Abstract

We used the ABCD law to derive the transfer matrix of beam propagation in a Kerr-lens mode-locked laser. On the basis of the transfer matrix and the formulas of the cavity stability G parameters that differ from the simple cavity g parameters, we give the expressions for Kerr-lens mode-locking (KLM) strength and some equations for cavity geometric parameters. The expressions and the equations can be used to construct a laser resonator to achieve self-starting oscillation of KLM. In addition we made a numerical simulation of the KLM strength at different positions in a mode-locked Ti:sapphire laser. The numerical results provide a good explanation of some of the physical phenomena observed in our experiments.

© 2002 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367–1369 (1992).
    [CrossRef] [PubMed]
  2. D. Georgiev, J. Herrmann, U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
    [CrossRef]
  3. M. T. Asaki, C. P. Huang, D. Garvey, “Generation of 11-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 18, 977–979 (1993).
    [CrossRef] [PubMed]
  4. K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, J. G. Fujimoto, “Unidirectional ring resonators for self-starting passively mode-locked lasers,” Opt. Lett. 18, 220–222 (1993).
    [CrossRef] [PubMed]
  5. V. Magni, G. Cerullo, S. D. Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
    [CrossRef]
  6. V. Magni, G. Cerullo, S. D. Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365–370 (1993).
    [CrossRef]
  7. G. Cerullo, S. D. Silvestri, V. Magni, “Self-starting Kerr-lens mode locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040–1042 (1994).
    [CrossRef] [PubMed]
  8. J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
    [CrossRef]
  9. G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
    [CrossRef]
  10. U. Morgner, F. X. Kartner, S. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, “Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24, 411–413 (1999).
    [CrossRef]
  11. M. A. Marioni, A. A. Hnilo, “Self-starting of self mode-locking Ti:sapphire lasers: description with a Poincaré map,” Opt. Commun. 147, 89–94 (1998).
    [CrossRef]
  12. W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-Verlag, New York, 1999), p. 538.

1999 (1)

1998 (1)

M. A. Marioni, A. A. Hnilo, “Self-starting of self mode-locking Ti:sapphire lasers: description with a Poincaré map,” Opt. Commun. 147, 89–94 (1998).
[CrossRef]

1997 (1)

G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
[CrossRef]

1996 (1)

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

1994 (1)

1993 (4)

M. T. Asaki, C. P. Huang, D. Garvey, “Generation of 11-fs pulses from a self-mode-locked Ti:sapphire laser,” Opt. Lett. 18, 977–979 (1993).
[CrossRef] [PubMed]

K. Tamura, J. Jacobson, E. P. Ippen, H. A. Haus, J. G. Fujimoto, “Unidirectional ring resonators for self-starting passively mode-locked lasers,” Opt. Lett. 18, 220–222 (1993).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. D. Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. D. Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365–370 (1993).
[CrossRef]

1992 (2)

B. E. Lemoff, C. P. J. Barty, “Generation of high-peak-power 20-fs pulses from a regeneratively initiated, self-mode-locked Ti:sapphire laser,” Opt. Lett. 17, 1367–1369 (1992).
[CrossRef] [PubMed]

D. Georgiev, J. Herrmann, U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Afonso, C. N.

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

Angelow, G.

Asaki, M. T.

Barry, N. P.

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

Barty, C. P. J.

Cerullo, G.

G. Cerullo, S. D. Silvestri, V. Magni, “Self-starting Kerr-lens mode locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040–1042 (1994).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. D. Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365–370 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. D. Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

Chen, Y.

Cho, S.

Feiran, H.

G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
[CrossRef]

French, P. M. W.

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

Fujimoto, J. G.

Garvey, D.

Georgiev, D.

D. Georgiev, J. Herrmann, U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Haus, H. A.

Herrmann, J.

D. Georgiev, J. Herrmann, U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Hnilo, A. A.

M. A. Marioni, A. A. Hnilo, “Self-starting of self mode-locking Ti:sapphire lasers: description with a Poincaré map,” Opt. Commun. 147, 89–94 (1998).
[CrossRef]

Huang, C. P.

Ippen, E. P.

Jacobson, J.

Kartner, F. X.

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-Verlag, New York, 1999), p. 538.

Lee, W. K.

G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
[CrossRef]

Lemoff, B. E.

Magni, V.

G. Cerullo, S. D. Silvestri, V. Magni, “Self-starting Kerr-lens mode locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040–1042 (1994).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. D. Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365–370 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. D. Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

Marioni, M. A.

M. A. Marioni, A. A. Hnilo, “Self-starting of self mode-locking Ti:sapphire lasers: description with a Poincaré map,” Opt. Commun. 147, 89–94 (1998).
[CrossRef]

Mellish, R.

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

Morgner, U.

Scheuer, V.

Siegel, J.

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

Silvestri, S. D.

G. Cerullo, S. D. Silvestri, V. Magni, “Self-starting Kerr-lens mode locking of a Ti:sapphire laser,” Opt. Lett. 19, 1040–1042 (1994).
[CrossRef] [PubMed]

V. Magni, G. Cerullo, S. D. Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365–370 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. D. Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

Solis, J.

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

Stamm, U.

D. Georgiev, J. Herrmann, U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Tamura, K.

Tschudi, T.

Wang, M. R.

G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
[CrossRef]

Xu, G. H.

G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
[CrossRef]

Opt. Commun. (6)

D. Georgiev, J. Herrmann, U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

V. Magni, G. Cerullo, S. D. Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

V. Magni, G. Cerullo, S. D. Silvestri, “Closed form Gaussian beam analysis of resonators containing a Kerr medium for femtosecond lasers,” Opt. Commun. 101, 365–370 (1993).
[CrossRef]

J. Solis, J. Siegel, C. N. Afonso, N. P. Barry, R. Mellish, P. M. W. French, “Experimental study of a self-starting Kerr-lens mode-locked titanium-doped sapphire laser,” Opt. Commun. 123, 547–552 (1996).
[CrossRef]

G. H. Xu, H. Feiran, W. K. Lee, M. R. Wang, “Cavity design of a compact Kerr-lens mode-locking laser,” Opt. Commun. 142, 249–252 (1997).
[CrossRef]

M. A. Marioni, A. A. Hnilo, “Self-starting of self mode-locking Ti:sapphire lasers: description with a Poincaré map,” Opt. Commun. 147, 89–94 (1998).
[CrossRef]

Opt. Lett. (5)

Other (1)

W. Koechner, Solid-State Laser Engineering, 5th ed. (Springer-Verlag, New York, 1999), p. 538.

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.


Metrics