Abstract

The theory of additive pulse mode locking (APM) is developed in closed form under a linearization approximation. The pulse parameters are determined in terms of the gain, the gain dispersion, the group-velocity dispersion, and the self-phase modulation. Stability regimes are established. Various possible configurations of laser systems that can produce APM are presented. Some of them permit single-cavity realizations that may not require interferometric length stabilization circuits. In general, the results are applicable to a wide range of fast saturable absorber mode-locked systems.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48 (1989).
    [CrossRef] [PubMed]
  2. E. P. Ippen, H. A. Haus, L. Y. Liu, “Additive pulse mode locking,” J. Opt. Soc. Am. B 6, 1736 (1989).
    [CrossRef]
  3. L. F. Mollenauer, R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13 (1984).
    [CrossRef] [PubMed]
  4. K. J. Blow, D. Wood, “Mode-locked lasers with nonlinear external cavities,” J. Opt. Soc. Am. B 5, 629 (1988).
    [CrossRef]
  5. K. J. Blow, B. P. Nelson, “Improved mode locking of an F-center laser with a nonlinear nonsoliton external cavity,” Opt. Lett. 13, 1026 (1988).
    [CrossRef] [PubMed]
  6. P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39 (1989).
    [CrossRef] [PubMed]
  7. C. P. Yakymyshyn, J. F. Pinto, C. R. Pollock, “Additive-pulse mode-locked NaCl:OH−laser,” Opt. Lett. 14, 621 (1989).
    [CrossRef] [PubMed]
  8. J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schulz, “Femtosecond passively mode-locked laser with a Ti:Al2O3nonlinear external cavity,” Opt. Lett. 14, 1125 (1989).
    [CrossRef] [PubMed]
  9. J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schulz, “Starting dynamics of additive pulse mode locking in the Ti:Al2O3laser,” Opt. Lett. 15, 1300 (1990).
    [CrossRef] [PubMed]
  10. E. P. Ippen, L. Y. Liu, H. A. Haus, “Self-starting condition for additive-pulse mode-locked lasers,” Opt. Lett. 15, 183 (1990).
    [CrossRef] [PubMed]
  11. J. Goodberlet, J. Jacobson, J. G. Fujimoto, P. A. Schulz, T. Y. Fan, “Self-starting additive-pulse mode-locked diode-pumped Nd:YAG laser,” Opt. Lett. 15, 504 (1990).
    [CrossRef] [PubMed]
  12. L. Y. Liu, J. M. Huxley, E. P. Ippen, H. A. Haus, “Self-starting additive-pulse mode locking of a Nd:YAG laser,” Opt. Lett. 15, 553 (1990).
    [CrossRef] [PubMed]
  13. J. M. Liu, J. K. Chee, “Passive mode locking of a cw Nd:YAG laser with a nonlinear external coupled cavity,” Opt. Lett. 15, 685 (1990).
    [CrossRef] [PubMed]
  14. F. Krausz, C. Spielmann, T. Brabec, E. Wintner, A. J. Schmidt, “Subpicosecond pulse generation from a Nd:glass laser using a nonlinear external cavity,” Opt. Lett. 15, 737 (1990).
    [CrossRef] [PubMed]
  15. W. Sibbett, “Hybrid and passive mode locking in coupled-cavity lasers,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), pp. 2–7.
    [CrossRef]
  16. J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
    [CrossRef]
  17. Y. Ishida, N. Sarukura, H. Nakano, “Soliton-like pulse shaping in a cw passively mode-locked Ti:Al2O3laser,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990) p. 75.
    [CrossRef]
  18. D. E. Spence, P. N. Kean, W. Sibbett, “Sub-100 fs pulse generation from a self-modelocked titanium-sapphire laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP10-1, p. 619.
  19. F. Ouellette, M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99 (1986).
    [CrossRef]
  20. H. Avramopoulos, H. Houh, N. A. Whitaker, M. C. Gabriel, “Passive modelocking of an erbium-doped fiber laser,” in Optical Amplifiers and Their Applications, Vol. 13 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper PdP8-1.
  21. A. G. Bulushev, E. M. Dianov, O. G. Okhotnikov, “Intracavity pulse compression in a laser with nonlinear resonator,” IEEE Photon. Tech. Lett. 2, 699 (1990).
    [CrossRef]
  22. I. N. Duling, “All-fiber modelocked figure eight laser,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 306–310.
  23. L. Dahlström, “Passive mode-locking and Q-switching of high power lasers by means of the optical Kerr effect,” Opt. Commun. 5, 157 (1972).
    [CrossRef]
  24. H. A. Haus, Y. Silberberg, “Laser mode locking with addition of nonlinear index,” IEEE J. Quantum Electron. QE-22, 325 (1986).
    [CrossRef]
  25. H. A. Haus, “A theory of fast saturable absorber modelocking,” J. Appl. Phys. 46, 3049 (1975).
    [CrossRef]
  26. O. E. Martinez, R. L. Fork, 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 (1985).
    [CrossRef]
  27. J. A. Valdmanis, R. L. Fork, J. P. Gordon, “Generation of optical pulses as short as 27 femtoseconds directly from a laser balancing self-phase modulation, group-velocity dispersion, saturable absorption, and saturation gain,” Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  28. C. Y. Wang, Y. Ishida, Y. Yamamoto, “Self-phase-modulation-controlled passively mode-locked dye laser,” Opt. Lett. 15, 965 (1990).
    [CrossRef] [PubMed]
  29. M. J. LaGasse, D. L. Wong, J. G. Fujimoto, H. A. Haus, “Ultrafast switching with a single-fiber interferometer,” Opt. Lett. 14, 311 (1989).
    [CrossRef] [PubMed]
  30. R. L. Fork, O. E. Martinez, J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150 (1984).
    [CrossRef] [PubMed]
  31. J. Jacobson, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication).
  32. D. K. Negus, L. Spinelli, N. Goldblatt, G. Feuget, “Sub-100 femtosecond pulse generation by Kerr lens modelocking in Ti:Al2O3,” in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), postdeadline paper.

1990

1989

1988

1986

F. Ouellette, M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99 (1986).
[CrossRef]

H. A. Haus, Y. Silberberg, “Laser mode locking with addition of nonlinear index,” IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

1985

1984

1975

H. A. Haus, “A theory of fast saturable absorber modelocking,” J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

1972

L. Dahlström, “Passive mode-locking and Q-switching of high power lasers by means of the optical Kerr effect,” Opt. Commun. 5, 157 (1972).
[CrossRef]

Avramopoulos, H.

H. Avramopoulos, H. Houh, N. A. Whitaker, M. C. Gabriel, “Passive modelocking of an erbium-doped fiber laser,” in Optical Amplifiers and Their Applications, Vol. 13 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper PdP8-1.

Baer, T.

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Blow, K. J.

Brabec, T.

Bulushev, A. G.

A. G. Bulushev, E. M. Dianov, O. G. Okhotnikov, “Intracavity pulse compression in a laser with nonlinear resonator,” IEEE Photon. Tech. Lett. 2, 699 (1990).
[CrossRef]

Chee, J. K.

Crust, D. W.

Dahlström, L.

L. Dahlström, “Passive mode-locking and Q-switching of high power lasers by means of the optical Kerr effect,” Opt. Commun. 5, 157 (1972).
[CrossRef]

Dianov, E. M.

A. G. Bulushev, E. M. Dianov, O. G. Okhotnikov, “Intracavity pulse compression in a laser with nonlinear resonator,” IEEE Photon. Tech. Lett. 2, 699 (1990).
[CrossRef]

Duling, I. N.

I. N. Duling, “All-fiber modelocked figure eight laser,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 306–310.

Fan, T. Y.

Feuget, G.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feuget, “Sub-100 femtosecond pulse generation by Kerr lens modelocking in Ti:Al2O3,” in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), postdeadline paper.

Fork, R. L.

Fujimoto, J. G.

Gabriel, M. C.

H. Avramopoulos, H. Houh, N. A. Whitaker, M. C. Gabriel, “Passive modelocking of an erbium-doped fiber laser,” in Optical Amplifiers and Their Applications, Vol. 13 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper PdP8-1.

Goldblatt, N.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feuget, “Sub-100 femtosecond pulse generation by Kerr lens modelocking in Ti:Al2O3,” in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), postdeadline paper.

Goodberlet, J.

Gordon, J. P.

Grant, R. S.

Hall, K. L.

Haus, H. A.

Houh, H.

H. Avramopoulos, H. Houh, N. A. Whitaker, M. C. Gabriel, “Passive modelocking of an erbium-doped fiber laser,” in Optical Amplifiers and Their Applications, Vol. 13 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper PdP8-1.

Huxley, J. M.

Ippen, E. P.

Ishida, Y.

C. Y. Wang, Y. Ishida, Y. Yamamoto, “Self-phase-modulation-controlled passively mode-locked dye laser,” Opt. Lett. 15, 965 (1990).
[CrossRef] [PubMed]

Y. Ishida, N. Sarukura, H. Nakano, “Soliton-like pulse shaping in a cw passively mode-locked Ti:Al2O3laser,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990) p. 75.
[CrossRef]

Jacobson, J.

Kafka, J. D.

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Kean, P. N.

P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39 (1989).
[CrossRef] [PubMed]

D. E. Spence, P. N. Kean, W. Sibbett, “Sub-100 fs pulse generation from a self-modelocked titanium-sapphire laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP10-1, p. 619.

Keirstead, M. S.

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Krausz, F.

LaGasse, M. J.

Langford, N.

Liu, J. M.

Liu, L. Y.

Mark, J.

Martinez, O. E.

Mollenauer, L. F.

Nakano, H.

Y. Ishida, N. Sarukura, H. Nakano, “Soliton-like pulse shaping in a cw passively mode-locked Ti:Al2O3laser,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990) p. 75.
[CrossRef]

Negus, D. K.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feuget, “Sub-100 femtosecond pulse generation by Kerr lens modelocking in Ti:Al2O3,” in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), postdeadline paper.

Nelson, B. P.

Okhotnikov, O. G.

A. G. Bulushev, E. M. Dianov, O. G. Okhotnikov, “Intracavity pulse compression in a laser with nonlinear resonator,” IEEE Photon. Tech. Lett. 2, 699 (1990).
[CrossRef]

Ouellette, F.

F. Ouellette, M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99 (1986).
[CrossRef]

Piché, M.

F. Ouellette, M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99 (1986).
[CrossRef]

Pinto, J. F.

Pollock, C. R.

Roach, D. J.

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Sarukura, N.

Y. Ishida, N. Sarukura, H. Nakano, “Soliton-like pulse shaping in a cw passively mode-locked Ti:Al2O3laser,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990) p. 75.
[CrossRef]

Schaaf, H. W.

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Schmidt, A. J.

Schulz, P. A.

Sibbett, W.

P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39 (1989).
[CrossRef] [PubMed]

W. Sibbett, “Hybrid and passive mode locking in coupled-cavity lasers,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), pp. 2–7.
[CrossRef]

D. E. Spence, P. N. Kean, W. Sibbett, “Sub-100 fs pulse generation from a self-modelocked titanium-sapphire laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP10-1, p. 619.

Silberberg, Y.

H. A. Haus, Y. Silberberg, “Laser mode locking with addition of nonlinear index,” IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

Spence, D. E.

D. E. Spence, P. N. Kean, W. Sibbett, “Sub-100 fs pulse generation from a self-modelocked titanium-sapphire laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP10-1, p. 619.

Spielmann, C.

Spinelli, L.

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feuget, “Sub-100 femtosecond pulse generation by Kerr lens modelocking in Ti:Al2O3,” in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), postdeadline paper.

Stolen, R. H.

Valdmanis, J. A.

Wang, C. Y.

Wang, J.

Watts, M. L.

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Whitaker, N. A.

H. Avramopoulos, H. Houh, N. A. Whitaker, M. C. Gabriel, “Passive modelocking of an erbium-doped fiber laser,” in Optical Amplifiers and Their Applications, Vol. 13 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper PdP8-1.

Wintner, E.

Wong, D. L.

Wood, D.

Yakymyshyn, C. P.

Yamamoto, Y.

Zhu, X.

IEEE J. Quantum Electron.

H. A. Haus, Y. Silberberg, “Laser mode locking with addition of nonlinear index,” IEEE J. Quantum Electron. QE-22, 325 (1986).
[CrossRef]

IEEE Photon. Tech. Lett.

A. G. Bulushev, E. M. Dianov, O. G. Okhotnikov, “Intracavity pulse compression in a laser with nonlinear resonator,” IEEE Photon. Tech. Lett. 2, 699 (1990).
[CrossRef]

J. Appl. Phys.

H. A. Haus, “A theory of fast saturable absorber modelocking,” J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

L. Dahlström, “Passive mode-locking and Q-switching of high power lasers by means of the optical Kerr effect,” Opt. Commun. 5, 157 (1972).
[CrossRef]

F. Ouellette, M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99 (1986).
[CrossRef]

Opt. Lett.

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

R. L. Fork, O. E. Martinez, J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150 (1984).
[CrossRef] [PubMed]

J. A. Valdmanis, R. L. Fork, J. P. Gordon, “Generation of optical pulses as short as 27 femtoseconds directly from a laser balancing self-phase modulation, group-velocity dispersion, saturable absorption, and saturation gain,” Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

K. J. Blow, B. P. Nelson, “Improved mode locking of an F-center laser with a nonlinear nonsoliton external cavity,” Opt. Lett. 13, 1026 (1988).
[CrossRef] [PubMed]

P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39 (1989).
[CrossRef] [PubMed]

J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48 (1989).
[CrossRef] [PubMed]

M. J. LaGasse, D. L. Wong, J. G. Fujimoto, H. A. Haus, “Ultrafast switching with a single-fiber interferometer,” Opt. Lett. 14, 311 (1989).
[CrossRef] [PubMed]

C. P. Yakymyshyn, J. F. Pinto, C. R. Pollock, “Additive-pulse mode-locked NaCl:OH−laser,” Opt. Lett. 14, 621 (1989).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schulz, “Femtosecond passively mode-locked laser with a Ti:Al2O3nonlinear external cavity,” Opt. Lett. 14, 1125 (1989).
[CrossRef] [PubMed]

E. P. Ippen, L. Y. Liu, H. A. Haus, “Self-starting condition for additive-pulse mode-locked lasers,” Opt. Lett. 15, 183 (1990).
[CrossRef] [PubMed]

J. Goodberlet, J. Jacobson, J. G. Fujimoto, P. A. Schulz, T. Y. Fan, “Self-starting additive-pulse mode-locked diode-pumped Nd:YAG laser,” Opt. Lett. 15, 504 (1990).
[CrossRef] [PubMed]

L. Y. Liu, J. M. Huxley, E. P. Ippen, H. A. Haus, “Self-starting additive-pulse mode locking of a Nd:YAG laser,” Opt. Lett. 15, 553 (1990).
[CrossRef] [PubMed]

J. M. Liu, J. K. Chee, “Passive mode locking of a cw Nd:YAG laser with a nonlinear external coupled cavity,” Opt. Lett. 15, 685 (1990).
[CrossRef] [PubMed]

F. Krausz, C. Spielmann, T. Brabec, E. Wintner, A. J. Schmidt, “Subpicosecond pulse generation from a Nd:glass laser using a nonlinear external cavity,” Opt. Lett. 15, 737 (1990).
[CrossRef] [PubMed]

C. Y. Wang, Y. Ishida, Y. Yamamoto, “Self-phase-modulation-controlled passively mode-locked dye laser,” Opt. Lett. 15, 965 (1990).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schulz, “Starting dynamics of additive pulse mode locking in the Ti:Al2O3laser,” Opt. Lett. 15, 1300 (1990).
[CrossRef] [PubMed]

Other

H. Avramopoulos, H. Houh, N. A. Whitaker, M. C. Gabriel, “Passive modelocking of an erbium-doped fiber laser,” in Optical Amplifiers and Their Applications, Vol. 13 of 1990 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper PdP8-1.

I. N. Duling, “All-fiber modelocked figure eight laser,” in Optical Society of America 1990 Annual Meeting, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), pp. 306–310.

W. Sibbett, “Hybrid and passive mode locking in coupled-cavity lasers,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), pp. 2–7.
[CrossRef]

J. D. Kafka, M. L. Watts, D. J. Roach, M. S. Keirstead, H. W. Schaaf, T. Baer, “Pulse compression of a mode-locked Ti:sapphire laser,” in Ultrafast Phenomena VIIC. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990), p. 66.
[CrossRef]

Y. Ishida, N. Sarukura, H. Nakano, “Soliton-like pulse shaping in a cw passively mode-locked Ti:Al2O3laser,” in Ultrafast Phenomena VII, C. B. Harris, E. P. Ippen, G. A. Mourou, A. H. Zewail, eds., Vol. 53 of Springer Series in Chemical Physics (Springer-Verlag, Berlin, 1990) p. 75.
[CrossRef]

D. E. Spence, P. N. Kean, W. Sibbett, “Sub-100 fs pulse generation from a self-modelocked titanium-sapphire laser,” in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1990), paper CPDP10-1, p. 619.

J. Jacobson, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication).

D. K. Negus, L. Spinelli, N. Goldblatt, G. Feuget, “Sub-100 femtosecond pulse generation by Kerr lens modelocking in Ti:Al2O3,” in Digest of Topical Meeting on Advanced Solid State Lasers (Optical Society of America, Washington, D.C., 1991), postdeadline paper.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic of ring cavity with gain, gain dispersion, SPM, GVD, fast saturable absorption, and linear loss and phase shift.

Fig. 2
Fig. 2

Pulse parameters versus normalized dispersion Dn for γ = 1 and different SPM parameters δ: (a) the chirp parameter β, (b) the inverse normalized pulse width τ, (c) the bandwidth (1 + β2)1/2/τ, (d) the stability criterion.

Fig. 3
Fig. 3

Pulse parameters versus normalized dispersion Dn for δ = 4 and different saturable absorption parameters γ: (a) the chirp parameter β, (b) the normalized pulse width τn, (c) the bandwidth (1 + β)1/2/τ (d) the stability criterion.

Fig. 4
Fig. 4

Schematic of the two-cavity APM system.

Fig. 5
Fig. 5

Interferometric APM systems. (a) Ring cavity with an interferometer. (b) Standing-wave cavity–half of the cavity of Fig. 4(a). (c) Two-cavity system with the properties of system (b); APM with an auxiliary cavity and a beam splitter. (d) Special case of (c) involving a linear cavity [simplified version of Fig. 4(c)].

Tables (1)

Tables Icon

Table 1 Signs of β and Signs of Square Root

Equations (55)

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

Δ a = - ( l + j x ) a
Δ a = g ( 1 + 1 Ω g 2 d 2 d t 2 ) a ,
Δ a = j D d 2 d t 2 a ,
D = 1 2 k d .
Δ a = - j δ a 2 a
δ = ω 0 c n 2 d A eff ,
Δ a = γ a 2 a ,
Δ a = exp ( - j ψ ) a - a = - j ψ a .
[ - j ψ - ( l + j x ) + g ( 1 + 1 Ω g 2 d 2 d t 2 ) + j D d 2 d t 2 + ( γ - j δ ) a 2 ] a = 0.
a = A sech ( t / τ ) exp [ j β l n sech ( t / τ ) ]
τ 2 d 2 d t 2 a = [ - ( 2 + 3 j β - β 2 ) sech 2 ( t τ ) + ( 1 + j β ) 2 ] a .
- j ψ + g - l - j x + ( 1 + j β ) 2 τ 2 ( g Ω g 2 + j D ) = 0 ,
1 τ 2 ( g Ω g 2 + j D ) ( 2 + 3 j β - β 2 ) = ( γ - j δ ) A 2 .
g = g 0 ( 1 + 2 A 2 τ / P s T R ) = g 0 1 + W / P s T R ,
τ n = ( W Ω g 2 / 2 g ) τ
D n = ( Ω g 2 / g ) D .
( 1 / τ n ) ( 1 + j D n ) ( 2 + 3 j β - β 2 ) = γ - j δ .
3 β 2 - β 2 = δ + γ D n δ D n - γ 1 χ .
β = - 3 2 χ ± [ ( 3 2 χ ) 2 + 2 ] 1 / 2 .
τ n = 2 - 3 β D n - β 2 γ = - 2 D n - 3 β + D n β 2 δ .
w n = ( 1 + β 2 ) 1 / 2 ( 1 / τ n ) .
g - l + 1 - β 2 τ 2 g Ω g 2 - 2 β D τ 2 = 0.
g - g cw = - ( 1 - β 2 ) g Ω g 2 τ 2 + 2 β D τ 2 < 0.
- a * [ g ( 1 + 1 Ω g 2 d 2 d τ 2 ) - l + γ a 2 ] a d t + c . c . = 0.
2 ( g - l ) - a 2 d t - 2 g Ω g 2 - | d a d t | 2 d t + 2 γ a 4 d t = 0.
[ 2 ( g - l ) - 2 3 g Ω g 2 τ 2 ( 1 + β 2 ) + 4 3 γ A 2 ] a 2 d t = 0.
( 1 - β 2 ) - 2 β D n > 0
b 1 = r a 1 + ( 1 - r 2 ) 1 / 2 a 2 ,
b 2 = ( 1 - r 2 ) 1 / 2 a 1 - r a 2 .
O ^ i = exp ( - j Φ 1 ) ( 1 + g i + g i 1 ω g i 2 d 2 d t 2 + j D i d 2 d t 2 ) 1 - j Φ i + g i ( 1 + 1 ω g i 2 d d t 2 ) + j D i d 2 d t 2 1 + o ^ i ,
Φ i = κ i a 1 2 ,             i = 1 , 2 ,
Γ = b 1 / a 1 = r + L ( 1 - r 2 ) exp ( - j ϕ ) O ^ 2 .
a 1 = O ^ 1 b 1 .
exp ( - j θ ) O ^ 1 Γ a 1 = a 1 .
exp ( - j θ 0 ) ( 1 + g 1 ) Γ 0 a 1 = a 1 ,
Γ 0 = r + L ( 1 - r 2 ) exp ( - j ϕ ) ( 1 + g 2 ) .
sin θ 0 θ 0 = - L 1 - r 2 r sin ϕ .
g Ω g 2 = r g 1 ω g 1 2 + L ( 1 - r 2 ) ( g 2 ω g 2 2 cos ϕ + D 2 sin ϕ ) ,
D = r D 1 + L ( 1 - r 2 ) ( D 2 cos ϕ - D 1 sin ϕ ) ,
γ = L ( 1 - r 2 ) ( κ 1 - κ 2 ) sin ϕ ,
δ = κ 1 + L ( 1 - r 2 ) κ 2 cos ϕ ,
l = 1 - Γ 0 ,
x = 0 ,
g = r g 1 + L ( 1 - r 2 ) g 2 cos ϕ .
exp ( - j θ ) [ r 2 O ^ 1 + ( 1 - r 2 ) exp ( - j ϕ ) O ^ 2 ] O ^ 3 a = a .
sin θ 0 θ 0 = - 1 - r 2 r 2 sin ϕ .
g Ω g 2 = r 2 g 1 ω g 1 2 + ( 1 - r 2 ) g 2 ω g 2 2 cos ϕ + g 3 ω g 3 2 - ( 1 - r 2 ) ( D 1 - D 2 ) sin ϕ ,
D = r 2 D 1 + ( 1 - r 2 ) D 2 + D 3 - ( 1 - r 2 ) × ( g 1 ω g 1 2 - g 2 ω g 2 2 sin ϕ ) ,
γ = ( κ 2 - κ 1 ) ( 1 - r 2 ) sin ϕ ,
δ = r 2 κ 1 + ( 1 - r 2 ) κ 2 cos ϕ + κ 3 ,
l = ( 1 - r 2 ) ( 1 - cos ϕ ) ,
x = ( sin ϕ ) ( 1 - r 2 ) ,
g = r 2 g 1 + ( 1 - r 2 ) g 2 cos ϕ + g 3 .
g / Ω g 2 τ 2 = γ A 2 / 2.
τ = ( 1 / Ω g ) 1 / 5 .

Metrics