Abstract

We report on the dynamics that accompany polarization switching induced by orthogonal optical injection in a vertical-cavity surface-emitting laser (VCSEL). As the injection strength increases, the VCSEL bifurcates to injection-locked steady states and time-periodic and possibly chaotic dynamics. Of particular interest is a two-mode injection-locking solution, i.e., locking of the two VCSEL polarization modes. A detailed stability analysis unveils new bistability mechanisms in optical injection problems.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
    [Crossref]
  2. Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
    [Crossref]
  3. Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
    [Crossref]
  4. K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
    [Crossref]
  5. H. Kawaguchi and I. S. Hidayat, Electron. Lett. 31, 1150 (1995).
    [Crossref]
  6. D. L. Boiko, G. M. Stéphan, and P. Besnard, J. Appl. Phys. 86, 4096 (1999).
    [Crossref]
  7. F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
    [Crossref]
  8. K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL v2.00, available at http://www.cs-kuleuven.ac.be/ koen/delay/ddebiftool.shtml
  9. J. Guckenheimer, P. Holmes, and F. John, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1997).

2004 (1)

F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
[Crossref]

2000 (1)

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

1999 (2)

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

D. L. Boiko, G. M. Stéphan, and P. Besnard, J. Appl. Phys. 86, 4096 (1999).
[Crossref]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[Crossref]

1995 (1)

H. Kawaguchi and I. S. Hidayat, Electron. Lett. 31, 1150 (1995).
[Crossref]

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[Crossref]

Asom, M. T.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Bache, M.

F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
[Crossref]

Berghmans, F.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Besnard, P.

D. L. Boiko, G. M. Stéphan, and P. Besnard, J. Appl. Phys. 86, 4096 (1999).
[Crossref]

Boiko, D. L.

D. L. Boiko, G. M. Stéphan, and P. Besnard, J. Appl. Phys. 86, 4096 (1999).
[Crossref]

Caccia, P.

F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
[Crossref]

Castelli, F.

F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
[Crossref]

Dagenais, M.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Danckaert, J.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Engelborghs, K.

K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL v2.00, available at http://www.cs-kuleuven.ac.be/ koen/delay/ddebiftool.shtml

Focht, M. W.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Ghisoni, M.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

Guckenheimer, J.

J. Guckenheimer, P. Holmes, and F. John, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1997).

Guth, G. D.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Halonen, J.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

Hidayat, I. S.

H. Kawaguchi and I. S. Hidayat, Electron. Lett. 31, 1150 (1995).
[Crossref]

Holmes, P.

J. Guckenheimer, P. Holmes, and F. John, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1997).

Hong, Y.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

Jiang, S.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

John, F.

J. Guckenheimer, P. Holmes, and F. John, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1997).

Kawaguchi, H.

H. Kawaguchi and I. S. Hidayat, Electron. Lett. 31, 1150 (1995).
[Crossref]

Kojima, K.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Larsson, A.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

Leibenguth, R. E.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Luzyanina, T.

K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL v2.00, available at http://www.cs-kuleuven.ac.be/ koen/delay/ddebiftool.shtml

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[Crossref]

Miguel, M. San

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[Crossref]

Morgan, R. A.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Pan, Z. G.

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Panajotov, K.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Peeters, M.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Prati, F.

F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
[Crossref]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[Crossref]

Samaey, G.

K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL v2.00, available at http://www.cs-kuleuven.ac.be/ koen/delay/ddebiftool.shtml

Shore, K. A.

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

Stéphan, G. M.

D. L. Boiko, G. M. Stéphan, and P. Besnard, J. Appl. Phys. 86, 4096 (1999).
[Crossref]

Thienpont, H.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Veretennicoff, I.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Verschaffelt, G.

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

Appl. Phys. Lett. (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, Appl. Phys. Lett. 63, 2999 (1993).
[Crossref]

Electron. Lett. (2)

Y. Hong, K. A. Shore, A. Larsson, M. Ghisoni, and J. Halonen, Electron. Lett. 36, 2019 (2000).
[Crossref]

H. Kawaguchi and I. S. Hidayat, Electron. Lett. 31, 1150 (1995).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[Crossref]

IEEE Photonics Technol. Lett. (1)

K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, and H. Thienpont, IEEE Photonics Technol. Lett. 11, 985 (1999).
[Crossref]

J. Appl. Phys. (1)

D. L. Boiko, G. M. Stéphan, and P. Besnard, J. Appl. Phys. 86, 4096 (1999).
[Crossref]

Phys. Rev. A (1)

F. Prati, P. Caccia, M. Bache, and F. Castelli, Phys. Rev. A 69, 033810 (2004).
[Crossref]

Other (2)

K. Engelborghs, T. Luzyanina, and G. Samaey, DDE-BIFTOOL v2.00, available at http://www.cs-kuleuven.ac.be/ koen/delay/ddebiftool.shtml

J. Guckenheimer, P. Holmes, and F. John, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, 1997).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(Color online) Bifurcation diagram of I x and I y versus P inj I 0 .

Fig. 2
Fig. 2

Time traces of I x , y for P inj I 0 = (a1), (a2) 0.03%; (b1), (b2) 0.16%; (c1), (c2) 0.18%; (d1), (d2) 0.35%; (e1), (e2) 0.47%; (f1), (f2) 0.51%; (g1), (g2) 0.54%; and (h1), (h2) 0.55%.

Fig. 3
Fig. 3

Steady states and their stability for Δ ω ( rad ns ) = (a) 16 , (b) 20 , (c) 28 , (d) 28.5 , (e) 30 , (f) 34 . I x ( I y ) is plotted in darker (lighter) points and curves as a function of P inj I 0 . Symbols are defined in the text. Inserts, enlargements around branches of EPIL solutions.

Fig. 4
Fig. 4

Top, mapping of the steady-state stability boundaries. Bifurcations on the y LP (two-mode) injection-locked solution are plotted in lighter (darker) curves. Symbols and labels are defined in the text. Bottom, comparison of the bifurcation boundaries on EPIL for (b1) γ p = 30 rad ns and (b2) γ p = 40 rad ns or for (c1) γ s = 50 ns 1 , (c2) γ s = 100 ns 1 , and (c3) γ s = 300 ns 1 , with the other parameters remaining the same. Inserts, enlargements around several parts of the map.

Equations (4)

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

F ̇ x = κ ( 1 + i α ) ( D F x + i d F y F x ) i ( γ p + Δ ω ) F x γ a F x ,
F ̇ y = κ ( 1 + i α ) ( D F y i d F x F y ) + i ( γ p Δ ω ) F y + γ a F y + κ inj E inj 0 ,
D ̇ = γ e D γ e D F x 2 γ e D F y 2 + γ e μ i γ e d ( F y F x * F x F y * ) ,
d ̇ = γ s d γ e d F x 2 γ e d F y 2 i γ e D ( F y F x * F x F y * ) .

Metrics