Abstract

We analyze theoretically a case of antiphase dynamics in the self-pulsing regime involving two orthogonal polarizations in intracavity second-harmonic generation. We show that, for this model, antiphase dynamics may lead to a nonreciprocal independence of the two polarizations as a result of partial overlap between the pulses. In the case in which two modes oscillate with one polarization and a single mode oscillates with orthogonal polarization, we find that the two modes can display chaos while the orthogonal mode remains periodic, despite coupling among all the modes.

© 1994 Optical Society of America

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References

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  1. K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
    [CrossRef]
  2. G. E. James, E. M. Harrell, R. Roy, Phys. Rev. A 41, 2778 (1990).
    [CrossRef] [PubMed]
  3. G. E. James, E. M. Harrell, C. Bracikowski, K. Wiesenfield, R. Roy, Opt. Lett. 15, 1141 (1990).
    [CrossRef] [PubMed]
  4. C. Bracikowski, R. Roy, Chaos 1, 49 (1991).
    [CrossRef] [PubMed]
  5. R. Roy, C. Bracikowski, G. E. James, in Proceedings of International Conference on Quantum Optics, R. Inguva, G. S. Agarwal, eds. (Plenum, New York, 1993), p. 231.
  6. J. Wang, P. Mandel, Phys. Rev. A 48, 671 (1993).
    [CrossRef]
  7. M. Oka, S. Kubota, Opt. Lett. 13, 805 (1988).
    [CrossRef] [PubMed]
  8. N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).
  9. It was shown in the first experimental report of Baer that chaos requires at least three modes, while the two-mode operation could display self-pulsing but not chaos:T. Baer, J. Opt. Soc. Am. B 3, 1175 (1986).
    [CrossRef]

1994

N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).

1993

J. Wang, P. Mandel, Phys. Rev. A 48, 671 (1993).
[CrossRef]

1991

C. Bracikowski, R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

1990

K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef]

G. E. James, E. M. Harrell, R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell, C. Bracikowski, K. Wiesenfield, R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

1988

1986

Abraham, N. B.

N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).

Baer, T.

Bracikowski, C.

C. Bracikowski, R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell, C. Bracikowski, K. Wiesenfield, R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef]

R. Roy, C. Bracikowski, G. E. James, in Proceedings of International Conference on Quantum Optics, R. Inguva, G. S. Agarwal, eds. (Plenum, New York, 1993), p. 231.

Everett, L. L.

N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).

Harrell, E. M.

Iwata, C.

N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).

James, G.

K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef]

James, G. E.

G. E. James, E. M. Harrell, C. Bracikowski, K. Wiesenfield, R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell, R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

R. Roy, C. Bracikowski, G. E. James, in Proceedings of International Conference on Quantum Optics, R. Inguva, G. S. Agarwal, eds. (Plenum, New York, 1993), p. 231.

Janicki, M. B.

N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).

Kubota, S.

Mandel, P.

J. Wang, P. Mandel, Phys. Rev. A 48, 671 (1993).
[CrossRef]

Oka, M.

Roy, R.

C. Bracikowski, R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

G. E. James, E. M. Harrell, C. Bracikowski, K. Wiesenfield, R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef]

G. E. James, E. M. Harrell, R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

R. Roy, C. Bracikowski, G. E. James, in Proceedings of International Conference on Quantum Optics, R. Inguva, G. S. Agarwal, eds. (Plenum, New York, 1993), p. 231.

Wang, J.

J. Wang, P. Mandel, Phys. Rev. A 48, 671 (1993).
[CrossRef]

Wiesenfield, K.

G. E. James, E. M. Harrell, C. Bracikowski, K. Wiesenfield, R. Roy, Opt. Lett. 15, 1141 (1990).
[CrossRef] [PubMed]

K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef]

Chaos

C. Bracikowski, R. Roy, Chaos 1, 49 (1991).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

G. E. James, E. M. Harrell, R. Roy, Phys. Rev. A 41, 2778 (1990).
[CrossRef] [PubMed]

J. Wang, P. Mandel, Phys. Rev. A 48, 671 (1993).
[CrossRef]

Phys. Rev. Lett.

K. Wiesenfield, C. Bracikowski, G. James, R. Roy, Phys. Rev. Lett. 65, 1749 (1990).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

N. B. Abraham, L. L. Everett, C. Iwata, M. B. Janicki, Proc. Soc. Photo-Opt. Instrum. Eng. 2095, 128 (1994).

Other

R. Roy, C. Bracikowski, G. E. James, in Proceedings of International Conference on Quantum Optics, R. Inguva, G. S. Agarwal, eds. (Plenum, New York, 1993), p. 231.

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Figures (4)

Fig. 1
Fig. 1

Intensity of the three modes for g = 0.5165 (the periodic regime). The fixed parameters are τc/τf = 0.002, β = 0.292, α = 0.02, γ = 0.095, and = 0.05.

Fig. 2
Fig. 2

Mode intensites for g = 0.5161 (the chaotic regime). The fixed parameters are as in Fig. 1.

Fig. 3
Fig. 3

Relaxation after an abrupt perturbation. The three modes are prepared in the state of Fig. 1. (a) At t = 0, I1, is changed from 0.108 to 0.8 and I2 is changed from 1.05 to 0.2; (b) at t = 0, I3 is changed from 0.001 to 0.5.

Fig. 4
Fig. 4

Response of the system to multiplicative noise. The three modes are prepared in the state of Fig. 1. (a) Noise is added to mode 1, (b) noise is added to mode 3.

Tables (1)

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Table 1 Dynamic Regimes as a Function of ga

Equations (2)

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τ c d I k d t = ( G k - α - g I k - 2 j k μ j k I j ) I k ,
τ f d G k d t = γ - ( 1 + I k + β j k I j ) G k ,

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