubMed]

Other (2)

V. Scheuer, M. Tilsch, and T. Tschudi, “Reduction of absorption losses in ion beam spattered deposition of optical coatings for the visible and near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 445–454 (1994).
[CrossRef]

M. Tilsch, V. Schener, J. Staub, and T. Tschudi, “Direct optical monitoring instrument with a double detection system for the control of multi-layer systems from the visible to the near-infrared,” in Optical Interference Coatings, F. Abeles, ed., Proc. SPIE2253, 414–422 (1994).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Simulation of the Hamiltonian problem. Intensity profiles at the center of the negatively dispersive segment are shown for successive round trips. The total extent is 1000 round trips. D=D(±)=±60 fs2/mm, segment or crystal length L=2 mm, τFWHM=5.5 fs, δ=0 for D<0, δ=1 (MW mm)-1 for D>0.

Fig. 2
Fig. 2

Pulse shaping in one round trip. The negative segment has no nonlinearity.

Fig. 3
Fig. 3

(a) Schematic of a Kerr-lens mode-locked Ti:sapphire laser: P’s, prisms; L, lens; DCM’s, double-chirped mirror; TiSa, Ti:sapphire. (b) Correspondence with dispersion-managed fiber transmission.

Fig. 4
Fig. 4

Simulation with gain and filtering added. The filter is Lorentzian, with a FWHM bandwidth five times the bandwidth of the pulse.

Fig. 5
Fig. 5

Sequence of pulse profiles in the center of the negatively dispersive segment for three magnitudes of SPM. to=3 fs, with solid curves (5.5 fs) for δ=1 (MW mm)-1, dashed–dotted curve (7 fs) for δ=0.5 (MW mm)-1, and dashed curves for no SPM of δ=0. The dispersion map is of Fig. 1. The output coupler loss is 3%.

Fig. 6
Fig. 6

Energy of the pulse in the lossless dispersion-managed system with stretching S=LD/τFWHM2 or for a fixed crystal length L and pulse width as parameters; D=60 fs2/mm for Ti:sapphire at 800 nm.

Fig. 7
Fig. 7

Experimental results: (a) reflectivity of the DCM’s and the output coupler (oc); (b) designed, desired, and measured dispersion of the DCM’s; (c) output spectrum; (d) intracavity spectrum computed from (c) and the output coupler reflectivity shown in (a).

Fig. 8
Fig. 8

Measured interferometric autocorrelation (filled circles), IAC derived from the spectrum of Fig. 7(c) assuming zero phase (solid curves), and IAC of a sinc pulse (dashed curve).

Equations (3)

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i uz=-D(z) 2t2u+δ(z)|u|2u.
A(t)=Ao sin(t/τ)t/τ
Aˆ(ω)=Aoτ/2|ω|<1/τ0|ω|>1/τ.

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