Abstract

A method is described for suppressing chaotic instabilities in lasers by use of a specific form of controlling-chaos feedback. The technique is easy to implement and requires only application of small perturbations to an accessible system parameter or variable.

© 1998 Optical Society of America

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References

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  1. D. J. Gauthier, Nonlinear Sci. Today 4(2), 1 (1994).
  2. E. Ott and M. Spano, Phys. Today 48 (5) , 34 (1995).
    [CrossRef]
  3. J.-H. Dai, H.-W. Yin, and H.-J. Zhang, Opt. Commun. 120, 85 (1995); T. W. Carr and I. B. Schwartz, Physica D 96, 17 (1996); D. Auerback and J. A. Yorke, J. Opt. Soc. Am. B 13, 2178 (1996); C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1997); R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996); W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 76, 3316 (1997); M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997); and N. A. Loiko, A. V. Naumenko, S. I. Turovets, P. S. Spencer, and K. A. Shore, Quantum Semiclass. Opt. 9, 853 (1997).
    [CrossRef] [PubMed]
  4. Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
    [CrossRef] [PubMed]
  5. A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).
  6. D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
    [CrossRef]
  7. K. Ogata, Modern Control Engineering, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1990), Sec. 4–6.
  8. B. Dahmani, L. Hollberg, and R. Drullinger, Opt. Lett. 12, 876 (1987).
    [CrossRef] [PubMed]

1997 (1)

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

1995 (2)

E. Ott and M. Spano, Phys. Today 48 (5) , 34 (1995).
[CrossRef]

J.-H. Dai, H.-W. Yin, and H.-J. Zhang, Opt. Commun. 120, 85 (1995); T. W. Carr and I. B. Schwartz, Physica D 96, 17 (1996); D. Auerback and J. A. Yorke, J. Opt. Soc. Am. B 13, 2178 (1996); C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1997); R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996); W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 76, 3316 (1997); M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997); and N. A. Loiko, A. V. Naumenko, S. I. Turovets, P. S. Spencer, and K. A. Shore, Quantum Semiclass. Opt. 9, 853 (1997).
[CrossRef] [PubMed]

1994 (1)

D. J. Gauthier, Nonlinear Sci. Today 4(2), 1 (1994).

1992 (1)

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

1987 (1)

Bienfang, J. C.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).

Bleich, M. E.

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

Chang, A.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).

Dahmani, B.

Dai, J.-H.

J.-H. Dai, H.-W. Yin, and H.-J. Zhang, Opt. Commun. 120, 85 (1995); T. W. Carr and I. B. Schwartz, Physica D 96, 17 (1996); D. Auerback and J. A. Yorke, J. Opt. Soc. Am. B 13, 2178 (1996); C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1997); R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996); W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 76, 3316 (1997); M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997); and N. A. Loiko, A. V. Naumenko, S. I. Turovets, P. S. Spencer, and K. A. Shore, Quantum Semiclass. Opt. 9, 853 (1997).
[CrossRef] [PubMed]

Drullinger, R.

Gardner, J. R.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).

Gauthier, D. J.

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

D. J. Gauthier, Nonlinear Sci. Today 4(2), 1 (1994).

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).

Gills, Z.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

Hall, G. M.

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).

Hollberg, L.

Iwata, C.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

Ogata, K.

K. Ogata, Modern Control Engineering, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1990), Sec. 4–6.

Ott, E.

E. Ott and M. Spano, Phys. Today 48 (5) , 34 (1995).
[CrossRef]

Roy, R.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

Schwartz, I. B.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

Socolar, J. E. S.

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

Spano, M.

E. Ott and M. Spano, Phys. Today 48 (5) , 34 (1995).
[CrossRef]

Sukow, D. W.

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

Triandaf, I.

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

Yin, H.-W.

J.-H. Dai, H.-W. Yin, and H.-J. Zhang, Opt. Commun. 120, 85 (1995); T. W. Carr and I. B. Schwartz, Physica D 96, 17 (1996); D. Auerback and J. A. Yorke, J. Opt. Soc. Am. B 13, 2178 (1996); C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1997); R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996); W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 76, 3316 (1997); M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997); and N. A. Loiko, A. V. Naumenko, S. I. Turovets, P. S. Spencer, and K. A. Shore, Quantum Semiclass. Opt. 9, 853 (1997).
[CrossRef] [PubMed]

Zhang, H.-J.

J.-H. Dai, H.-W. Yin, and H.-J. Zhang, Opt. Commun. 120, 85 (1995); T. W. Carr and I. B. Schwartz, Physica D 96, 17 (1996); D. Auerback and J. A. Yorke, J. Opt. Soc. Am. B 13, 2178 (1996); C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1997); R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996); W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 76, 3316 (1997); M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997); and N. A. Loiko, A. V. Naumenko, S. I. Turovets, P. S. Spencer, and K. A. Shore, Quantum Semiclass. Opt. 9, 853 (1997).
[CrossRef] [PubMed]

Chaos (1)

D. W. Sukow, M. E. Bleich, D. J. Gauthier, and J. E. S. Socolar, Chaos 7, 560 (1997).
[CrossRef]

Nonlinear Sci. Today (1)

D. J. Gauthier, Nonlinear Sci. Today 4(2), 1 (1994).

Opt. Commun. (1)

J.-H. Dai, H.-W. Yin, and H.-J. Zhang, Opt. Commun. 120, 85 (1995); T. W. Carr and I. B. Schwartz, Physica D 96, 17 (1996); D. Auerback and J. A. Yorke, J. Opt. Soc. Am. B 13, 2178 (1996); C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1997); R. Martin, A. J. Scroggie, G.-L. Oppo, and W. J. Firth, Phys. Rev. Lett. 77, 4007 (1996); W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 76, 3316 (1997); M. E. Bleich, D. Hochheiser, J. V. Moloney, and J. E. S. Socolar, Phys. Rev. E 55, 2119 (1997); and N. A. Loiko, A. V. Naumenko, S. I. Turovets, P. S. Spencer, and K. A. Shore, Quantum Semiclass. Opt. 9, 853 (1997).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. A 47, R2492 (1993); J. M. Perez, J. Steinshnider, R. E. Stallcup, and A. F. Aviles, Appl. Phys. Lett. 65, 1216 (1994); R. Meucci, A. Labate, and M. Ciofini, Phys. Rev. E 56, 2829 (1997).
[CrossRef] [PubMed]

Phys. Today (1)

E. Ott and M. Spano, Phys. Today 48 (5) , 34 (1995).
[CrossRef]

Other (2)

A. Chang, J. C. Bienfang, G. M. Hall, J. R. Gardner, and D. J. Gauthier, “Stabilizing unstable steady states using extended time-delay autosynchronization,” Chaos (to be published).

K. Ogata, Modern Control Engineering, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1990), Sec. 4–6.

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Figures (3)

Fig. 1
Fig. 1

Chaotic attractor of the single-mode laser.

Fig. 2
Fig. 2

(a) Possible realization of the incoherent control scheme with (b) its associated domain of control. The USS is unstable in the absence of control at wp=12.

Fig. 3
Fig. 3

(a) Possible realization of the coherent control scheme with (b) its associated domain of control.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

d/dt=-ω0+γdξ/dt,
dE/dt=-κE-v+Einj,
dv/dt=-v-Ew,
dw/dt=-γw+Ev-wp,
d/dt=-ω0+γidI/dt.
1>γi>1-1+γ+κκ+w¯p/2κw¯p-1.
dEinj/dt=-ω0Einj+γcTmdE/dt,
γc>12κκ2γ+1/γ+1+γ+14γwpκ/γ+1-1+γ+12-κ6γ2+4γ-κ-2/γ+121/2.

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