Abstract

The relaxation of a geometrically unstable Fabry–Perot cavity is theoretically and experimentally investigated. It is observed that the usual sum of the exponential decays of the intensities in the different transverse modes of the cavity is replaced by a more complex behavior. In particular, light couplings into the fundamental mode of the cavity with initial wave excitation factors larger than unity, i.e., larger than in the case of mode-matched injection, are directly observed. The influence of the cavity Fresnel number and of transverse mode crossings and anticrossings on these cavity decays is isolated.

© 1999 Optical Society of America

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  2. A. E. Siegman, Phys. Rev. A 39, 1253, 1264 (1989).
  3. M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
    [CrossRef]
  4. W. A. Hamel and J. P. Woerdman, Phys. Rev. Lett. 64, 1506 (1990).
    [CrossRef] [PubMed]
  5. A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
    [CrossRef]
  6. O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
    [CrossRef]
  7. Y. J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
    [CrossRef] [PubMed]
  8. M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
    [CrossRef] [PubMed]
  9. K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
    [CrossRef]
  10. A. E. Siegman, Appl. Phys. B 60, 247 (1995).
    [CrossRef]
  11. A. E. Siegman, in Coherence and Quantum Optics VII, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1996), p. 229.
    [CrossRef]
  12. P. Goldberg, P. W. Milonni, and B. Sundaram, J. Mod. Opt. 38, 1421 (1991)Phys. Rev. A 44, 1969 (1991).
    [CrossRef]
  13. G. H. C. New, J. Mod. Opt. 42, 799 (1995).
    [CrossRef]
  14. Ph. Grangier and J.-Ph. Poizat, Eur. Phys. J. D 1, 97 (1998).
    [CrossRef]
  15. J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
    [CrossRef] [PubMed]
  16. P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
    [CrossRef]

1998 (3)

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
[CrossRef]

Ph. Grangier and J.-Ph. Poizat, Eur. Phys. J. D 1, 97 (1998).
[CrossRef]

P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
[CrossRef]

1997 (2)

M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
[CrossRef]

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

1996 (3)

Y. J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
[CrossRef] [PubMed]

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

1995 (2)

A. E. Siegman, Appl. Phys. B 60, 247 (1995).
[CrossRef]

G. H. C. New, J. Mod. Opt. 42, 799 (1995).
[CrossRef]

1991 (1)

P. Goldberg, P. W. Milonni, and B. Sundaram, J. Mod. Opt. 38, 1421 (1991)Phys. Rev. A 44, 1969 (1991).
[CrossRef]

1990 (1)

W. A. Hamel and J. P. Woerdman, Phys. Rev. Lett. 64, 1506 (1990).
[CrossRef] [PubMed]

1989 (1)

A. E. Siegman, Phys. Rev. A 39, 1253, 1264 (1989).

1979 (1)

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

Bretenaker, F.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
[CrossRef]

M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
[CrossRef]

Brunel, M.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
[CrossRef]

M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
[CrossRef]

Cheng, Y. J.

Y. J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

Eberly, J. H.

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

Emile, O.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
[CrossRef]

Fanning, C. G.

Y. J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

Goldberg, P.

P. Goldberg, P. W. Milonni, and B. Sundaram, J. Mod. Opt. 38, 1421 (1991)Phys. Rev. A 44, 1969 (1991).
[CrossRef]

Grangier, Ph.

Ph. Grangier and J.-Ph. Poizat, Eur. Phys. J. D 1, 97 (1998).
[CrossRef]

Grobe, R.

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

Hamel, W. A.

W. A. Hamel and J. P. Woerdman, Phys. Rev. Lett. 64, 1506 (1990).
[CrossRef] [PubMed]

Le Floch, A.

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
[CrossRef]

M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
[CrossRef]

Leung, P. T.

P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
[CrossRef]

Lindberg, Å. M.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
[CrossRef] [PubMed]

Miemeret, A. L.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

Milonni, P. W.

P. Goldberg, P. W. Milonni, and B. Sundaram, J. Mod. Opt. 38, 1421 (1991)Phys. Rev. A 44, 1969 (1991).
[CrossRef]

New, G. H. C.

G. H. C. New, J. Mod. Opt. 42, 799 (1995).
[CrossRef]

Petermann, K.

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

Poizat, J.-Ph.

Ph. Grangier and J.-Ph. Poizat, Eur. Phys. J. D 1, 97 (1998).
[CrossRef]

Rahman, A.

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

Ropars, G.

M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
[CrossRef]

Siegman, A. E.

Y. J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

A. E. Siegman, Appl. Phys. B 60, 247 (1995).
[CrossRef]

A. E. Siegman, Phys. Rev. A 39, 1253, 1264 (1989).

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

A. E. Siegman, in Coherence and Quantum Optics VII, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1996), p. 229.
[CrossRef]

Suen, W. M.

P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
[CrossRef]

Sun, C. P.

P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
[CrossRef]

Sundaram, B.

P. Goldberg, P. W. Milonni, and B. Sundaram, J. Mod. Opt. 38, 1421 (1991)Phys. Rev. A 44, 1969 (1991).
[CrossRef]

Thijssen, M. S.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
[CrossRef] [PubMed]

van der Lee, A. M.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

van Druten, N. J.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

van Eijkelenborg, M. A.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
[CrossRef] [PubMed]

van Exter, M. P.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

Woerdman, J. P.

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
[CrossRef] [PubMed]

W. A. Hamel and J. P. Woerdman, Phys. Rev. Lett. 64, 1506 (1990).
[CrossRef] [PubMed]

Young, K.

P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
[CrossRef]

Appl. Phys. B (1)

A. E. Siegman, Appl. Phys. B 60, 247 (1995).
[CrossRef]

Eur. Phys. J. D (1)

Ph. Grangier and J.-Ph. Poizat, Eur. Phys. J. D 1, 97 (1998).
[CrossRef]

Europhys. Lett. (1)

O. Emile, M. Brunel, A. Le Floch, and F. Bretenaker, Europhys. Lett. 43, 153 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

J. Mod. Opt. (2)

P. Goldberg, P. W. Milonni, and B. Sundaram, J. Mod. Opt. 38, 1421 (1991)Phys. Rev. A 44, 1969 (1991).
[CrossRef]

G. H. C. New, J. Mod. Opt. 42, 799 (1995).
[CrossRef]

Phys. Rev. A (2)

A. E. Siegman, Phys. Rev. A 39, 1253, 1264 (1989).

M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 55, 4563 (1997).
[CrossRef]

Phys. Rev. E (1)

P. T. Leung, W. M. Suen, C. P. Sun, and K. Young, Phys. Rev. E 57, 6101 (1998), and references therein .
[CrossRef]

Phys. Rev. Lett. (5)

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

W. A. Hamel and J. P. Woerdman, Phys. Rev. Lett. 64, 1506 (1990).
[CrossRef] [PubMed]

A. M. van der Lee, N. J. van Druten, A. L. Miemeret, M. A. van Eijkelenborg, Å. M. Lindberg, M. P. van Exter, and J. P. Woerdman, Phys. Rev. Lett. 79, 4357 (1997).
[CrossRef]

Y. J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996)Phys. Rev. A 55, 4556 (1997).
[CrossRef] [PubMed]

Other (2)

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

A. E. Siegman, in Coherence and Quantum Optics VII, J. H. Eberly, L. Mandel, and E. Wolf, eds. (Plenum, New York, 1996), p. 229.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of the system. A short pulse with a Gaussian wave front is incident upon a Fabry–Perot cavity of length L terminated by mirrors M1 and M2. ϕ, aperture diameter; D, detector.

Fig. 2
Fig. 2

(a) Theoretical and (b) experimental evolutions of the intensities of the successive pulses emerging from the unstable cavity of Fig.  1 for R1=-5 m, R2=10 m, L=2.5 m, R=0.94, w=4.5 mm, ρ=12.5 m, and Neq=0.5. Diagonal lines, the backward extrapolation of the last pulse intensities. (c), (d) Same as (a) and (b) for a stable cavity with R1=, R2=5 m, L=2 m, R=0.94, w=8.5 mm, ρ=, and ϕ=2.50 mm. Arrows, initial wave excitation factors obtained by backward extrapolation of the successive intensities.

Fig. 3
Fig. 3

Same as Figs.  2(a) and 2(b) but for Neq=1.0.

Fig. 4
Fig. 4

Same as Figs.  2(a) and 2(b) for (a), (b) Neq=1.5 and (c), (d) Neq=2.5.

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