Abstract

A ring resonator containing a Kerr lens and a Gaussian slit is analyzed. From the point of view of Kerr lens mode locking, it is shown that a self-defocusing nonlinear element is as effective as a self-focusing one and that the positioning of the Kerr element introduces trade-offs between self-starting and operational stabilization. The nonlinearity can lead to unidirectional lasing.

© 1993 Optical Society of America

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  1. R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
    [CrossRef]
  2. F. Ouellette, M. Piché, Opt. Commun. 60, 99 (1986).
    [CrossRef]
  3. K. J. Blow, B. P. Nelson, Opt. Lett. 13, 1026 (1988).
    [CrossRef] [PubMed]
  4. P. N. Kean, X. Zhu, D. W. Crust, R. S. Grant, N. Langford, W. Sibbett, Opt. Lett. 14, 39 (1989).
    [CrossRef] [PubMed]
  5. J. G. Fujimoto, Opt. Photon. News 2(3), 8 (1991).
    [CrossRef]
  6. A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).
  7. D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  8. M. Piché, Opt. Commun. 86, 156 (1991).
    [CrossRef]
  9. F. Salin, J. Squier, M. Piché, Opt. Lett. 16, 1674 (1991).
    [CrossRef] [PubMed]
  10. G. P. A. Malcolm, A. I. Ferguson, Opt. Lett. 16, 1967 (1991).
    [CrossRef] [PubMed]
  11. H. Kogelnik, T. Li, Am. J. Phys. 5, 1550 (1966).
  12. E. M. Wright, D. P. O’Brien, W. J. Firth, IEEE J. Quantum Electron. QE-20, 1307 (1984).
    [CrossRef]
  13. M. Piché, P.-A. Bélanger, IEEE J. Quantum Electron. QE-20, 1303 (1984).
    [CrossRef]
  14. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  15. R. S. Grant, W. Sibbett, Appl. Phys. Lett. 58, 1119 (1991).
    [CrossRef]
  16. K. L. Hall, G. Lenz, E. P. Ippen, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1992), p. 522.
  17. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 793.

1991 (6)

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1989 (1)

1988 (1)

1987 (1)

A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).

1986 (1)

F. Ouellette, M. Piché, Opt. Commun. 60, 99 (1986).
[CrossRef]

1984 (2)

E. M. Wright, D. P. O’Brien, W. J. Firth, IEEE J. Quantum Electron. QE-20, 1307 (1984).
[CrossRef]

M. Piché, P.-A. Bélanger, IEEE J. Quantum Electron. QE-20, 1303 (1984).
[CrossRef]

1983 (1)

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

1966 (1)

H. Kogelnik, T. Li, Am. J. Phys. 5, 1550 (1966).

Barthelemy, A.

A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).

Bélanger, P.-A.

M. Piché, P.-A. Bélanger, IEEE J. Quantum Electron. QE-20, 1303 (1984).
[CrossRef]

Blow, K. J.

Crust, D. W.

Ferguson, A. I.

Firth, W. J.

E. M. Wright, D. P. O’Brien, W. J. Firth, IEEE J. Quantum Electron. QE-20, 1307 (1984).
[CrossRef]

Fork, R. L.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Froehly, C.

A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).

Fujimoto, J. G.

J. G. Fujimoto, Opt. Photon. News 2(3), 8 (1991).
[CrossRef]

Grant, R. S.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Hall, K. L.

K. L. Hall, G. Lenz, E. P. Ippen, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1992), p. 522.

Hirlimann, C. A.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Ippen, E. P.

K. L. Hall, G. Lenz, E. P. Ippen, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1992), p. 522.

Kean, P. N.

Kogelnik, H.

H. Kogelnik, T. Li, Am. J. Phys. 5, 1550 (1966).

Langford, N.

Lenz, G.

K. L. Hall, G. Lenz, E. P. Ippen, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1992), p. 522.

Li, T.

H. Kogelnik, T. Li, Am. J. Phys. 5, 1550 (1966).

Malcolm, G. P. A.

Maneuf, S.

A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).

Nelson, B. P.

O’Brien, D. P.

E. M. Wright, D. P. O’Brien, W. J. Firth, IEEE J. Quantum Electron. QE-20, 1307 (1984).
[CrossRef]

Ouellette, F.

F. Ouellette, M. Piché, Opt. Commun. 60, 99 (1986).
[CrossRef]

Piché, M.

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

F. Salin, J. Squier, M. Piché, Opt. Lett. 16, 1674 (1991).
[CrossRef] [PubMed]

F. Ouellette, M. Piché, Opt. Commun. 60, 99 (1986).
[CrossRef]

M. Piché, P.-A. Bélanger, IEEE J. Quantum Electron. QE-20, 1303 (1984).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Salin, F.

Shank, C. V.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sheng, G.

A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).

Sibbett, W.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 793.

Spence, D. E.

Squier, J.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wright, E. M.

E. M. Wright, D. P. O’Brien, W. J. Firth, IEEE J. Quantum Electron. QE-20, 1307 (1984).
[CrossRef]

Yen, R.

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Zhu, X.

Am. J. Phys. (1)

H. Kogelnik, T. Li, Am. J. Phys. 5, 1550 (1966).

Appl. Phys. Lett. (1)

R. S. Grant, W. Sibbett, Appl. Phys. Lett. 58, 1119 (1991).
[CrossRef]

IEEE J. Quantum Electron. (4)

E. M. Wright, D. P. O’Brien, W. J. Firth, IEEE J. Quantum Electron. QE-20, 1307 (1984).
[CrossRef]

M. Piché, P.-A. Bélanger, IEEE J. Quantum Electron. QE-20, 1303 (1984).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE J. Quantum Electron. QE-19, 500 (1983).
[CrossRef]

Opt. Commun. (2)

F. Ouellette, M. Piché, Opt. Commun. 60, 99 (1986).
[CrossRef]

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

Opt. Lett. (5)

Opt. Photon. News (1)

J. G. Fujimoto, Opt. Photon. News 2(3), 8 (1991).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. Barthelemy, C. Froehly, S. Maneuf, G. Sheng, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 387 (1987).

Other (2)

K. L. Hall, G. Lenz, E. P. Ippen, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1992), p. 522.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 793.

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Figures (4)

Fig. 1
Fig. 1

(a) Cavity geometry in terms of the spacings L, the focal length of the lenses f, the free-space wave vector k, and the Gaussian slit parameter γ. (b) Beam widths for the counterprogagating linear eigenmodes. For the parameters chosen, the waist is 44 μm. Note that in (a) and (b) the ring cavity is opened out.

Fig. 2
Fig. 2

Change in single-pass transmission with change in power (dTrans/dP) as a function of Kerr-medium offset (l) for self-focusing (dotted curve) and self-defocusing (solid curve) nonlinearity. Vertical axis is in arbitrary units; horizontal axis is measured from the midpoint between the lenses in Fig. 1(a) and is in units of L.

Fig. 3
Fig. 3

Single-pass transmission (SPT) versus l for a self-defocusing nonlinearity for beam powers P. The solid curve corresponds to the near-linear regime of Fig. 2.

Fig. 4
Fig. 4

Single-pass transmission (SPT) versus power at two values of l. Note that the position for the solid curve is at the peak of the solid curve of Fig. 2.

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