Abstract

We have experimentally controlled the chaotic output of a single-mode semiconductor laser pumped near threshold and subject to optical feedback. We used a novel technique called dynamic targeting, which was theoretically proposed by Wieland et al. [Opt. Lett. 22, 469 (1997)]. Optical feedback causes the semiconductor laser to undergo a bifurcation cascade that exhibits regions of stability, periodicity, chaos, and coherence collapse. By adjusting the feedback phase simultaneously as the feedback strength was varied we steered the laser into the stable maximum gain mode, and thus we stabilized the system at maximum intensity.

© 1998 Optical Society of America

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  1. D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE–25, 674 (1985).
    [CrossRef]
  2. C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
    [CrossRef]
  3. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
    [CrossRef]
  4. J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
    [CrossRef]
  5. S. I. Turovets, J. Dellunde, and K. A. Shore, presented at the European Quantum Electronics Conference, Hamburg, Germany, September 8–13, 1996.
  6. J. Wieland, C. R. Mirasso, and D. Lenstra, Opt. Lett. 22, 469 (1997).
    [CrossRef] [PubMed]
  7. B. Tromborg and J. Mork, IEEE Photon. Technol. Lett. 2, 549 (1990).
    [CrossRef]
  8. A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
    [CrossRef]
  9. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  10. P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
    [CrossRef] [PubMed]
  11. D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 225 (1984).
  12. T. Sano, Phys. Rev. A 50, 2719 (1995).
    [CrossRef]
  13. G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
    [CrossRef]

1997

J. Wieland, C. R. Mirasso, and D. Lenstra, Opt. Lett. 22, 469 (1997).
[CrossRef] [PubMed]

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
[CrossRef]

1996

P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
[CrossRef] [PubMed]

1995

T. Sano, Phys. Rev. A 50, 2719 (1995).
[CrossRef]

A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

1994

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

1990

B. Tromborg and J. Mork, IEEE Photon. Technol. Lett. 2, 549 (1990).
[CrossRef]

1985

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE–25, 674 (1985).
[CrossRef]

1984

D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 225 (1984).

1982

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

1980

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

1977

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Alsing, P.

P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
[CrossRef] [PubMed]

Dellunde, J.

S. I. Turovets, J. Dellunde, and K. A. Shore, presented at the European Quantum Electronics Conference, Hamburg, Germany, September 8–13, 1996.

den Boef, A. J.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE–25, 674 (1985).
[CrossRef]

Erneux, T.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
[CrossRef]

P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
[CrossRef] [PubMed]

A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

Gauthier, D. J.

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Gavrielides, A.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
[CrossRef]

P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
[CrossRef] [PubMed]

Grebogi, C.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

Jaskorzynska, B.

D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 225 (1984).

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Kovanis, V.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
[CrossRef]

P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
[CrossRef] [PubMed]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Lenstra, D.

J. Wieland, C. R. Mirasso, and D. Lenstra, Opt. Lett. 22, 469 (1997).
[CrossRef] [PubMed]

A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE–25, 674 (1985).
[CrossRef]

D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 225 (1984).

Levine, A. M.

A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

Lythe, G.

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
[CrossRef]

Mirasso, C. R.

Mork, J.

B. Tromborg and J. Mork, IEEE Photon. Technol. Lett. 2, 549 (1990).
[CrossRef]

Ott, E.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

Risch, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Sano, T.

T. Sano, Phys. Rev. A 50, 2719 (1995).
[CrossRef]

Shore, K. A.

S. I. Turovets, J. Dellunde, and K. A. Shore, presented at the European Quantum Electronics Conference, Hamburg, Germany, September 8–13, 1996.

Socolar, J. E. S.

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Sukow, D. W.

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Tromborg, B.

B. Tromborg and J. Mork, IEEE Photon. Technol. Lett. 2, 549 (1990).
[CrossRef]

Turovets, S. I.

S. I. Turovets, J. Dellunde, and K. A. Shore, presented at the European Quantum Electronics Conference, Hamburg, Germany, September 8–13, 1996.

van Tartwijk, G. H. M.

A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

van Vaalen, M.

D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 225 (1984).

Verbeek, B. H.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE–25, 674 (1985).
[CrossRef]

Voumard, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Wieland, J.

Yorke, J. A.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

IEEE J. Quantum Electron.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE–25, 674 (1985).
[CrossRef]

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

IEEE Photon. Technol. Lett.

B. Tromborg and J. Mork, IEEE Photon. Technol. Lett. 2, 549 (1990).
[CrossRef]

J. Appl. Phys.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Opt. Lett.

Phys. Rev. A

T. Sano, Phys. Rev. A 50, 2719 (1995).
[CrossRef]

G. Lythe, T. Erneux, A. Gavrielides, and V. Kovanis, Phys. Rev. A 55, 4443 (1997).
[CrossRef]

A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
[CrossRef]

P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
[CrossRef] [PubMed]

Phys. Rev. E

J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E 50, 3245 (1994).
[CrossRef]

Phys. Rev. Lett.

C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982).
[CrossRef]

Physica C

D. Lenstra, M. van Vaalen, and B. Jaskorzynska, Physica C 125, 225 (1984).

Other

S. I. Turovets, J. Dellunde, and K. A. Shore, presented at the European Quantum Electronics Conference, Hamburg, Germany, September 8–13, 1996.

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Figures (2)

Fig. 1
Fig. 1

(a) The dots show the computed bifurcation cascade for the semiconductor laser pumped 0.001 above threshold and subject to optical feedback. The laser response shows regions of stability where it operates in the MGM and regions of instabilities where it exhibits chaos and low-frequency fluctuations. The dashed curve shows the stabilized laser intensity as the feedback phase is adjusted by means of ω0 as the feedback strength is increased. (b) Stabilization of the laser intensity as we control the feedback phase by varying the pump current by ΔP=0.17Δω0, which corresponds to 1.1 GHz/mA. The intensity is stabilized and falls off as the pump current is decreased.

Fig. 2
Fig. 2

(a) Mean intensities plotted with their standard deviations as error bars for a fixed current at 27.00  mA as the feedback strength is increased. We observe regimes in which the laser intensity is high and the fluctuations are very small, indicating that the laser is in the stable MGM. Yet there are also regimes in which the laser intensity is comparatively low and the standard deviation is very high, indicating that the laser intensity fluctuates strongly. (b) Experimental implementation of dynamic targeting by decreasing the pump current from 31 to 27  mA as the feedback strength is varied. We can clearly see that the laser always operates in the stable mode and that all instabilities have been eliminated.

Equations (7)

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

dEdE=1+iαNE+κEs-τexp-iω0τ,
TdNds=P-N-1+2NE2.
Es2=P+κ cosΔ1-2κ cosΔ,Ns=-κ cosΔ,
Δ-ω0τ=-κτα cosΔ+sinΔ;
1-κτα sinΔ-cosΔ>0
ω0τ=κτα mod 2π.
dEds=1+iαNE+κEs-τexp-iω0+xτ,

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