Abstract

Analytical expressions for the spot size and the Kerr-lens mode-locking (LM) strength can be represented as explicit functions of the position in the cavity, the laser power, and the stability parameter for a four-mirror figure-Z laser resonator. The results indicate that the KLM strength achieves its maximum value at the edge of the stability range. Self-amplitude modulation and group-velocity dispersion compensation can be established by a prism pair. Simultaneously obtaining a large pumping efficiency and KLM is possible for this cavity.

© 1994 Optical Society of America

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References

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  1. C.-P. Huang, M. T. Asaki, S. Backus, M. M. Murnane, and H. C. Kapteyn, Opt. Lett. 17, 1289 (1992).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. T. Brabec, Ch. Spielmann, P. E. Curley, and F. Krausz, Opt. Lett. 17, 1292 (1992).
    [Crossref] [PubMed]
  4. D. Georgiev, J. Herrmann, and U. Stamm, Opt. Commun. 92, 368 (1992).
    [Crossref]
  5. V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
    [Crossref]
  6. J. L. A. Chilla and O. E. Martínez, J. Opt. Soc. Am. B 10, 638 (1993).
    [Crossref]
  7. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
    [Crossref]
  8. D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, Opt. Lett. 17, 511 (1992).
    [Crossref] [PubMed]
  9. F. Krausz, E. Witner, A. J. Schmidt, and A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
    [Crossref]
  10. P. F. Moulton, IEEE J. Quantum Electron. QE-21, 1582 (1985).
    [Crossref]

1993 (3)

1992 (5)

1990 (1)

F. Krausz, E. Witner, A. J. Schmidt, and A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[Crossref]

1985 (1)

P. F. Moulton, IEEE J. Quantum Electron. QE-21, 1582 (1985).
[Crossref]

Acioli, L. H.

Asaki, M. T.

Backus, S.

Brabec, T.

Cerullo, G.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[Crossref]

Chilla, J. L. A.

Curley, P. E.

Curley, P. F.

Dienes, A.

F. Krausz, E. Witner, A. J. Schmidt, and A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[Crossref]

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[Crossref]

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, Opt. Lett. 17, 511 (1992).
[Crossref] [PubMed]

Georgiev, D.

D. Georgiev, J. Herrmann, and U. Stamm, Opt. Commun. 92, 368 (1992).
[Crossref]

Haus, H. A.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[Crossref]

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, Opt. Lett. 17, 511 (1992).
[Crossref] [PubMed]

Herrmann, J.

D. Georgiev, J. Herrmann, and U. Stamm, Opt. Commun. 92, 368 (1992).
[Crossref]

Huang, C.-P.

Huang, D.

Ippen, E. P.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[Crossref]

Kapteyn, H. C.

Krausz, F.

Magni, V.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[Crossref]

Martínez, O. E.

Moulton, P. F.

P. F. Moulton, IEEE J. Quantum Electron. QE-21, 1582 (1985).
[Crossref]

Murnane, M. M.

Schmidt, A. J.

P. F. Curley, Ch. Spielmann, T. Brabec, F. Krausz, E. Wintner, and A. J. Schmidt, Opt. Lett. 18, 54 (1993).
[Crossref] [PubMed]

F. Krausz, E. Witner, A. J. Schmidt, and A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[Crossref]

Silvestri, S. D.

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[Crossref]

Spielmann, Ch.

Stamm, U.

D. Georgiev, J. Herrmann, and U. Stamm, Opt. Commun. 92, 368 (1992).
[Crossref]

Ulman, M.

Wintner, E.

Witner, E.

F. Krausz, E. Witner, A. J. Schmidt, and A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[Crossref]

IEEE J. Quantum Electron. (3)

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, IEEE J. Quantum Electron. 28, 2086 (1992).
[Crossref]

F. Krausz, E. Witner, A. J. Schmidt, and A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[Crossref]

P. F. Moulton, IEEE J. Quantum Electron. QE-21, 1582 (1985).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

D. Georgiev, J. Herrmann, and U. Stamm, Opt. Commun. 92, 368 (1992).
[Crossref]

V. Magni, G. Cerullo, and S. D. Silvestri, Opt. Commun. 96, 348 (1993).
[Crossref]

Opt. Lett. (4)

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Figures (6)

Fig. 1
Fig. 1

Four-mirror figure-Z laser cavity with a Kerr medium of length s placed between curved mirrors. M1 and M4 are flat mirrors. M2 and M3 are curved mirrors with focal length f.

Fig. 2
Fig. 2

Calculated spot size: curve (a) at M1 and curve (b) at M2 as functions of the stability parameter under cw operation.

Fig. 3
Fig. 3

Curve (a) KLM strength versus position measured from M1 at δ = 6 mm (left vertical scale); curve (b) KLM strength versus stability parameter calculated at z = 80 cm (right vertical scale).

Fig. 4
Fig. 4

Calculated power-dependent spot size at 80 cm for M1 [curve (a) left vertical scale] and the center of Kerr medium [curve (b) right vertical scale].

Fig. 5
Fig. 5

Calculated spot size versus position inside the Kerr medium for various cavity powers P.

Fig. 6
Fig. 6

Pumping design to favor KLM operation. The pump beam must be focused to match the cavity mode.

Equations (14)

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Δ Φ = 2 π λ n 2 A 0 2 exp ( - 2 r 2 / w 2 ) d z 2 π λ n 2 A 0 2 ( 1 - 2 r 2 w 2 ) d z .
- d d z ( 1 q ) = 1 q 2 + K Im 2 ( 1 q ) ,
K = 8 P π ( π λ ) 2 n 0 n 2 ,
1 q = Re [ 1 q ] + j Im [ 1 q ] 1 - K ,
- d d z ( 1 q ) = 1 q 2 ,
[ A 1 B 1 C 1 D 1 ] ,
[ A 2 B 2 C 2 D 2 ] .
a 4 ( y 1 2 ) 4 + a 3 ( y 1 2 ) 3 + a 2 ( y 1 2 ) 2 + a 1 ( y 1 2 ) + a 0 = 0 ,
1 q I = Re ( 1 q I ) + j Im ( 1 q I ) 1 - K = - y 1 2 ( f - r ) + ( f - d ) ( r f + d f - r d ) - j y 1 f 2 1 - K y 1 2 ( f - r ) 2 + ( r f + d f - r d ) 2 .
a ( y 1 2 ) 2 + b ( y 1 2 ) + c = 0 ,
a = ( f - r ) 2 ( L + 2 r - 2 f ) , b = 2 ( f - r ) ( r f + d f - r d ) [ ( L + 2 r ) ( d - f ) - 2 d f + f 2 ] + L f 4 ( 1 - K ) , c = ( d - f ) ( r f + d f - r d ) 2 [ ( L + 2 r ) ( d - f ) - 2 d f ] = ( d - f ) 2 ( r f + d f - r d ) 2 ( L + 2 r - 2 d f d - f ) .
F = - 1 w d w d P | K = 0 = - 8 π n 0 n 2 α λ 2 1 4 y 2 d y 2 d K | K = 0 .
F 0 = r ( x , y , z ) s ( x , y , z ) d v ,
t = [ y 0 ( y p - y 0 ) ] 1 / 2 , f p = ( y 0 2 + t 2 ) / t ,

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