Abstract

We experimentally study the polarization dynamics of a single-mode CO2 laser during the switch-on transient of the laser intensity. We find a strong competition between two linearly polarized fields, which finally collapse into a single field. As a result of this competition, the two coexisting fields oscillate out of phase by π rad for time intervals much longer than that of the relaxation oscillation. One can control the oscillation frequency of the two polarized fields by varying the intracavity anisotropies. This phenomenon is interpreted in the framework of Maxwell–Bloch equations by addition of nonlinear terms to the polarization equations that allow the fields to compete while they interact with the same population inversion.

© 2001 Optical Society of America

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References

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  1. P. Paddon, E. Sjerve, A. D. May, M. Bourois, and G. Stephan, J. Opt. Soc. Am. B 9, 574 (1992).
    [CrossRef]
  2. C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
    [CrossRef]
  3. G. C. Puccioni, G. L. Lippi, and N. B. Abraham, Opt. Commun. 72, 361 (1989).
    [CrossRef]
  4. C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
    [CrossRef]
  5. G. C. Puccioni, M. V. Trantnik, J. E. Sipe, and G. L. Oppo, Opt. Lett. 12, 242 (1987).
    [CrossRef] [PubMed]
  6. N. B. Abraham, M. D. Matlin, and R. S. Gioggia, Phys. Rev. A 53, 3514 (1996).
    [CrossRef] [PubMed]
  7. M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
    [CrossRef]
  8. A. Labate, R. Meucci, and M. Ciofini, Opt. Commun. 141, 150 (1997).
    [CrossRef]

2000 (1)

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

1997 (2)

C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
[CrossRef]

A. Labate, R. Meucci, and M. Ciofini, Opt. Commun. 141, 150 (1997).
[CrossRef]

1996 (1)

N. B. Abraham, M. D. Matlin, and R. S. Gioggia, Phys. Rev. A 53, 3514 (1996).
[CrossRef] [PubMed]

1995 (1)

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

1992 (1)

1989 (1)

G. C. Puccioni, G. L. Lippi, and N. B. Abraham, Opt. Commun. 72, 361 (1989).
[CrossRef]

1987 (1)

Abraham, N. B.

C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
[CrossRef]

N. B. Abraham, M. D. Matlin, and R. S. Gioggia, Phys. Rev. A 53, 3514 (1996).
[CrossRef] [PubMed]

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

G. C. Puccioni, G. L. Lippi, and N. B. Abraham, Opt. Commun. 72, 361 (1989).
[CrossRef]

Bourois, M.

Ciofini, M.

C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
[CrossRef]

A. Labate, R. Meucci, and M. Ciofini, Opt. Commun. 141, 150 (1997).
[CrossRef]

Crawford, T.

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

Degen, C.

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

Elsasser, W.

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

Fisher, I.

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

Gioggia, R. S.

N. B. Abraham, M. D. Matlin, and R. S. Gioggia, Phys. Rev. A 53, 3514 (1996).
[CrossRef] [PubMed]

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

Glorieux, P.

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

Jennemann, G.

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

Krauskopf, B.

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

Labate, A.

A. Labate, R. Meucci, and M. Ciofini, Opt. Commun. 141, 150 (1997).
[CrossRef]

Lippi, G. L.

G. C. Puccioni, G. L. Lippi, and N. B. Abraham, Opt. Commun. 72, 361 (1989).
[CrossRef]

Matlin, M. D.

N. B. Abraham, M. D. Matlin, and R. S. Gioggia, Phys. Rev. A 53, 3514 (1996).
[CrossRef] [PubMed]

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

May, A. D.

Meucci, R.

C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
[CrossRef]

A. Labate, R. Meucci, and M. Ciofini, Opt. Commun. 141, 150 (1997).
[CrossRef]

Oppo, G. L.

Paddon, P.

Puccioni, G. C.

G. C. Puccioni, G. L. Lippi, and N. B. Abraham, Opt. Commun. 72, 361 (1989).
[CrossRef]

G. C. Puccioni, M. V. Trantnik, J. E. Sipe, and G. L. Oppo, Opt. Lett. 12, 242 (1987).
[CrossRef] [PubMed]

Sipe, J. E.

Sjerve, E.

Stephan, G.

Taggiasco, C.

C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
[CrossRef]

Trantnik, M. V.

J. Opt. B (1)

C. Degen, B. Krauskopf, G. Jennemann, I. Fisher, and W. Elsasser, J. Opt. B 2, 517 (2000).
[CrossRef]

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

Opt. Commun. (4)

M. D. Matlin, R. S. Gioggia, N. B. Abraham, P. Glorieux, and T. Crawford, Opt. Commun. 120, 204 (1995).
[CrossRef]

A. Labate, R. Meucci, and M. Ciofini, Opt. Commun. 141, 150 (1997).
[CrossRef]

G. C. Puccioni, G. L. Lippi, and N. B. Abraham, Opt. Commun. 72, 361 (1989).
[CrossRef]

C. Taggiasco, R. Meucci, M. Ciofini, and N. B. Abraham, Opt. Commun. 133, 507 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

N. B. Abraham, M. D. Matlin, and R. S. Gioggia, Phys. Rev. A 53, 3514 (1996).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: M1, total reflecting flat mirror; D, iris diaphragm; W1, ZnSe antireflection window; W2, ZnSe antireflection window; Ch, intracavity chopper; W3, additional intracavity window; M2, outcoupler mirror; Pol, polarizer; Det1, fast detector for the vertical component; Det2, fast detector for the horizontal component.

Fig. 2
Fig. 2

Experimental measurement of (a) total intensity, (b) the transmitted polarized component when the polarizer in set at 45° with respect to the x axis, and (c) the reflected polarized component when the polarizer in set at 45° with respect to the x axis. The curves are not to scale because of different sensitivities and bias of the photodiodes.

Fig. 3
Fig. 3

Linear dependence of the competition oscillation frequency: (a) experimental, as a function of the tilt of window W3; (b) numerical, as a function of coupling parameter ε.

Fig. 4
Fig. 4

Experimental samples with different competition frequency durations. Equivalent numerical results obtained for (a) δ=0.005, ε=0.8, and ν=330 kHz and (b) δ=0.05, ε=0.8, and ν=330 kHz.

Equations (6)

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E˙x=κPx-Ex,
E˙y=κPy-Ey,
P˙x=-γ1+iδPx-DEx+εEy,
P˙y=-γ1+iδPy-DEy-εEx,
D˙=-γD-r+1/2ExPx*+Ex*Px+EyPy*+Ey*Py,
κt=K1+K2-K1exp-t/s,

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