Abstract

By distributing the output coupling and the coupling of the external nonlinear cavity along the gain medium of the main cavity, I derive a nonlinear differential equation for a pulse envelope propagating through a coupled-cavity laser. For a phase-mismatch angle of π/2 between the two cavities, a stable hyperbolic-secant short pulse is a solution of the differential equation for negative dispersion (of the soliton into the fiber) as well as for positive dispersion of the nonlinear external medium. The width of the predicted pulse is a function of the coupling factor and the intensity traveling through the optical fiber. The operation of the coupled-cavity laser for this stable regime is shown to be completely similar to passive mode locking by a fast saturable absorber.

© 1991 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984).
    [CrossRef] [PubMed]
  2. F. M. Mitschke and L. F. Mollenauer, “Stabilizing the soliton laser,” IEEE J. Quantum Electron. QE-22, 2242–2250 (1986).
    [CrossRef]
  3. F. M. Mitschke and L. F. Mollenauer, “Ultrashort pulses from the soliton laser,” Opt. Lett. 12, 407–409 (1987).
    [CrossRef] [PubMed]
  4. X. Zhu, P. N. Kean, and W. Sibbett, “Spectral and temporal characterizations of coupled-cavity mode locking in a KCl:Tl color center laser,” IEEE J. Quantum Electron. 25, 2445–2453 (1989).
    [CrossRef]
  5. H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. QE-21, 1172–1188 (1985).
    [CrossRef]
  6. F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
    [CrossRef]
  7. K. J. Blow and D. Wood, “Stability and compression of pulses in the soliton laser,” IEEE J. Quantum Electron. QE-22, 1109–1116 (1986).
    [CrossRef]
  8. P. A. Bélanger, “Soliton laser. I: A simplified model,” J. Opt. Soc. Am. B 5, 793–798 (1988).
    [CrossRef]
  9. K. J. Blow and D. Wood, “Mode-locked lasers with nonlinear external cavities,” J. Opt. Soc. Am. B 5, 629–632 (1988).
    [CrossRef]
  10. K. J. Blow and B. P. Nelson, “Improved mode locking of a F-center laser with a nonlinear nonsoliton cavity,” Opt. Lett. 13, 1026–1028 (1988).
    [CrossRef] [PubMed]
  11. P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, and W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39–41 (1989).
    [CrossRef] [PubMed]
  12. J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, and E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48–50 (1989).
    [CrossRef] [PubMed]
  13. J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Femtosecond passively mode-locked Ti:Al2O3laser with a nonlinear external cavity,” Opt. Lett. 14, 1125–1127 (1989).
    [CrossRef] [PubMed]
  14. C. P. Yakymyshyn, J. F. Pinto, and C. R. Pollock, “Additive-pulse mode-locked NaCl:OH laser,” Opt. Lett. 14, 621–623 (1989).
    [CrossRef] [PubMed]
  15. S. M. J. Kelly, “Mode-locking dynamics of a laser coupled to an empty external cavity,” Opt. Commun. 70, 495–501 (1989).
    [CrossRef]
  16. E. P. Ippen, H. A. Haus, and L. Y. Liu, “Additive pulse mode locking,” J. Opt. Soc. Am. B 6, 1736–1745 (1989).
    [CrossRef]
  17. M. Morin and M. Piché, “Interferential mode-locking: Gaussian pulse analysis,” Opt. Lett. 14, 1119–1121 (1989).
    [CrossRef] [PubMed]
  18. P. A. Bélanger, L. Gagnon, and C. Paré, “Solitary pulses in an amplified nonlinear dispersive medium,” Opt. Lett. 14, 943–945 (1989).
    [CrossRef] [PubMed]
  19. The Fourier transform of this chirped solution is in C. Paré, L. Gagnon, and P. A. Bélanger, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
    [CrossRef]
  20. L. Y. Liu, J. M. Huxley, E. P. Ippen, and H. A. Haus, “Self-starting additive-pulse mode locking of a Nd:YAGlaser,” Opt. Lett. 15, 553–555 (1990).
    [CrossRef] [PubMed]
  21. J. M. Liu and J. K. Chee, “Passive mode locking of a cw Nd:YLF laser with a nonlinear external coupled cavity,” Opt. Lett. 15, 685–687 (1990).
    [CrossRef] [PubMed]
  22. X. Zhu, A. Finch, and W. Sibbett, “Pulse-shaping effects in a coupled-cavity mode-locked KCl:Tl laser,” J. Opt. Soc. Am. B 7, 1221–1224 (1990).
    [CrossRef]
  23. F. Krausz, Ch. Spielman, T. Brabec, E. Wintner, and A. J. Schmidt, “Subpicosecond pulse generation from a Nd:glass laser using a nonlinear external cavity,” Opt. Lett. 15, 737–739 (1990).
    [CrossRef] [PubMed]
  24. A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Passive mode locking a laser with a nonlinear fiber reflector,” Opt. Lett. 15, 968–970 (1990).
    [CrossRef] [PubMed]
  25. F. Krausz, Ch. Spielmann, T. Brabec, E. Wintner, and A. J. Schmidt, “Self-starting additive-pulse mode locking of a Nd:glass laser,” Opt. Lett. 15, 1082–1084 (1990).
    [CrossRef] [PubMed]
  26. X. Zhu and W. Sibbett, “Experimental study of the primary mode-locking parameters of a coupled-cavity KCl:Tl color-center laser,” J. Opt. Soc. Am. B 7, 2187–2191 (1990).
    [CrossRef]
  27. G. P. A. Malcolm, P. F. Curley, and A. I. Ferguson, “Additive-pulse mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 15, 1303–1305 (1990).
    [CrossRef] [PubMed]
  28. E. P. Ippen, L. Y. Liu, and H. A. Haus, “Self-starting condition for additive-pulse mode-locked lasers,” Opt. Lett. 15, 183–185 (1990).
    [CrossRef] [PubMed]
  29. J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Starting dynamics of additive-pulse mode locking in the Ti:Al2O3laser,” Opt. Lett. 15, 1300–1302 (1990).
    [CrossRef] [PubMed]
  30. 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]
  31. R. S. Grant, P. N. Kean, D. Burns, and W. Sibbett, “Passive coupled-cavity mode-locked color-center lasers,” Opt. Lett. 16, 384–386 (1991).
    [CrossRef] [PubMed]
  32. U. Keller, T. K. Woodward, D. L. Sivco, and A. Y. Cho, “Coupled-cavity resonant passive mode-locked Nd:yttrium lithium fluoride laser,” Opt. Lett. 16, 390–392 (1991).
    [CrossRef] [PubMed]
  33. F. Ouellette and M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99–103 (1989).
    [CrossRef]

1991 (2)

1990 (10)

L. Y. Liu, J. M. Huxley, E. P. Ippen, and H. A. Haus, “Self-starting additive-pulse mode locking of a Nd:YAGlaser,” Opt. Lett. 15, 553–555 (1990).
[CrossRef] [PubMed]

J. M. Liu and J. K. Chee, “Passive mode locking of a cw Nd:YLF laser with a nonlinear external coupled cavity,” Opt. Lett. 15, 685–687 (1990).
[CrossRef] [PubMed]

X. Zhu, A. Finch, and W. Sibbett, “Pulse-shaping effects in a coupled-cavity mode-locked KCl:Tl laser,” J. Opt. Soc. Am. B 7, 1221–1224 (1990).
[CrossRef]

F. Krausz, Ch. Spielman, T. Brabec, E. Wintner, and A. J. Schmidt, “Subpicosecond pulse generation from a Nd:glass laser using a nonlinear external cavity,” Opt. Lett. 15, 737–739 (1990).
[CrossRef] [PubMed]

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Passive mode locking a laser with a nonlinear fiber reflector,” Opt. Lett. 15, 968–970 (1990).
[CrossRef] [PubMed]

F. Krausz, Ch. Spielmann, T. Brabec, E. Wintner, and A. J. Schmidt, “Self-starting additive-pulse mode locking of a Nd:glass laser,” Opt. Lett. 15, 1082–1084 (1990).
[CrossRef] [PubMed]

X. Zhu and W. Sibbett, “Experimental study of the primary mode-locking parameters of a coupled-cavity KCl:Tl color-center laser,” J. Opt. Soc. Am. B 7, 2187–2191 (1990).
[CrossRef]

G. P. A. Malcolm, P. F. Curley, and A. I. Ferguson, “Additive-pulse mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 15, 1303–1305 (1990).
[CrossRef] [PubMed]

E. P. Ippen, L. Y. Liu, and H. A. Haus, “Self-starting condition for additive-pulse mode-locked lasers,” Opt. Lett. 15, 183–185 (1990).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Starting dynamics of additive-pulse mode locking in the Ti:Al2O3laser,” Opt. Lett. 15, 1300–1302 (1990).
[CrossRef] [PubMed]

1989 (11)

F. Ouellette and M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99–103 (1989).
[CrossRef]

X. Zhu, P. N. Kean, and W. Sibbett, “Spectral and temporal characterizations of coupled-cavity mode locking in a KCl:Tl color center laser,” IEEE J. Quantum Electron. 25, 2445–2453 (1989).
[CrossRef]

P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, and W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39–41 (1989).
[CrossRef] [PubMed]

J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, and E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48–50 (1989).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Femtosecond passively mode-locked Ti:Al2O3laser with a nonlinear external cavity,” Opt. Lett. 14, 1125–1127 (1989).
[CrossRef] [PubMed]

C. P. Yakymyshyn, J. F. Pinto, and C. R. Pollock, “Additive-pulse mode-locked NaCl:OH laser,” Opt. Lett. 14, 621–623 (1989).
[CrossRef] [PubMed]

S. M. J. Kelly, “Mode-locking dynamics of a laser coupled to an empty external cavity,” Opt. Commun. 70, 495–501 (1989).
[CrossRef]

E. P. Ippen, H. A. Haus, and L. Y. Liu, “Additive pulse mode locking,” J. Opt. Soc. Am. B 6, 1736–1745 (1989).
[CrossRef]

M. Morin and M. Piché, “Interferential mode-locking: Gaussian pulse analysis,” Opt. Lett. 14, 1119–1121 (1989).
[CrossRef] [PubMed]

P. A. Bélanger, L. Gagnon, and C. Paré, “Solitary pulses in an amplified nonlinear dispersive medium,” Opt. Lett. 14, 943–945 (1989).
[CrossRef] [PubMed]

The Fourier transform of this chirped solution is in C. Paré, L. Gagnon, and P. A. Bélanger, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

1988 (3)

1987 (1)

1986 (3)

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

K. J. Blow and D. Wood, “Stability and compression of pulses in the soliton laser,” IEEE J. Quantum Electron. QE-22, 1109–1116 (1986).
[CrossRef]

F. M. Mitschke and L. F. Mollenauer, “Stabilizing the soliton laser,” IEEE J. Quantum Electron. QE-22, 2242–2250 (1986).
[CrossRef]

1985 (2)

1984 (1)

Bélanger, P. A.

The Fourier transform of this chirped solution is in C. Paré, L. Gagnon, and P. A. Bélanger, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

P. A. Bélanger, L. Gagnon, and C. Paré, “Solitary pulses in an amplified nonlinear dispersive medium,” Opt. Lett. 14, 943–945 (1989).
[CrossRef] [PubMed]

P. A. Bélanger, “Soliton laser. I: A simplified model,” J. Opt. Soc. Am. B 5, 793–798 (1988).
[CrossRef]

Blow, K. J.

Brabec, T.

Bulushev, A. G.

Burns, D.

Chee, J. K.

Cho, A. Y.

Christensen, P. L.

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

Crust, D. W.

Curley, P. F.

Dianov, E. M.

Elgin, J. N.

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

Ferguson, A. I.

Finch, A.

Fork, R. L.

Fujimoto, J. G.

Gagnon, L.

The Fourier transform of this chirped solution is in C. Paré, L. Gagnon, and P. A. Bélanger, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

P. A. Bélanger, L. Gagnon, and C. Paré, “Solitary pulses in an amplified nonlinear dispersive medium,” Opt. Lett. 14, 943–945 (1989).
[CrossRef] [PubMed]

Gibson, J. P.

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

Goodberlet, J.

Gordon, J. P.

Grant, R. S.

Hall, K. L.

Haus, H. A.

Huxley, J. M.

If, F.

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

Ippen, E. P.

Islam, M. N.

H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. QE-21, 1172–1188 (1985).
[CrossRef]

Kean, P. N.

Keller, U.

Kelly, S. M. J.

S. M. J. Kelly, “Mode-locking dynamics of a laser coupled to an empty external cavity,” Opt. Commun. 70, 495–501 (1989).
[CrossRef]

Krausz, F.

Langford, N.

Liu, J. M.

Liu, L. Y.

Malcolm, G. P. A.

Mark, J.

Martinez, O. E.

Mitschke, F. M.

F. M. Mitschke and L. F. Mollenauer, “Ultrashort pulses from the soliton laser,” Opt. Lett. 12, 407–409 (1987).
[CrossRef] [PubMed]

F. M. Mitschke and L. F. Mollenauer, “Stabilizing the soliton laser,” IEEE J. Quantum Electron. QE-22, 2242–2250 (1986).
[CrossRef]

Mollenauer, L. F.

Morin, M.

Nelson, B. P.

Okhotnikov, O. G.

Ouellette, F.

F. Ouellette and M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99–103 (1989).
[CrossRef]

Paré, C.

The Fourier transform of this chirped solution is in C. Paré, L. Gagnon, and P. A. Bélanger, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

P. A. Bélanger, L. Gagnon, and C. Paré, “Solitary pulses in an amplified nonlinear dispersive medium,” Opt. Lett. 14, 943–945 (1989).
[CrossRef] [PubMed]

Piché, M.

M. Morin and M. Piché, “Interferential mode-locking: Gaussian pulse analysis,” Opt. Lett. 14, 1119–1121 (1989).
[CrossRef] [PubMed]

F. Ouellette and M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99–103 (1989).
[CrossRef]

Pinto, J. F.

Pollock, C. R.

Schmidt, A. J.

Schulz, P. A.

Sibbett, W.

Sivco, D. L.

Skovgaard, O.

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

Spielman, Ch.

Spielmann, Ch.

Stolen, R. H.

Wang, J.

Wintner, E.

Wood, D.

K. J. Blow and D. Wood, “Mode-locked lasers with nonlinear external cavities,” J. Opt. Soc. Am. B 5, 629–632 (1988).
[CrossRef]

K. J. Blow and D. Wood, “Stability and compression of pulses in the soliton laser,” IEEE J. Quantum Electron. QE-22, 1109–1116 (1986).
[CrossRef]

Woodward, T. K.

Yakymyshyn, C. P.

Zhu, X.

IEEE J. Quantum Electron. (4)

K. J. Blow and D. Wood, “Stability and compression of pulses in the soliton laser,” IEEE J. Quantum Electron. QE-22, 1109–1116 (1986).
[CrossRef]

F. M. Mitschke and L. F. Mollenauer, “Stabilizing the soliton laser,” IEEE J. Quantum Electron. QE-22, 2242–2250 (1986).
[CrossRef]

X. Zhu, P. N. Kean, and W. Sibbett, “Spectral and temporal characterizations of coupled-cavity mode locking in a KCl:Tl color center laser,” IEEE J. Quantum Electron. 25, 2445–2453 (1989).
[CrossRef]

H. A. Haus and M. N. Islam, “Theory of the soliton laser,” IEEE J. Quantum Electron. QE-21, 1172–1188 (1985).
[CrossRef]

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

Opt. Commun. (4)

The Fourier transform of this chirped solution is in C. Paré, L. Gagnon, and P. A. Bélanger, “Spatial solitary wave in a weakly saturated amplifying/absorbing medium,” Opt. Commun. 74, 228–232 (1989).
[CrossRef]

F. Ouellette and M. Piché, “Pulse shaping and passive mode-locking with a nonlinear Michelson interferometer,” Opt. Commun. 60, 99–103 (1989).
[CrossRef]

S. M. J. Kelly, “Mode-locking dynamics of a laser coupled to an empty external cavity,” Opt. Commun. 70, 495–501 (1989).
[CrossRef]

F. If, P. L. Christensen, J. N. Elgin, J. P. Gibson, and O. Skovgaard, “A theoretical and computational study of the soliton laser,” Opt. Commun. 57, 350–354 (1986).
[CrossRef]

Opt. Lett. (19)

F. M. Mitschke and L. F. Mollenauer, “Ultrashort pulses from the soliton laser,” Opt. Lett. 12, 407–409 (1987).
[CrossRef] [PubMed]

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

M. Morin and M. Piché, “Interferential mode-locking: Gaussian pulse analysis,” Opt. Lett. 14, 1119–1121 (1989).
[CrossRef] [PubMed]

P. A. Bélanger, L. Gagnon, and C. Paré, “Solitary pulses in an amplified nonlinear dispersive medium,” Opt. Lett. 14, 943–945 (1989).
[CrossRef] [PubMed]

K. J. Blow and B. P. Nelson, “Improved mode locking of a F-center laser with a nonlinear nonsoliton cavity,” Opt. Lett. 13, 1026–1028 (1988).
[CrossRef] [PubMed]

P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, and W. Sibbett, “Enhanced mode locking of color-center lasers,” Opt. Lett. 14, 39–41 (1989).
[CrossRef] [PubMed]

J. Mark, L. Y. Liu, K. L. Hall, H. A. Haus, and E. P. Ippen, “Femtosecond pulse generation in a laser with a nonlinear external resonator,” Opt. Lett. 14, 48–50 (1989).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Femtosecond passively mode-locked Ti:Al2O3laser with a nonlinear external cavity,” Opt. Lett. 14, 1125–1127 (1989).
[CrossRef] [PubMed]

C. P. Yakymyshyn, J. F. Pinto, and C. R. Pollock, “Additive-pulse mode-locked NaCl:OH laser,” Opt. Lett. 14, 621–623 (1989).
[CrossRef] [PubMed]

L. Y. Liu, J. M. Huxley, E. P. Ippen, and H. A. Haus, “Self-starting additive-pulse mode locking of a Nd:YAGlaser,” Opt. Lett. 15, 553–555 (1990).
[CrossRef] [PubMed]

J. M. Liu and J. K. Chee, “Passive mode locking of a cw Nd:YLF laser with a nonlinear external coupled cavity,” Opt. Lett. 15, 685–687 (1990).
[CrossRef] [PubMed]

R. S. Grant, P. N. Kean, D. Burns, and W. Sibbett, “Passive coupled-cavity mode-locked color-center lasers,” Opt. Lett. 16, 384–386 (1991).
[CrossRef] [PubMed]

U. Keller, T. K. Woodward, D. L. Sivco, and A. Y. Cho, “Coupled-cavity resonant passive mode-locked Nd:yttrium lithium fluoride laser,” Opt. Lett. 16, 390–392 (1991).
[CrossRef] [PubMed]

G. P. A. Malcolm, P. F. Curley, and A. I. Ferguson, “Additive-pulse mode locking of a diode-pumped Nd:YLF laser,” Opt. Lett. 15, 1303–1305 (1990).
[CrossRef] [PubMed]

E. P. Ippen, L. Y. Liu, and H. A. Haus, “Self-starting condition for additive-pulse mode-locked lasers,” Opt. Lett. 15, 183–185 (1990).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, and P. A. Schulz, “Starting dynamics of additive-pulse mode locking in the Ti:Al2O3laser,” Opt. Lett. 15, 1300–1302 (1990).
[CrossRef] [PubMed]

F. Krausz, Ch. Spielman, T. Brabec, E. Wintner, and A. J. Schmidt, “Subpicosecond pulse generation from a Nd:glass laser using a nonlinear external cavity,” Opt. Lett. 15, 737–739 (1990).
[CrossRef] [PubMed]

A. G. Bulushev, E. M. Dianov, and O. G. Okhotnikov, “Passive mode locking a laser with a nonlinear fiber reflector,” Opt. Lett. 15, 968–970 (1990).
[CrossRef] [PubMed]

F. Krausz, Ch. Spielmann, T. Brabec, E. Wintner, and A. J. Schmidt, “Self-starting additive-pulse mode locking of a Nd:glass laser,” Opt. Lett. 15, 1082–1084 (1990).
[CrossRef] [PubMed]

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 a coupled-cavity laser system.

Fig. 2
Fig. 2

Schematic of the distributed propagation model. According to self-consistent equation (5) the main part of the pulse is modified during propagation only by the gain medium, and the small coupled part (Δ) of the pulse with phase difference ϕ2 is modified by the gain and the nonlinear dispersion.

Fig. 3
Fig. 3

Time-bandwidth product versus chirp parameter β.

Fig. 4
Fig. 4

Chirp parameter β versus phase-mismatch angle ϕ2.12

Fig. 5
Fig. 5

Relative gain condition versus phase-mismatch angle ϕ2.15

Tables (1)

Tables Icon

Table 1 Unchirped Solitary-Pulse Solutions and Their Proper Operating Points

Equations (27)

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

exp ( - j ϕ ) S 1 ( t ) = r G [ S 1 ( t ) ] + Γ 0 2 exp ( j ϕ 2 ) D { G [ S 1 ( t ) ] } ,
r exp ( - γ x ) ,
Γ 0 2 Δ exp ( - γ x ) ,
Δ = Γ 0 2 / r .
exp ( - j ϕ ) S 1 ( t ) = exp ( - γ x ) G [ S 1 ( t ) ] + Δ exp ( j ϕ 2 ) exp ( - γ x ) D { G [ S 1 ( t 1 ) ] } .
2 j S x = 2 j ( g - γ ) S + j B 2 S t 2 .
2 j S x = 2 j ( g - γ ) S + ( j B - A ) 2 S t 2 + n 2 k 0 S 2 S .
2 j S 1 x = 2 j ( g - γ ) S 1 + j B 2 S 1 t 2 - Δ exp ( j ϕ 2 ) 1 + Δ exp ( j ϕ 2 ) × [ A 2 S 1 t 2 - ( n 2 k 0 Δ ) S 1 2 S 1 ] .
Δ exp ( j ϕ 2 ) 1 + Δ exp ( j ϕ 2 ) Δ exp ( j ϕ 2 ) .
2 j S 1 x = 2 j ( g - γ ) S 1 + ( j B - Δ exp ( j ϕ 2 ) A ) 2 S 1 t 2 + Δ exp ( j ϕ 2 ) k 0 ( n 2 Δ ) S 1 2 S 1 .
S 1 ( t , x ) = S 10 sech ( t T ) exp { j [ Γ x - β ln sech ( t T ) ] } .
( β 2 - 2 ) cos ϕ 2 + 3 β ( sin ϕ 2 - D ) = 0 ,
D = Δ A / B .
( g - γ ) L = Δ Φ M β 2 sin ϕ 2 + β cos ϕ 2 β 2 + 4 ,
Φ M = ½ n 2 k 0 L Δ S 10 2 .
( T T 0 ) 2 = g L Δ ϕ M ( β 2 + 1 ) ( β 2 + 4 ) × ( cos 2 ϕ 2 / 3 ) + ( D - sin ϕ 2 ) sin ϕ 2 ( β 2 - 2 ) sin ϕ 2 + β cos ϕ 2 ,
Γ L = - Δ Φ M β 2 + 4 [ ( β 2 + 2 ) cos ϕ 2 + β ( β 2 + 1 ) sin ϕ 2 ] .
2 S 1 x = 2 ( g - γ ) S 1 + ( B Δ A ) 2 S 1 t 2 ± n 2 k 0 Δ 2 S 1 2 S 1 .
S 1 ( t , x ) = S 10 sech ( t / T ) ,
T 2 = L Δ Φ M ( ± B - Δ A )
( g - γ ) L = ½ Δ Φ M .
S 1 ( t , x ) = S 10 tanh ( t / T ) ,
T 2 = L Δ Φ M ( B + Δ A )
( g - γ ) L = Δ Φ M .
S 30 2 = S 0 2 ( 1 + B / Δ A ) .
T / T 0 = 0.65 ( g L / Δ ) 1 / 2
γ ef = γ k 0 n 2 Δ 2 S 1 2 / 2 ,

Metrics