Abstract

We study the unstable behavior of a liquid-crystal hybrid bistable device with two time delays in the feedback mechanism. We report the observation of frustrated instability, frequency locking, and hysteresis on varying the control parameters. The results of our experiments are in agreement with the theoretical analysis presented by Ikeda and Mizuno [Phys. Rev. Lett. 53, (1984)].

© 1986 Optical Society of America

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References

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  1. B. V. Chirikov, Phys. Rep. 52, 263 (1979); L. Glass, R. Perez, Phys. Rev. Lett. 48, 1722 (1982); Phys. Lett. 90A, 441 (1982); S. J. Shenker, Physica 5D, 405 (1982); M. R. Guevara, L. Glass, A. Shrier, Science 214, 1350 (1981).
    [CrossRef] [PubMed]
  2. V. N. Belykh, N. F. Pedersen, O. H. Soerensen, Phys. Rev. B 16, 4853, 4860 (1977).
    [CrossRef]
  3. K. Tomita, I. Tsuda, Prog. Theor. Phys. 64, 1138 (1980); I. Tsuda, Phys. Lett. 85A, 4 (1981).
    [CrossRef]
  4. P. Bak, Rep. Prog. Phys. 45, 588 (1982).
    [CrossRef]
  5. S. L. McCall, Appl. Phys. Lett. 32, 284 (1978); M. M. Cheung, S. D. Durbin, Y. R. Shen, Opt. Lett. 8, 39 (1983).
    [CrossRef] [PubMed]
  6. K. Ikeda, M. Mizuno, Phys. Rev. Lett. 53, 1340 (1984).
    [CrossRef]
  7. H. J. Zhang, J. H. Dai, P. Y. Wang, Z. D. Jian, J. Opt. Soc. Am. B 3, 231 (1986).
    [CrossRef]
  8. K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); H. M. Gibbs, F. A. Hopf, D. L. Kaplan, R. L. Shoemaker, Phys. Rev. Lett. 46, 474 (1981); F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, Phys. Rev. A 25, 2172 (1982); J. Y. Gao, L. M. Narducci, L. S. Schulman, M. Squicciarini, J. M. Yuan, Phys. Rev. A 28, 2910 (1983).
    [CrossRef]
  9. H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983), pp. 42 and 239.

1986 (1)

1984 (1)

K. Ikeda, M. Mizuno, Phys. Rev. Lett. 53, 1340 (1984).
[CrossRef]

1982 (1)

P. Bak, Rep. Prog. Phys. 45, 588 (1982).
[CrossRef]

1980 (1)

K. Tomita, I. Tsuda, Prog. Theor. Phys. 64, 1138 (1980); I. Tsuda, Phys. Lett. 85A, 4 (1981).
[CrossRef]

1979 (2)

K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); H. M. Gibbs, F. A. Hopf, D. L. Kaplan, R. L. Shoemaker, Phys. Rev. Lett. 46, 474 (1981); F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, Phys. Rev. A 25, 2172 (1982); J. Y. Gao, L. M. Narducci, L. S. Schulman, M. Squicciarini, J. M. Yuan, Phys. Rev. A 28, 2910 (1983).
[CrossRef]

B. V. Chirikov, Phys. Rep. 52, 263 (1979); L. Glass, R. Perez, Phys. Rev. Lett. 48, 1722 (1982); Phys. Lett. 90A, 441 (1982); S. J. Shenker, Physica 5D, 405 (1982); M. R. Guevara, L. Glass, A. Shrier, Science 214, 1350 (1981).
[CrossRef] [PubMed]

1978 (1)

S. L. McCall, Appl. Phys. Lett. 32, 284 (1978); M. M. Cheung, S. D. Durbin, Y. R. Shen, Opt. Lett. 8, 39 (1983).
[CrossRef] [PubMed]

1977 (1)

V. N. Belykh, N. F. Pedersen, O. H. Soerensen, Phys. Rev. B 16, 4853, 4860 (1977).
[CrossRef]

Bak, P.

P. Bak, Rep. Prog. Phys. 45, 588 (1982).
[CrossRef]

Belykh, V. N.

V. N. Belykh, N. F. Pedersen, O. H. Soerensen, Phys. Rev. B 16, 4853, 4860 (1977).
[CrossRef]

Chirikov, B. V.

B. V. Chirikov, Phys. Rep. 52, 263 (1979); L. Glass, R. Perez, Phys. Rev. Lett. 48, 1722 (1982); Phys. Lett. 90A, 441 (1982); S. J. Shenker, Physica 5D, 405 (1982); M. R. Guevara, L. Glass, A. Shrier, Science 214, 1350 (1981).
[CrossRef] [PubMed]

Dai, J. H.

Haken, H.

H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983), pp. 42 and 239.

Ikeda, K.

K. Ikeda, M. Mizuno, Phys. Rev. Lett. 53, 1340 (1984).
[CrossRef]

K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); H. M. Gibbs, F. A. Hopf, D. L. Kaplan, R. L. Shoemaker, Phys. Rev. Lett. 46, 474 (1981); F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, Phys. Rev. A 25, 2172 (1982); J. Y. Gao, L. M. Narducci, L. S. Schulman, M. Squicciarini, J. M. Yuan, Phys. Rev. A 28, 2910 (1983).
[CrossRef]

Jian, Z. D.

McCall, S. L.

S. L. McCall, Appl. Phys. Lett. 32, 284 (1978); M. M. Cheung, S. D. Durbin, Y. R. Shen, Opt. Lett. 8, 39 (1983).
[CrossRef] [PubMed]

Mizuno, M.

K. Ikeda, M. Mizuno, Phys. Rev. Lett. 53, 1340 (1984).
[CrossRef]

Pedersen, N. F.

V. N. Belykh, N. F. Pedersen, O. H. Soerensen, Phys. Rev. B 16, 4853, 4860 (1977).
[CrossRef]

Soerensen, O. H.

V. N. Belykh, N. F. Pedersen, O. H. Soerensen, Phys. Rev. B 16, 4853, 4860 (1977).
[CrossRef]

Tomita, K.

K. Tomita, I. Tsuda, Prog. Theor. Phys. 64, 1138 (1980); I. Tsuda, Phys. Lett. 85A, 4 (1981).
[CrossRef]

Tsuda, I.

K. Tomita, I. Tsuda, Prog. Theor. Phys. 64, 1138 (1980); I. Tsuda, Phys. Lett. 85A, 4 (1981).
[CrossRef]

Wang, P. Y.

Zhang, H. J.

Appl. Phys. Lett. (1)

S. L. McCall, Appl. Phys. Lett. 32, 284 (1978); M. M. Cheung, S. D. Durbin, Y. R. Shen, Opt. Lett. 8, 39 (1983).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, O. Akimoto, Phys. Rev. Lett. 45, 709 (1980); H. M. Gibbs, F. A. Hopf, D. L. Kaplan, R. L. Shoemaker, Phys. Rev. Lett. 46, 474 (1981); F. A. Hopf, D. L. Kaplan, H. M. Gibbs, R. L. Shoemaker, Phys. Rev. A 25, 2172 (1982); J. Y. Gao, L. M. Narducci, L. S. Schulman, M. Squicciarini, J. M. Yuan, Phys. Rev. A 28, 2910 (1983).
[CrossRef]

Phys. Rep. (1)

B. V. Chirikov, Phys. Rep. 52, 263 (1979); L. Glass, R. Perez, Phys. Rev. Lett. 48, 1722 (1982); Phys. Lett. 90A, 441 (1982); S. J. Shenker, Physica 5D, 405 (1982); M. R. Guevara, L. Glass, A. Shrier, Science 214, 1350 (1981).
[CrossRef] [PubMed]

Phys. Rev. B (1)

V. N. Belykh, N. F. Pedersen, O. H. Soerensen, Phys. Rev. B 16, 4853, 4860 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

K. Ikeda, M. Mizuno, Phys. Rev. Lett. 53, 1340 (1984).
[CrossRef]

Prog. Theor. Phys. (1)

K. Tomita, I. Tsuda, Prog. Theor. Phys. 64, 1138 (1980); I. Tsuda, Phys. Lett. 85A, 4 (1981).
[CrossRef]

Rep. Prog. Phys. (1)

P. Bak, Rep. Prog. Phys. 45, 588 (1982).
[CrossRef]

Other (1)

H. Haken, Advanced Synergetics (Springer-Verlag, Berlin, 1983), pp. 42 and 239.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the hybrid optical bistable device with two time delays in the feedback loops. He–Ne, laser; D, photodetector; AMP, amplifier; BUF, microcomputer buffer; A/D, analog-to-digital converter; D/A, digital-to-analog converter; LC, liquid crystal.

Fig. 2
Fig. 2

Typical waveform and its power spectrum in the case of single-frequency oscillations.

Fig. 3
Fig. 3

Frequency F of single-frequency oscillations as a function of the ratio of the delay times for τ = 20 and t1 = 2.5 sec Points show the quasi-periodic motion.

Fig. 4
Fig. 4

Waveform and its power spectrum for quasi-periodic motion; Iin = 180 mV, VB = 0.9 V, ω = 0.5.

Fig. 5
Fig. 5

Beat pattern for ω = 0.9, Iin = 170 mV, VB = 1.7 V.

Fig. 6
Fig. 6

Frequency locking as a function of the input intensity for fixed XB.

Fig. 7
Fig. 7

Frequency locking as a function of the bias voltage for fixed Iin.

Fig. 8
Fig. 8

Typical results from the numerical integration of Eq. (3); ω = 0.95, A = 2, Xb = −1.

Equations (4)

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ω = t 1 - t 2 / ( t 1 + t 2 ) ,
γ - 1 d ϕ / d t = - ϕ + E ( t - t 1 ) 2 + E ( t - t 2 ) 2 ,
E ( t ) 2 = A 2 { 1 + 2 B cos [ ϕ ( t ) - ϕ 0 ] } .
γ - 1 d X ( t ) / d t = - X ( t ) + A sin 2 [ X ( t - t 1 ) + X ( t - t 2 ) - X b ] ,

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