Abstract

We investigate the dynamical behavior of two laser diodes coupled through mutual injection of their optical fields when placed face to face with a small separation between them. We report symmetry breaking in periodic solutions at low coupling rates. In addition, we demonstrate that at higher coupling rates both lasers exhibit very fast periodic oscillations. The system is of practical interest, since it constitutes a tunable all-optical source of microwave oscillations.

© 2003 Optical Society of America

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  1. J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
    [CrossRef]
  2. C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
    [CrossRef]
  3. S. Donati and C. R. Mirasso, IEEE J. Quantum Electron. 38, 1138 (2002).
    [CrossRef]
  4. K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
    [CrossRef]
  5. A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
    [CrossRef]
  6. T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
    [CrossRef] [PubMed]
  7. J. Mulet, C. Masoller, and C. Mirasso, Phys. Rev. A 65, 063815 (2002).
    [CrossRef]
  8. C. Z. Ning, Opt. Lett. 27, 912 (2002).
    [CrossRef]
  9. T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
    [CrossRef]
  10. T. Erneux, A. Gavrielides, and M. Sciamanna, Phys. Rev. A 66, 033809 (2002).
    [CrossRef]

2002 (4)

S. Donati and C. R. Mirasso, IEEE J. Quantum Electron. 38, 1138 (2002).
[CrossRef]

J. Mulet, C. Masoller, and C. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

C. Z. Ning, Opt. Lett. 27, 912 (2002).
[CrossRef]

T. Erneux, A. Gavrielides, and M. Sciamanna, Phys. Rev. A 66, 033809 (2002).
[CrossRef]

2001 (2)

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
[CrossRef]

2000 (1)

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
[CrossRef]

1997 (2)

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
[CrossRef]

1988 (1)

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Carr, T. W.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Donati, S.

S. Donati and C. R. Mirasso, IEEE J. Quantum Electron. 38, 1138 (2002).
[CrossRef]

Elsässer, W.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Erneux, T.

T. Erneux, A. Gavrielides, and M. Sciamanna, Phys. Rev. A 66, 033809 (2002).
[CrossRef]

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
[CrossRef]

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
[CrossRef]

Fischer, I.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

García-Ojalvo, J.

C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
[CrossRef]

Gavrielides, A.

T. Erneux, A. Gavrielides, and M. Sciamanna, Phys. Rev. A 66, 033809 (2002).
[CrossRef]

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
[CrossRef]

Heil, T.

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Hohl, A.

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
[CrossRef]

Kovanis, V.

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
[CrossRef]

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
[CrossRef]

Leger, J. R.

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Li, R.-D.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Masoller, C.

J. Mulet, C. Masoller, and C. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

Mirasso, C.

J. Mulet, C. Masoller, and C. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

Mirasso, C. R.

S. Donati and C. R. Mirasso, IEEE J. Quantum Electron. 38, 1138 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Möller, M.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Mulet, J.

J. Mulet, C. Masoller, and C. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

Ning, C. Z.

Rogister, F.

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
[CrossRef]

Roy, R.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Sciamanna, M.

T. Erneux, A. Gavrielides, and M. Sciamanna, Phys. Rev. A 66, 033809 (2002).
[CrossRef]

Scott, M. L.

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Serrat, C.

C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
[CrossRef]

Thornburg, K. S.

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Torrent, M. C.

C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Vilaseca, R.

C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
[CrossRef]

Appl. Phys. Lett. (1)

J. R. Leger, M. L. Scott, and W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Donati and C. R. Mirasso, IEEE J. Quantum Electron. 38, 1138 (2002).
[CrossRef]

Opt. Commun. (1)

T. Erneux, F. Rogister, A. Gavrielides, and V. Kovanis, Opt. Commun. 183, 467 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, and T. Erneux, Phys. Rev. E 55, 3865 (1997).
[CrossRef]

Phys. Rev. A (3)

J. Mulet, C. Masoller, and C. Mirasso, Phys. Rev. A 65, 063815 (2002).
[CrossRef]

C. Serrat, M. C. Torrent, J. García-Ojalvo, and R. Vilaseca, Phys. Rev. A 64, 041802(R) (2001).
[CrossRef]

T. Erneux, A. Gavrielides, and M. Sciamanna, Phys. Rev. A 66, 033809 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

A. Hohl, A. Gavrielides, T. Erneux, and V. Kovanis, Phys. Rev. Lett. 78, 4745 (1997).
[CrossRef]

T. Heil, I. Fischer, W. Elsässer, J. Mulet, and C. R. Mirasso, Phys. Rev. Lett. 86, 795 (2001).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Bifurcation diagrams of the optical power emitted by (a), (c) laser 1 and (b), (d) laser 2. (c), (d) Enlarged views of (a) and (b), respectively. The coupling rate is the bifurcation parameter.

Fig. 2
Fig. 2

(a), (b) Time traces of the outputs of laser 1 (solid curve) and laser 2 (dotted curve) for η=5×10-4 and η=1.5×10-3, respectively. (c) Optical spectrum of laser 1 for η=5×10-4. (d), (e) Optical spectra of laser 1 and laser 2, respectively, for η=1.5×10-3.

Fig. 3
Fig. 3

(a) Time traces of the output of laser 1 (solid curve) and laser 2 (dotted curve). (b) Optical spectrum of laser 1. The coupling strength is η=0.16.

Fig. 4
Fig. 4

Frequency of periodic solutions versus coupling rate as obtained numerically (circles) from Eqs. (1) and (2) and analytically (squares) from Eqs. (5)–(7).

Equations (7)

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

dE1,2ds=1+iαN1,2E1,2+ηE2,1s-θexp-iΩθ,
TdN1,2ds=P-N1,2-1+2N1,2E1,22.
Ejs=Aja expiΔa-Ωs+Ajb expiΔb-Ωs,
Ejs2=Aja2+Ajb2+2AjaAjbcosωs+ϕj,
ηk=-Δaθ+2k+1π/2/θ sinΔaθ,
ωk=2Δaθ+2k+1π/θ,
α cotΔaθΔaθ+2k+1π2=-Ωθ-2k+1π2.

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