Abstract

Extensive experimental and numerical investigations of feedback-induced instabilities in single-mode distributed-feedback lasers are presented that confirm the basic assumptions of the Lang–Kobayashi model. We give experimental evidence of the occurrence of low-frequency fluctuation (LFF), alternation between LFF and stable emission, and coherence collapse during single-mode operation of the laser. We have obtained quantitative agreement between modeling and experiment in long-time statistical investigations of the time intervals between subsequent LFF dropouts. In particular, we show that even the dependence of the dynamics on the injection current, which results in a scaling law, is quantitatively identical in modeling and experiment.

© 1999 Optical Society of America

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  1. J. Mørk, B. Tromborg, and L. Christiansen, IEEE J. Quantum Electron. 24, 123 (1988).
    [CrossRef]
  2. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
    [CrossRef]
  3. G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
    [CrossRef]
  4. D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
    [CrossRef]
  5. C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1996).
    [CrossRef]
  6. C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, IEEE Photon. Technol. Lett. 8, 299 (1996).
    [CrossRef]
  7. A. Hohl and A. Gavrielides, Opt. Lett. 23, 1606 (1998).
    [CrossRef]
  8. J. Wieland, C. R. Mirasso, and D. Lenstra, Opt. Lett. 22, 469 (1997).
    [CrossRef] [PubMed]
  9. A. M. Levine, G. H. M. van Tartwijk, D. Lenstra, and T. Erneux, Phys. Rev. A 52, R3436 (1995).
    [CrossRef]
  10. T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 58, R2672 (1998).
    [CrossRef]
  11. T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 60, 634 (1999).
    [CrossRef]
  12. C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. 22, 294 (1986).
    [CrossRef]
  13. D. W. Sukow, J. R. Gardner, and D. J. Gauthier, Phys. Rev. A 52, R3370 (1997).
    [CrossRef]
  14. J. Mulet and C. R. Mirasso, Phys. Rev. E 59, 5400 (1999).
    [CrossRef]

1999

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 60, 634 (1999).
[CrossRef]

J. Mulet and C. R. Mirasso, Phys. Rev. E 59, 5400 (1999).
[CrossRef]

1998

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

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 58, R2672 (1998).
[CrossRef]

1997

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

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, Phys. Rev. A 52, R3370 (1997).
[CrossRef]

1996

C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1996).
[CrossRef]

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

1995

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

1988

J. Mørk, B. Tromborg, and L. Christiansen, IEEE J. Quantum Electron. 24, 123 (1988).
[CrossRef]

1986

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. 22, 294 (1986).
[CrossRef]

1980

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

Balle, S.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

Christiansen, L.

J. Mørk, B. Tromborg, and L. Christiansen, IEEE J. Quantum Electron. 24, 123 (1988).
[CrossRef]

Colet, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Elsässer, W.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 60, 634 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 58, R2672 (1998).
[CrossRef]

Erneux, T.

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

Fischer, I.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 60, 634 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 58, R2672 (1998).
[CrossRef]

Garcia-Fernandez, P.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Gardner, J. R.

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, Phys. Rev. A 52, R3370 (1997).
[CrossRef]

Gauthier, D. J.

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, Phys. Rev. A 52, R3370 (1997).
[CrossRef]

Gavrielides, A.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

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

Giudici, M.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

Heil, T.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 60, 634 (1999).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 58, R2672 (1998).
[CrossRef]

Henry, C. H.

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. 22, 294 (1986).
[CrossRef]

Hess, O.

C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1996).
[CrossRef]

Hohl, A.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

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

Kazarinov, R. F.

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. 22, 294 (1986).
[CrossRef]

Kobayashi, K.

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

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 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]

Levine, A. M.

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

Menoni, C. S.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

Mirasso, C. R.

J. Mulet and C. R. Mirasso, Phys. Rev. E 59, 5400 (1999).
[CrossRef]

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

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Mørk, J.

J. Mørk, B. Tromborg, and L. Christiansen, IEEE J. Quantum Electron. 24, 123 (1988).
[CrossRef]

Mulet, J.

J. Mulet and C. R. Mirasso, Phys. Rev. E 59, 5400 (1999).
[CrossRef]

Rocca, J. J.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

Simmendinger, C.

C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1996).
[CrossRef]

Sukow, D. W.

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, Phys. Rev. A 52, R3370 (1997).
[CrossRef]

Tredicce, J. R.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

Tromborg, B.

J. Mørk, B. Tromborg, and L. Christiansen, IEEE J. Quantum Electron. 24, 123 (1988).
[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]

Vaschenko, G.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

Wieland, J.

IEEE J. Quantum Electron.

J. Mørk, B. Tromborg, and L. Christiansen, IEEE J. Quantum Electron. 24, 123 (1988).
[CrossRef]

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

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. 22, 294 (1986).
[CrossRef]

IEEE Photon. Technol. Lett.

C. R. Mirasso, P. Colet, and P. Garcia-Fernandez, IEEE Photon. Technol. Lett. 8, 299 (1996).
[CrossRef]

Opt. Lett.

Phys. Lett. A

C. Simmendinger and O. Hess, Phys. Lett. A 216, 97 (1996).
[CrossRef]

Phys. Rev. A

D. W. Sukow, T. Heil, I. Fischer, A. Gavrielides, A. Hohl, and W. Elsässer, Phys. Rev. A 60, 667 (1999).
[CrossRef]

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

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 58, R2672 (1998).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, Phys. Rev. A 60, 634 (1999).
[CrossRef]

D. W. Sukow, J. R. Gardner, and D. J. Gauthier, Phys. Rev. A 52, R3370 (1997).
[CrossRef]

Phys. Rev. E

J. Mulet and C. R. Mirasso, Phys. Rev. E 59, 5400 (1999).
[CrossRef]

Phys. Rev. Lett.

G. Vaschenko, M. Giudici, J. J. Rocca, C. S. Menoni, J. R. Tredicce, and S. Balle, Phys. Rev. Lett. 81, 5536 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Optical spectra of the DFB laser. Solid curve, the solitary laser; dashed curve, the laser with feedback under coherence-collapsed operation. J=1.18 Jth.

Fig. 2
Fig. 2

Time traces showing alternation between LFF and stable operation: (a) experiment, (b) numerical simulations. The inset shows in ηN space how the trajectory reaches the HGM.

Fig. 3
Fig. 3

PDF’s fT of time interval T between subsequent LFF dropouts: (a) J=0.98 Jth, (b) J=1.04 Jth, (c) J=1.08 Jth. Diamonds and dashed curve, experimental data; stars and solid curves, numerical simulations. Note the different scales of fT and T in (a)–(c).

Fig. 4
Fig. 4

Ln–ln plot of the average time interval between subsequent dropouts T versus normalized injection current ϵ=J/JthLFF-1. Diamonds and dashed curve, experimental data; stars and solid curve, numerical simulations. The dotted curve corresponds to a linear fit Tϵ-1; the dashed–dotted curve, to results obtained from the Henry–Kazarinov12 model.

Equations (3)

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dEtdt=121+iαG-Γ0Et+γEt-τ×exp-iω0τ+FEt,
dNtdt=pJthq-NtT1-GPt,
GN,P=ξN-Nt1+ϵP,P=E2.

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