Abstract

We demonstrate numerically that low-frequency fluctuations (LFF’s) observed in a laser diode subjected to a first optical feedback with a short delay are suppressed by means of an adequate second optical feedback. The general idea of this technique is based on the observation that second feedback can suppress the antimodes that are responsible for the crises in the LFF regime. Furthermore, we observe that the second optical feedback can steer an unstable laser that is biased near threshold into a stable regime.

© 1999 Optical Society of America

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  1. J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
    [CrossRef]
  2. D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985).
    [CrossRef]
  3. C. Rish and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
    [CrossRef]
  4. J. Wieland, C. R. Mirasso, and D. Lenstra, Opt. Lett. 22, 469 (1997).
    [CrossRef] [PubMed]
  5. A. Hohl and A. Gavrielides, Opt. Lett. 23, 1606 (1998).
    [CrossRef]
  6. Y. Liu and J. Ohtsubo, IEEE J. Quantum Electron. 33, 1163 (1997).
    [CrossRef]
  7. A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
    [CrossRef]
  8. T. Sano, Phys. Rev. A 50, 2719 (1994).
    [CrossRef] [PubMed]
  9. A. Hohl and A. Gavrielides, Phys. Rev. Lett. 82, 1148 (1999).
    [CrossRef]
  10. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  11. P. Alsing, V. Kovanis, A. Gavrielides, and T. Erneux, Phys. Rev. A 53, 4429 (1996).
    [CrossRef] [PubMed]
  12. H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).
    [CrossRef]

1999

A. Hohl and A. Gavrielides, Phys. Rev. Lett. 82, 1148 (1999).
[CrossRef]

1998

1997

Y. Liu and J. Ohtsubo, IEEE J. Quantum Electron. 33, 1163 (1997).
[CrossRef]

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

1996

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

1995

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

1994

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef] [PubMed]

1992

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

1986

H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).
[CrossRef]

1985

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985).
[CrossRef]

1980

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

1977

C. Rish 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]

den Boef, A. J.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985).
[CrossRef]

Erneux, T.

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]

Gavrielides, A.

A. Hohl and A. Gavrielides, Phys. Rev. Lett. 82, 1148 (1999).
[CrossRef]

A. Hohl and A. Gavrielides, Opt. Lett. 23, 1606 (1998).
[CrossRef]

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

Hohl, A.

A. Hohl and A. Gavrielides, Phys. Rev. Lett. 82, 1148 (1999).
[CrossRef]

A. Hohl and A. Gavrielides, Opt. Lett. 23, 1606 (1998).
[CrossRef]

Kobayashi, K.

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

Kovanis, V.

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-21, 674 (1985).
[CrossRef]

Levine, A. M.

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

Liu, Y.

Y. Liu and J. Ohtsubo, IEEE J. Quantum Electron. 33, 1163 (1997).
[CrossRef]

Mark, J.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Mirasso, C. R.

Mork, J.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

Ohtsubo, J.

Y. Liu and J. Ohtsubo, IEEE J. Quantum Electron. 33, 1163 (1997).
[CrossRef]

Olesen, H.

H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).
[CrossRef]

Osmundsen, J. H.

H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).
[CrossRef]

Rish, C.

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

Sano, T.

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef] [PubMed]

Tromborg, B.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).
[CrossRef]

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]

Verbeek, B. H.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985).
[CrossRef]

Voumard, C.

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

Wieland, J.

IEEE J. Quantum Electron.

J. Mork, B. Tromborg, and J. Mark, IEEE J. Quantum Electron. 28, 93 (1992).
[CrossRef]

D. Lenstra, B. H. Verbeek, and A. J. den Boef, IEEE J. Quantum Electron. QE-21, 674 (1985).
[CrossRef]

Y. Liu and J. Ohtsubo, IEEE J. Quantum Electron. 33, 1163 (1997).
[CrossRef]

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

H. Olesen, J. H. Osmundsen, and B. Tromborg, IEEE J. Quantum Electron. QE-22, 762 (1986).
[CrossRef]

J. Appl. Phys.

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

Opt. Lett.

Phys. Rev. A

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

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef] [PubMed]

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

Phys. Rev. Lett.

A. Hohl and A. Gavrielides, Phys. Rev. Lett. 82, 1148 (1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic configuration of a laser diode subjected to optical feedback from a double cavity.

Fig. 2
Fig. 2

(a) Stationary angular frequencies Δ as a function of κ2. Thick curves, antimodes; thin curves, external-cavity modes. (b) Bifurcation diagram of the phase-difference function ϕt-ϕt-τ1+Ωτ1. The second-feedback strength κ2 is the bifurcation variable. Arrow 1 indicates the disappearance of the antimode that is responsible for the crisis, and arrow 2 indicates the corresponding LFF suppression.

Fig. 3
Fig. 3

Phase trajectories observed in the space ϕt-ϕt-τ1+Ωτ1,Nt. Asterisks, antimodes; open circles, unstable external-cavity modes; filled circles, stable external-cavity modes. (a) LFF for κ2=0. (b) Quasi-periodic behavior with frequency locking for κ2=0.5×10-3. (c) Limit cycle corresponding to periodic behavior for κ2=1×10-3. (d) Stationary behavior for κ2=4×10-3: The laser locks into a stable external-cavity mode. The first-feedback strength is κ1=4.6×10-3 in all cases.

Equations (3)

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

dE/ds=1+iαNE+κ1Es-τ1exp-iΩτ1+κ2Es-τ2exp-iΩτ2, TdN/ds=P-N-1+2NE2,
Δ=Ω-κ1α cosΔτ1+sinΔτ1-κ2α cosΔτ2+sinΔτ2,
As2=P-Ns1+2 Ns, Ns=-κ1 cosΔτ1-κ2 cosΔτ2.

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