Abstract

Chaos has been controlled with the occasional proportional feedback technique in a delayed optical bistable system that consists of a laser-diode interferometer with a delayed optoelectronic feedback. A variety of subharmonic periodic orbits and high mode oscillations are stabilized at different time delays. No knowledge about the dynamical equation is required for the control. The synchronizing frequency can be readily estimated from the ratio of the delay and the system relaxation times.

© 1994 Optical Society of America

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References

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  1. E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
    [Crossref] [PubMed]
  2. W. L. Ditto, S. N. Rauseo, M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
    [Crossref] [PubMed]
  3. J. Singer, Y-Z. Wang, H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
    [Crossref] [PubMed]
  4. A. Azevedo, S. M. Rezende, Phys. Rev. Lett. 66, 1342 (1991).
    [Crossref] [PubMed]
  5. R. W. Rollins, P. Parmananda, P. Sherard, Phys. Rev. A 47, R780 (1993).
  6. E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
    [Crossref] [PubMed]
  7. R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
    [Crossref] [PubMed]
  8. Y. Liu, J. Ohtsubo, J. Opt. Soc. Am. B 9, 261 (1992).
    [Crossref]
  9. Y. Liu, J. Ohtsubo, Opt. Commun. 85, 457 (1991); Opt. Commun. 93, 311 (1992).
    [Crossref]
  10. Y. Liu, J. Ohtsubo, Y. Shoji, Opt. Commun. 105, 193 (1994).
    [Crossref]
  11. Y. Liu, J. Ohtsubo, Phys. Rev. A 47, 4392 (1993).
    [Crossref] [PubMed]
  12. R. Vallée, C. Delisle, Phys. Rev. A 31, 2390 (1985); Phys. Rev. A 34, 309 (1986).
    [Crossref] [PubMed]

1994 (1)

Y. Liu, J. Ohtsubo, Y. Shoji, Opt. Commun. 105, 193 (1994).
[Crossref]

1993 (2)

Y. Liu, J. Ohtsubo, Phys. Rev. A 47, 4392 (1993).
[Crossref] [PubMed]

R. W. Rollins, P. Parmananda, P. Sherard, Phys. Rev. A 47, R780 (1993).

1992 (2)

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Y. Liu, J. Ohtsubo, J. Opt. Soc. Am. B 9, 261 (1992).
[Crossref]

1991 (4)

Y. Liu, J. Ohtsubo, Opt. Commun. 85, 457 (1991); Opt. Commun. 93, 311 (1992).
[Crossref]

E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
[Crossref] [PubMed]

J. Singer, Y-Z. Wang, H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
[Crossref] [PubMed]

A. Azevedo, S. M. Rezende, Phys. Rev. Lett. 66, 1342 (1991).
[Crossref] [PubMed]

1990 (2)

E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

W. L. Ditto, S. N. Rauseo, M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
[Crossref] [PubMed]

1985 (1)

R. Vallée, C. Delisle, Phys. Rev. A 31, 2390 (1985); Phys. Rev. A 34, 309 (1986).
[Crossref] [PubMed]

Azevedo, A.

A. Azevedo, S. M. Rezende, Phys. Rev. Lett. 66, 1342 (1991).
[Crossref] [PubMed]

Bau, H. H.

J. Singer, Y-Z. Wang, H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
[Crossref] [PubMed]

Delisle, C.

R. Vallée, C. Delisle, Phys. Rev. A 31, 2390 (1985); Phys. Rev. A 34, 309 (1986).
[Crossref] [PubMed]

Ditto, W. L.

W. L. Ditto, S. N. Rauseo, M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
[Crossref] [PubMed]

Gills, Z.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Grebogi, C.

E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

Hunt, E. R.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, J. Ohtsubo, Y. Shoji, Opt. Commun. 105, 193 (1994).
[Crossref]

Y. Liu, J. Ohtsubo, Phys. Rev. A 47, 4392 (1993).
[Crossref] [PubMed]

Y. Liu, J. Ohtsubo, J. Opt. Soc. Am. B 9, 261 (1992).
[Crossref]

Y. Liu, J. Ohtsubo, Opt. Commun. 85, 457 (1991); Opt. Commun. 93, 311 (1992).
[Crossref]

Maier, T. D.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Murphy, T. W.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Ohtsubo, J.

Y. Liu, J. Ohtsubo, Y. Shoji, Opt. Commun. 105, 193 (1994).
[Crossref]

Y. Liu, J. Ohtsubo, Phys. Rev. A 47, 4392 (1993).
[Crossref] [PubMed]

Y. Liu, J. Ohtsubo, J. Opt. Soc. Am. B 9, 261 (1992).
[Crossref]

Y. Liu, J. Ohtsubo, Opt. Commun. 85, 457 (1991); Opt. Commun. 93, 311 (1992).
[Crossref]

Ott, E.

E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

Parmananda, P.

R. W. Rollins, P. Parmananda, P. Sherard, Phys. Rev. A 47, R780 (1993).

Rauseo, S. N.

W. L. Ditto, S. N. Rauseo, M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
[Crossref] [PubMed]

Rezende, S. M.

A. Azevedo, S. M. Rezende, Phys. Rev. Lett. 66, 1342 (1991).
[Crossref] [PubMed]

Rollins, R. W.

R. W. Rollins, P. Parmananda, P. Sherard, Phys. Rev. A 47, R780 (1993).

Roy, R.

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

Sherard, P.

R. W. Rollins, P. Parmananda, P. Sherard, Phys. Rev. A 47, R780 (1993).

Shoji, Y.

Y. Liu, J. Ohtsubo, Y. Shoji, Opt. Commun. 105, 193 (1994).
[Crossref]

Singer, J.

J. Singer, Y-Z. Wang, H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
[Crossref] [PubMed]

Spano, M. L.

W. L. Ditto, S. N. Rauseo, M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
[Crossref] [PubMed]

Vallée, R.

R. Vallée, C. Delisle, Phys. Rev. A 31, 2390 (1985); Phys. Rev. A 34, 309 (1986).
[Crossref] [PubMed]

Wang, Y-Z.

J. Singer, Y-Z. Wang, H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
[Crossref] [PubMed]

Yorke, J. A.

E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

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

Opt. Commun. (2)

Y. Liu, J. Ohtsubo, Opt. Commun. 85, 457 (1991); Opt. Commun. 93, 311 (1992).
[Crossref]

Y. Liu, J. Ohtsubo, Y. Shoji, Opt. Commun. 105, 193 (1994).
[Crossref]

Phys. Rev. A (3)

Y. Liu, J. Ohtsubo, Phys. Rev. A 47, 4392 (1993).
[Crossref] [PubMed]

R. Vallée, C. Delisle, Phys. Rev. A 31, 2390 (1985); Phys. Rev. A 34, 309 (1986).
[Crossref] [PubMed]

R. W. Rollins, P. Parmananda, P. Sherard, Phys. Rev. A 47, R780 (1993).

Phys. Rev. Lett. (6)

E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
[Crossref] [PubMed]

R. Roy, T. W. Murphy, T. D. Maier, Z. Gills, E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992).
[Crossref] [PubMed]

E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
[Crossref] [PubMed]

W. L. Ditto, S. N. Rauseo, M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
[Crossref] [PubMed]

J. Singer, Y-Z. Wang, H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
[Crossref] [PubMed]

A. Azevedo, S. M. Rezende, Phys. Rev. Lett. 66, 1342 (1991).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the delayed optical bistable system and the OPF controller: PD, photodiode; S/H, sample-and-hold circuit; AMP’s, amplifiers.

Fig. 2
Fig. 2

Experimental results for tr = 0.12 ms and Ib = 60.75 mA: (a) without the control, (b) fs = 2.45 kHz, (c) fs = 0.61 kHz.

Fig. 3
Fig. 3

Experimental results for tr = 2.0 ms and Ib = 56.44 mA: (a) without the control, (b) fs = 2.64 kHz, (c) fs = 5.04 kHz.

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