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 (June 1999).
    [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. SPIE 2253, 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. SPIE 2253, 414–422 (1994).
    [CrossRef]

1999 (3)

1998 (4)

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]

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]

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]

1997 (3)

1996 (3)

1995 (1)

1994 (6)

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]

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

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. SPIE 2253, 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. SPIE 2253, 414–422 (1994).
[CrossRef]

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

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.

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. SPIE 2253, 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. SPIE 2253, 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. SPIE 2253, 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. SPIE 2253, 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. SPIE 2253, 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. SPIE 2253, 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. SPIE 2253, 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]

Proc. SPIE (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. SPIE 2253, 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. SPIE 2253, 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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