Abstract

The pulse duration tp of a colliding-pulse mode-locked dye laser is measured versus the intracavity third-order dispersion (TOD), where the group-velocity dispersion is optimized by a four-prism sequence. The intracavity TOD is varied by the addition of layers on quarter-wave dielectric-multilayer mirrors. The shortest pulse is observed at a nonzero TOD. The TOD dependence of tp is explained by a new model that describes the saturation of absorption and gain dyes in the frequency domain, with the assumption of a steady sech2-shaped pulse with weak chirp and a negligible fast self-phase modulation.

© 1991 Optical Society of America

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  1. J. J. Fontaine, W. Dietel, J. C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
    [CrossRef]
  2. J. A. Valdmanis, R. L. Fork, “Design considerations for a femtosecond pulse laser balancing self phase modulation, group velocity dispersion, saturable absorption and saturable gain,” IEEE J. Quantum Electron. QE-22, 112 (1986).
    [CrossRef]
  3. J. Heppner, J. Kuhl, “Intracavity chirp compensation in a colliding pulse mode-locked laser using thin-film interferometers,” Appl. Phys. Lett. 47, 453 (1985).
    [CrossRef]
  4. M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, “Femtosecond-pulse laser chirp compensated by cavity-mirror dispersion,” Opt. Lett. 11, 504 (1986).
    [CrossRef] [PubMed]
  5. M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident-angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. QE-23, 2005 (1987).
    [CrossRef]
  6. M. Yamashita, S. Kaga, K. Torizuka, “Chirp-compensation cavity-mirrors with minimal third-order dispersion for use in a femtosecond pulse laser,” Opt. Commun. 76, 363 (1990).
    [CrossRef]
  7. 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 saturable gain,” Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  8. R. S. Miranda, G. R. Jacobovitz, C. H. Brito Cruz, M. A. F. Scarparo, “Positive and negative chirping of laser pulses shorter than 100 fsec in a saturable absorber,” Opt. Lett. 11, 224 (1986).
    [CrossRef] [PubMed]
  9. G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum. Electron. QE-10, 115 (1974).
    [CrossRef]
  10. H. A. Haus, “Parameter ranges for cw passive mode locking,” IEEE J. Quantum Electron. QE-12, 169 (1976).
    [CrossRef]
  11. D. Khühlke, W. Rudolph, B. Wilhelmi, “Influence of transient absorber gratings on the pulse parameters of passively mode-locked cw dye ring lasers,” Appl. Phys. Lett. 42, 325 (1983).
    [CrossRef]
  12. J. Herrmann, B. Wilhelmi, Lasers for Ultrashort Light Pulses (North-Holland, Amsterdam, 1987), Chap. 6.
  13. S. Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-20, 533 (1984).
    [CrossRef]
  14. 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]
  15. H. A. Haus, Y. Silberberg, “Laser mode locking with addition of a nonlinear index,” IEEE J. Quantum Electron. QE-22, 325 (1986).
    [CrossRef]
  16. F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
    [CrossRef]
  17. F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
    [CrossRef] [PubMed]
  18. F. W. Wise, I. A. Walmsley, C. L. Tang, “Simultaneous formation of solitons and dispersive waves in a femtosecond ring dye laser,” Opt. Lett. 13, 129 (1988).
    [CrossRef] [PubMed]
  19. C. Wang, Y. Ishida, Y. Yamamoto, “Self-phase-modulation-controlled passively mode-locked dye laser,” Opt. Lett. 15, 965 (1990).
    [CrossRef] [PubMed]
  20. H. Avramopoulos, G. H. C. New, “A numerical model for the study of phase effects in passive mode-locking,” Opt. Commun. 71, 370 (1989).
    [CrossRef]
  21. H. Avramopoulos, R. L. Fork, “Bandwidth limitation and distinct operating regimes of passively mode-locked dye lasers using strong phase shaping,” J. Opt. Soc. Am. B 8, 117 (1990).
    [CrossRef]
  22. D. Khühlke, T. Bonkhofer, D. Von der Linde, “Pulse fluctuations and chirp compensation in colliding-pulse mode-locked dye lasers,” Opt. Commun. 59, 208 (1986).
    [CrossRef]
  23. R. L. Fork, C. H. Brito Cruz, P. C. Becker, C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483 (1987).
    [CrossRef] [PubMed]
  24. M. R. X. de Barros, R. S. Miranda, C. H. Brito Cruz, “Third-order group-velocity dispersion in a colliding-pulse mode-locked dye laser,” Opt. Lett. 15, 127 (1990).
    [CrossRef] [PubMed]
  25. H. Goto, K. Ueda, S. Hashiguti, Y. Kawano, “Generation of the range of 20 to 30 fs light pulses by 3-rd order phase dispersion compensation,” in Extended Abstracts No. 3 The 37-th Spring Meeting (Japan Society of Applied Physics, Tokyo, 1990), paper 30p-G-10, p. 866.
  26. F. Salin, P. Grangier, P. Georges, A. Brun, “Pulse propagation near zero group-velocity dispersion in a femtosecond dye laser,” Opt. Lett. 15, 1374 (1990).
    [CrossRef] [PubMed]

1990

1989

H. Avramopoulos, G. H. C. New, “A numerical model for the study of phase effects in passive mode-locking,” Opt. Commun. 71, 370 (1989).
[CrossRef]

1988

F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
[CrossRef] [PubMed]

F. W. Wise, I. A. Walmsley, C. L. Tang, “Simultaneous formation of solitons and dispersive waves in a femtosecond ring dye laser,” Opt. Lett. 13, 129 (1988).
[CrossRef] [PubMed]

1987

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident-angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. QE-23, 2005 (1987).
[CrossRef]

R. L. Fork, C. H. Brito Cruz, P. C. Becker, C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

1986

D. Khühlke, T. Bonkhofer, D. Von der Linde, “Pulse fluctuations and chirp compensation in colliding-pulse mode-locked dye lasers,” Opt. Commun. 59, 208 (1986).
[CrossRef]

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

F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
[CrossRef]

R. S. Miranda, G. R. Jacobovitz, C. H. Brito Cruz, M. A. F. Scarparo, “Positive and negative chirping of laser pulses shorter than 100 fsec in a saturable absorber,” Opt. Lett. 11, 224 (1986).
[CrossRef] [PubMed]

J. A. Valdmanis, R. L. Fork, “Design considerations for a femtosecond pulse laser balancing self phase modulation, group velocity dispersion, saturable absorption and saturable gain,” IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, “Femtosecond-pulse laser chirp compensated by cavity-mirror dispersion,” Opt. Lett. 11, 504 (1986).
[CrossRef] [PubMed]

1985

1984

S. Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

1983

D. Khühlke, W. Rudolph, B. Wilhelmi, “Influence of transient absorber gratings on the pulse parameters of passively mode-locked cw dye ring lasers,” Appl. Phys. Lett. 42, 325 (1983).
[CrossRef]

J. J. Fontaine, W. Dietel, J. C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

1976

H. A. Haus, “Parameter ranges for cw passive mode locking,” IEEE J. Quantum Electron. QE-12, 169 (1976).
[CrossRef]

1974

G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum. Electron. QE-10, 115 (1974).
[CrossRef]

Avramopoulos, H.

H. Avramopoulos, R. L. Fork, “Bandwidth limitation and distinct operating regimes of passively mode-locked dye lasers using strong phase shaping,” J. Opt. Soc. Am. B 8, 117 (1990).
[CrossRef]

H. Avramopoulos, G. H. C. New, “A numerical model for the study of phase effects in passive mode-locking,” Opt. Commun. 71, 370 (1989).
[CrossRef]

Becker, P. C.

Bonkhofer, T.

D. Khühlke, T. Bonkhofer, D. Von der Linde, “Pulse fluctuations and chirp compensation in colliding-pulse mode-locked dye lasers,” Opt. Commun. 59, 208 (1986).
[CrossRef]

Brito Cruz, C. H.

Brun, A.

F. Salin, P. Grangier, P. Georges, A. Brun, “Pulse propagation near zero group-velocity dispersion in a femtosecond dye laser,” Opt. Lett. 15, 1374 (1990).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
[CrossRef]

de Barros, M. R. X.

Diels, J. C.

J. J. Fontaine, W. Dietel, J. C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

Dietel, W.

J. J. Fontaine, W. Dietel, J. C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

Fontaine, J. J.

J. J. Fontaine, W. Dietel, J. C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

Fork, R. L.

Georges, P.

Gordon, J. P.

Goto, H.

H. Goto, K. Ueda, S. Hashiguti, Y. Kawano, “Generation of the range of 20 to 30 fs light pulses by 3-rd order phase dispersion compensation,” in Extended Abstracts No. 3 The 37-th Spring Meeting (Japan Society of Applied Physics, Tokyo, 1990), paper 30p-G-10, p. 866.

Grangier, P.

F. Salin, P. Grangier, P. Georges, A. Brun, “Pulse propagation near zero group-velocity dispersion in a femtosecond dye laser,” Opt. Lett. 15, 1374 (1990).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
[CrossRef]

Hashiguti, S.

H. Goto, K. Ueda, S. Hashiguti, Y. Kawano, “Generation of the range of 20 to 30 fs light pulses by 3-rd order phase dispersion compensation,” in Extended Abstracts No. 3 The 37-th Spring Meeting (Japan Society of Applied Physics, Tokyo, 1990), paper 30p-G-10, p. 866.

Haus, H. A.

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

H. A. Haus, “Parameter ranges for cw passive mode locking,” IEEE J. Quantum Electron. QE-12, 169 (1976).
[CrossRef]

Heppner, J.

J. Heppner, J. Kuhl, “Intracavity chirp compensation in a colliding pulse mode-locked laser using thin-film interferometers,” Appl. Phys. Lett. 47, 453 (1985).
[CrossRef]

Herrmann, J.

J. Herrmann, B. Wilhelmi, Lasers for Ultrashort Light Pulses (North-Holland, Amsterdam, 1987), Chap. 6.

Ishida, Y.

Ishikawa, M.

Jacobovitz, G. R.

Kaga, S.

M. Yamashita, S. Kaga, K. Torizuka, “Chirp-compensation cavity-mirrors with minimal third-order dispersion for use in a femtosecond pulse laser,” Opt. Commun. 76, 363 (1990).
[CrossRef]

Kawano, Y.

H. Goto, K. Ueda, S. Hashiguti, Y. Kawano, “Generation of the range of 20 to 30 fs light pulses by 3-rd order phase dispersion compensation,” in Extended Abstracts No. 3 The 37-th Spring Meeting (Japan Society of Applied Physics, Tokyo, 1990), paper 30p-G-10, p. 866.

Khühlke, D.

D. Khühlke, T. Bonkhofer, D. Von der Linde, “Pulse fluctuations and chirp compensation in colliding-pulse mode-locked dye lasers,” Opt. Commun. 59, 208 (1986).
[CrossRef]

D. Khühlke, W. Rudolph, B. Wilhelmi, “Influence of transient absorber gratings on the pulse parameters of passively mode-locked cw dye ring lasers,” Appl. Phys. Lett. 42, 325 (1983).
[CrossRef]

Kuhl, J.

J. Heppner, J. Kuhl, “Intracavity chirp compensation in a colliding pulse mode-locked laser using thin-film interferometers,” Appl. Phys. Lett. 47, 453 (1985).
[CrossRef]

Laporta, P.

S. Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

Martinez, O. E.

Miranda, R. S.

New, G. H. C.

H. Avramopoulos, G. H. C. New, “A numerical model for the study of phase effects in passive mode-locking,” Opt. Commun. 71, 370 (1989).
[CrossRef]

G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum. Electron. QE-10, 115 (1974).
[CrossRef]

Roger, G.

F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
[CrossRef]

Rudolph, W.

D. Khühlke, W. Rudolph, B. Wilhelmi, “Influence of transient absorber gratings on the pulse parameters of passively mode-locked cw dye ring lasers,” Appl. Phys. Lett. 42, 325 (1983).
[CrossRef]

Salin, F.

F. Salin, P. Grangier, P. Georges, A. Brun, “Pulse propagation near zero group-velocity dispersion in a femtosecond dye laser,” Opt. Lett. 15, 1374 (1990).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
[CrossRef] [PubMed]

F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
[CrossRef]

Sato, T.

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident-angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. QE-23, 2005 (1987).
[CrossRef]

M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, “Femtosecond-pulse laser chirp compensated by cavity-mirror dispersion,” Opt. Lett. 11, 504 (1986).
[CrossRef] [PubMed]

Scarparo, M. A. F.

Shank, C. V.

Silberberg, Y.

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

Silvestri, S.

S. Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

Svelto, O.

S. Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

Tang, C. L.

Torizuka, K.

M. Yamashita, S. Kaga, K. Torizuka, “Chirp-compensation cavity-mirrors with minimal third-order dispersion for use in a femtosecond pulse laser,” Opt. Commun. 76, 363 (1990).
[CrossRef]

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident-angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. QE-23, 2005 (1987).
[CrossRef]

M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, “Femtosecond-pulse laser chirp compensated by cavity-mirror dispersion,” Opt. Lett. 11, 504 (1986).
[CrossRef] [PubMed]

Ueda, K.

H. Goto, K. Ueda, S. Hashiguti, Y. Kawano, “Generation of the range of 20 to 30 fs light pulses by 3-rd order phase dispersion compensation,” in Extended Abstracts No. 3 The 37-th Spring Meeting (Japan Society of Applied Physics, Tokyo, 1990), paper 30p-G-10, p. 866.

Valdmanis, J. A.

J. A. Valdmanis, R. L. Fork, “Design considerations for a femtosecond pulse laser balancing self phase modulation, group velocity dispersion, saturable absorption and saturable gain,” IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

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 saturable gain,” Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

Von der Linde, D.

D. Khühlke, T. Bonkhofer, D. Von der Linde, “Pulse fluctuations and chirp compensation in colliding-pulse mode-locked dye lasers,” Opt. Commun. 59, 208 (1986).
[CrossRef]

Walmsley, I. A.

Wang, C.

Wilhelmi, B.

D. Khühlke, W. Rudolph, B. Wilhelmi, “Influence of transient absorber gratings on the pulse parameters of passively mode-locked cw dye ring lasers,” Appl. Phys. Lett. 42, 325 (1983).
[CrossRef]

J. Herrmann, B. Wilhelmi, Lasers for Ultrashort Light Pulses (North-Holland, Amsterdam, 1987), Chap. 6.

Wise, F. W.

Yamamoto, Y.

Yamashita, M.

M. Yamashita, S. Kaga, K. Torizuka, “Chirp-compensation cavity-mirrors with minimal third-order dispersion for use in a femtosecond pulse laser,” Opt. Commun. 76, 363 (1990).
[CrossRef]

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident-angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. QE-23, 2005 (1987).
[CrossRef]

M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, “Femtosecond-pulse laser chirp compensated by cavity-mirror dispersion,” Opt. Lett. 11, 504 (1986).
[CrossRef] [PubMed]

Appl. Phys. Lett.

J. Heppner, J. Kuhl, “Intracavity chirp compensation in a colliding pulse mode-locked laser using thin-film interferometers,” Appl. Phys. Lett. 47, 453 (1985).
[CrossRef]

D. Khühlke, W. Rudolph, B. Wilhelmi, “Influence of transient absorber gratings on the pulse parameters of passively mode-locked cw dye ring lasers,” Appl. Phys. Lett. 42, 325 (1983).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Haus, “Parameter ranges for cw passive mode locking,” IEEE J. Quantum Electron. QE-12, 169 (1976).
[CrossRef]

S. Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

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

J. J. Fontaine, W. Dietel, J. C. Diels, “Chirp in a mode-locked ring dye laser,” IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

J. A. Valdmanis, R. L. Fork, “Design considerations for a femtosecond pulse laser balancing self phase modulation, group velocity dispersion, saturable absorption and saturable gain,” IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

M. Yamashita, K. Torizuka, T. Sato, “A chirp-compensation technique using incident-angle changes of cavity mirrors in a femtosecond pulse laser,” IEEE J. Quantum Electron. QE-23, 2005 (1987).
[CrossRef]

IEEE J. Quantum. Electron.

G. H. C. New, “Pulse evolution in mode-locked quasi-continuous lasers,” IEEE J. Quantum. Electron. QE-10, 115 (1974).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

D. Khühlke, T. Bonkhofer, D. Von der Linde, “Pulse fluctuations and chirp compensation in colliding-pulse mode-locked dye lasers,” Opt. Commun. 59, 208 (1986).
[CrossRef]

H. Avramopoulos, G. H. C. New, “A numerical model for the study of phase effects in passive mode-locking,” Opt. Commun. 71, 370 (1989).
[CrossRef]

M. Yamashita, S. Kaga, K. Torizuka, “Chirp-compensation cavity-mirrors with minimal third-order dispersion for use in a femtosecond pulse laser,” Opt. Commun. 76, 363 (1990).
[CrossRef]

Opt. Lett.

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 saturable gain,” Opt. Lett. 10, 131 (1985).
[CrossRef] [PubMed]

R. S. Miranda, G. R. Jacobovitz, C. H. Brito Cruz, M. A. F. Scarparo, “Positive and negative chirping of laser pulses shorter than 100 fsec in a saturable absorber,” Opt. Lett. 11, 224 (1986).
[CrossRef] [PubMed]

M. Yamashita, M. Ishikawa, K. Torizuka, T. Sato, “Femtosecond-pulse laser chirp compensated by cavity-mirror dispersion,” Opt. Lett. 11, 504 (1986).
[CrossRef] [PubMed]

F. Salin, P. Grangier, P. Georges, A. Brun, “Pulse propagation near zero group-velocity dispersion in a femtosecond dye laser,” Opt. Lett. 15, 1374 (1990).
[CrossRef] [PubMed]

F. W. Wise, I. A. Walmsley, C. L. Tang, “Simultaneous formation of solitons and dispersive waves in a femtosecond ring dye laser,” Opt. Lett. 13, 129 (1988).
[CrossRef] [PubMed]

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

R. L. Fork, C. H. Brito Cruz, P. C. Becker, C. V. Shank, “Compression of optical pulses to six femtoseconds by using cubic phase compensation,” Opt. Lett. 12, 483 (1987).
[CrossRef] [PubMed]

M. R. X. de Barros, R. S. Miranda, C. H. Brito Cruz, “Third-order group-velocity dispersion in a colliding-pulse mode-locked dye laser,” Opt. Lett. 15, 127 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

F. Salin, P. Grangier, G. Roger, A. Brun, “Observation of high-order solitons directly produced by a femtosecond ring laser,” Phys. Rev. Lett. 36, 1132 (1986).
[CrossRef]

F. Salin, P. Grangier, G. Roger, A. Brun, “Experimental observation of nonsymmetrical N= 2 solitons in a femtosecond laser,” Phys. Rev. Lett. 60, 569 (1988).
[CrossRef] [PubMed]

Other

J. Herrmann, B. Wilhelmi, Lasers for Ultrashort Light Pulses (North-Holland, Amsterdam, 1987), Chap. 6.

H. Goto, K. Ueda, S. Hashiguti, Y. Kawano, “Generation of the range of 20 to 30 fs light pulses by 3-rd order phase dispersion compensation,” in Extended Abstracts No. 3 The 37-th Spring Meeting (Japan Society of Applied Physics, Tokyo, 1990), paper 30p-G-10, p. 866.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the cavity configurations. The ring cavity-length is ~4 m (Abs., absorber).

Fig. 2
Fig. 2

Calculated frequency dependencies of the second-order dispersion φ i ( 2 ) (dashed curves) and the TOD’s φ i ( 3 ) (solid curves) of TOD-tuning mirrors a and b.

Fig. 3
Fig. 3

Higher-order dispersions in the expansions at frequency ω0 = 2.98 × 1015 rad/s. Mirrors a and b are the same as those in Fig. 2.

Fig. 4
Fig. 4

Pulse duration tp versus the negative TOD φ(3). Gain dye, Rh6G 2.9 mM: Kiton Red 0.8 mM; saturable absorber, DODCI 1.0 mM (triangles), 1.5 mM (circles), and 3.8 mM (crosses).

Fig. 5
Fig. 5

Schematic diagram of the analytical model. The complex propagators of the saturable gain γg, the saturable absorption γa, and the nonlinear refractive material γf are dependent on the pulse amplitude and phase. The cavity loss is mainly due to the transmission ∑iti of the mirrors. The phase delay of the mirrors ∑iφi and the prism sequence φps are controlled in the experiments.

Fig. 6
Fig. 6

Pulse durations versus GVD, calculated by the frequency-domain model for the present CPM dye laser. In addition to the results obtained for the weak-chirp model of Eq. (2) (solid curves), the results for the usual chirping model (see text; dashed curves) with various fast SPM’s and κΓT equal to 0, 0.4, and 0.8 fs are shown as curves A, B, and C, respectively.

Fig. 7
Fig. 7

Theoretical curves for pulse durations versus TOD for positive r and s. The normalization factors τ0 and φ 0 ( 3 ) are given in the text.

Equations (22)

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[ L ( 0.206 λ 0 ) - H ( 0.206 λ 0 ) ] 3 - [ L ( 0.264 λ 0 ) - H ( 0.264 λ 0 ) ] 12 , [ L ( 0.177 λ 0 ) - H ( 0.177 λ 0 ) ] 3 - [ L ( 0.248 λ 0 ) - H ( 0.248 λ 0 ) ] 12 , [ L ( 0.193 λ 0 ) - H ( 0.193 λ 0 ) ] 4 - [ L ( 0.237 λ 0 ) - H ( 0.237 λ 0 ) ] 12 ,
( t ) = E ( t ) exp ( i ω 0 t ) + E * ( t ) exp ( - i ω 0 t ) ,
E ( t ) = E 0 [ sech ( t / τ ) ] exp [ i Φ ( t / τ ) ] ,
exp [ i Φ ( t / τ ) ] = 1 + i [ c 2 2 ( t τ ) 2 + c 3 6 ( t τ ) 3 ] .
γ g = α g + i d g α g E ˜ ( ω ) - d t E ( t ) exp [ - Γ ( t ) Γ g - i Δ ω t ] , γ a = - α a - i d a α a E ˜ ( ω ) - d t E ( t ) exp [ - Γ ( t ) Γ a - i Δ ω t ] ,
Γ ( t ) = - t d t I ( t )
γ f = - i κ E ˜ ( ω ) - d t E ( t ) I ( t ) exp ( - i Δ ω t ) ,
γ = - i t i ,             γ = φ ps + i φ i .
γ g + γ a + γ f + γ m = i ( a + b τ Δ ω ) ,
P 1 + ( c 2 / 2 ) P 2 + ( c 3 / 6 ) P 3 + γ ( 0 ) = 0 ,
Q 1 + ( c 2 / 2 ) Q 2 + ( c 3 / 6 ) Q 3 + [ γ ( 1 ) / τ ] = 0 ,
R 1 + ( c 2 / 2 ) R 2 + ( c 3 / 6 ) R 3 + [ γ ( 2 ) / τ 2 ] = 0 ,
S 1 + ( c 2 / 2 ) S 2 + ( c 3 / 6 ) - ( κ Γ T / 2 τ ) + [ φ ( 2 ) / τ 2 ] = 0 ,
T 1 + ( c 2 / 2 ) T 2 + ( c 3 / 6 ) T 3 + [ γ ( 3 ) / τ 3 ] = 0 ,
U 1 + ( c 2 / 2 ) U 2 + ( c 3 / 6 ) U 3 + [ φ ( 3 ) / τ 3 ] = 0 ,
τ 2 - [ - κ Γ T τ + φ ( 2 ) ] p + q γ ( 2 ) = 0 ,
p = R 2 R 1 S 2 - R 2 S 1 ,             q = S 2 R 1 S 2 - R 2 S 1 .
τ 3 + r τ ( 2 ) τ + s φ ( 3 ) = 0 ,
r = | T 2 T 3 U 2 U 3 | / | R 1 R 2 R 3 T 1 T 2 T 3 U 1 U 2 U 3 | , s = | R 2 R 3 T 2 T 3 | / | R 1 R 2 R 3 T 1 T 2 T 3 U 1 U 2 U 3 | .
P i = P i g - P i a Q i = Q i g - Q i a , R i = R i g - R i a , S i = S i g - S i a , T i = T i g - T i a , U i = U i g - U i a ,
R g , a ( n ) = 1 π - d η η n ( sech η ) exp [ - Γ T 2 Γ g , a ( 1 + tanh η ) ] ,
P 1 g = α g R g ( 0 ) ,             P 2 g = - α g d g [ R g ( 2 ) - ( π / 2 ) 2 R g ( 0 ) ] , P 3 g = - α g d g R g ( 3 ) ,             Q 1 g = α g d g R g ( 1 ) , Q 2 g = α g [ R g ( 3 ) - ( π / 2 ) 2 R g ( 1 ) ] ,             Q 3 g = α g [ R g ( 4 ) - 5 ( π / 2 ) 4 R g ( 0 ) ] , R 1 g = - α g [ R g ( 2 ) - ( π / 2 ) 2 R g ( 0 ) ] , S 2 g = - α g [ R g ( 4 ) - 2 ( π / 2 ) 2 R g ( 2 ) - 3 ( π / 2 ) 4 R g ( 0 ) ] , S 3 g = - α g [ R g ( 5 ) - ( π / 2 ) 2 R g ( 3 ) - 10 ( π / 2 ) 4 R g ( 1 ) ] , S 1 g = d g R 1 g ,             R 2 g = - d g S 2 g ,             R 3 g = - d g S 3 g , T 2 g = - α g [ R g ( 5 ) - 4 ( π / 2 ) 2 R g ( 3 ) - 9 ( π / 2 ) 4 R g ( 1 ) ] , T 3 g = - α g [ R g ( 6 ) - 3 ( π / 2 ) 2 R g ( 4 ) - 15 ( π / 2 ) 4 R g ( 2 ) - 31 ( π / 2 ) 6 R g ( 0 ) ] , U 1 g = α g [ R g ( 3 ) - 3 ( π / 2 ) 2 R g ( 1 ) ] ,             T 1 g = - d g U 1 g , U 2 g = d g T 2 g ,             U 3 g = d g T 3 g .

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