Abstract

Self-focusing in conjunction with an intracavity aperture creates a power-dependent amplitude modulation in laser oscillators, which allows passive mode locking. A simple analytical formalism yields closed-form expressions for the depth of passive amplitude modulation introduced by either the spatial gain profile or a hard aperture inserted in the resonator. Design issues for this mode-locking technique are discussed.

© 1992 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. A. Miller, P. Li Kam Wa, B. H. T. Chai, E. W. Van Stryland, Opt. Lett. 17, 195 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. P. A. Belanger, C. Paré, Appl Opt. 22, 1293 (1983).
    [CrossRef] [PubMed]
  14. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
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    [CrossRef]

1992 (2)

1991 (9)

1990 (1)

F. Krausz, E. Wintner, A. J. Schmidt, A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[CrossRef]

1983 (1)

P. A. Belanger, C. Paré, Appl Opt. 22, 1293 (1983).
[CrossRef] [PubMed]

1975 (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1969 (1)

E. L. Dawson, J. H. Marburger, Phys. Rev. 179, 862 (1969).
[CrossRef]

1965 (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Acioli, L. H.

Belanger, P. A.

P. A. Belanger, C. Paré, Appl Opt. 22, 1293 (1983).
[CrossRef] [PubMed]

Brabec, T.

Chai, B. H. T.

Chen, S.

Couilland, B.

L. Spinelli, B. Couilland, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1991), paper CPDP7.

Cunningham, J. E.

Curley, P. F.

Dawson, E. L.

E. L. Dawson, J. H. Marburger, Phys. Rev. 179, 862 (1969).
[CrossRef]

Dienes, A.

F. Krausz, E. Wintner, A. J. Schmidt, A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[CrossRef]

Ferguson, A. I.

Fujimoto, J. G.

Gabetta, G.

Goldblatt, N.

L. Spinelli, B. Couilland, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1991), paper CPDP7.

Haus, H. A.

Huang, D.

Ippen, E. P.

Jacobson, J.

Kean, P. N.

Keiler, U.

Knox, W. H.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Krausz, F.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A.J. Schmidt, Opt. Lett. 16, 1180 (1991).
[CrossRef] [PubMed]

F. Krausz, E. Wintner, A. J. Schmidt, A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[CrossRef]

Li Kam Wa, P.

Malcolm, G. P. A.

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

E. L. Dawson, J. H. Marburger, Phys. Rev. 179, 862 (1969).
[CrossRef]

Miller, A.

Negus, D. K.

L. Spinelli, B. Couilland, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1991), paper CPDP7.

Paré, C.

P. A. Belanger, C. Paré, Appl Opt. 22, 1293 (1983).
[CrossRef] [PubMed]

Piché, M.

Ramaswamy, M.

Salin, F.

Schmidt, A. J.

F. Krausz, E. Wintner, A. J. Schmidt, A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[CrossRef]

Schmidt, A.J.

Sibbett, W.

Spence, D. E.

Spielmann, Ch.

Spinelli, L.

L. Spinelli, B. Couilland, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1991), paper CPDP7.

Squier, J.

'tHooft, G. W.

Ulman, M.

Van Stryland, E. W.

Wang, J.

Wintner, E.

Ch. Spielmann, F. Krausz, T. Brabec, E. Wintner, A.J. Schmidt, Opt. Lett. 16, 1180 (1991).
[CrossRef] [PubMed]

F. Krausz, E. Wintner, A. J. Schmidt, A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[CrossRef]

Appl Opt. (1)

P. A. Belanger, C. Paré, Appl Opt. 22, 1293 (1983).
[CrossRef] [PubMed]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

IEEE J. Quantum Electron. (1)

F. Krausz, E. Wintner, A. J. Schmidt, A. Dienes, IEEE J. Quantum Electron. 26, 158 (1990).
[CrossRef]

Opt. Commun. (1)

M. Piché, Opt. Commun. 86, 156 (1991).
[CrossRef]

Opt. Lett. (10)

Phys. Rev. (1)

E. L. Dawson, J. H. Marburger, Phys. Rev. 179, 862 (1969).
[CrossRef]

Prog. Quantum Electron. (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Other (1)

L. Spinelli, B. Couilland, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington D.C., 1991), paper CPDP7.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the cavity used in our calculations. The distances d1 and d2 and the length of the Kerr medium l are taken to be 80, 120, and 1.6 cm, respectively, throughout this Letter. The refractive index of the Kerr medium is assumed to have the value n = 1.76.

Fig. 2
Fig. 2

Absolute change in gain Δg versus normalized intracavity power for a gain aperture within the Kerr medium. gs = 0.1, Is = 300 kW/cm2, Pav = 2 W, and δ = R2/2. Curves 1 and 3 are the analytical and numerical solutions for f1 = f2 = 6 cm, zr0 = 0.26 cm, and zp = 0.22 cm; curves 2 and 4 are the analytical and numerical solutions for f1 = f2 = 10 cm, zr0 = 0.73 cm, and zp = 0.22 cm.

Fig. 3
Fig. 3

Absolute change in gain versus the normalized stability parameter. δmax = R1 + R2 and L = 0.1, P = 0.25, and f1 = f2 = 6 cm. The vertical lines denote the limits of the stability range. Curves 1 and 2 show the results for the aperture inserted at the output coupler of the short arm and of the long arm, respectively. The solid curves are for = 0, and the dotted curves are for = 0.25.

Equations (5)

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R ¯ 1 ( η ) = l x 1 ( η ) n { 1 + [ z r ( η ) l x 1 ( η ) η ] 2 } ,
R ¯ 1 ² ( η ) R ¯ 1 ( η ) { R ¯ 10 + [ 1 x 10 1 x 1 ( η ) η 2 ] n l B 1 D 1 A 1 C 1 } 1 η 2 n 2 B 1 D 1 A 1 C 1 = 0 ,
T ^ 1 = [ A 1 B 1 C 1 D 1 ] = [ f 1 R 1 f 1 R 1 { R 1 [ l x 10 n δ ( δ + R 2 ) 2 δ + ( R 1 + R 2 ) ] } 1 f 1 1 f 1 [ l x 10 n δ ( δ + R 2 ) 2 δ + ( R 1 + R 2 ) ] ] .
Δ g g s 2 P ¯ 1 + S ,
Δ g 1 , 2 P n L R 1 , 2 l P cr [ 1 + ( l 2 z r 0 ) 2 ] { 1 R 1 ² R 2 ² ( R 1 + R 2 + 2 δ ) 2 ± 8 l ɛ n [ 1 + ( l 2 z r 0 ) 2 ] 1 R 1 + R 2 + 2 δ } ,

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