Abstract

We present a model for the dynamics of distributed-feedback fiber lasers that includes the effect of nonlinear refraction. The model predicts antiphase and in-phase self-pulsations, asymmetric output, and deterministic chaos if the nonlinear refractive index of the fiber material is sufficiently large. Self-pulsations with frequencies of tens to hundreds of megahertz and pulse widths of several nanoseconds are observed in computer simulations.

© 1996 Optical Society of America

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  1. J. K. Kringlebotn, J.-L. Archambault, L. Reekie, D. N. Payne, Opt. Lett. 19, 2101 (1994).
    [CrossRef] [PubMed]
  2. A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
    [CrossRef]
  3. W. H. Loh, R. I. Laming, Electron. Lett. 31, 1440 (1995).
    [CrossRef]
  4. M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
    [CrossRef]
  5. H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
    [CrossRef]
  6. S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
    [CrossRef]
  7. H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
    [CrossRef]
  8. W. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
    [CrossRef]
  9. D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
    [CrossRef] [PubMed]
  10. C. Martijn de Sterke, K. R. Jackson, B. D. Robert, J. Opt. Soc. Am. B 8, 403 (1991).
    [CrossRef]
  11. M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
    [CrossRef]
  12. Y. T. Chieng, G. J. Cowle, Electron. Lett. 30, 1419 (1994).
    [CrossRef]
  13. R. Schatz, IEEE J. Quantum Electron. 28, 1443 (1992).
    [CrossRef]
  14. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 13.
  15. K. A. Shore, T. E. Rozzi, in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, San Diego, Calif., 1988), pp. 417–433.
  16. L. Rahman, H. G. Winful, IEEE J. Quantum Electron. 30, 1405 (1994).
    [CrossRef]
  17. F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
    [CrossRef] [PubMed]

1995 (4)

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

W. H. Loh, R. I. Laming, Electron. Lett. 31, 1440 (1995).
[CrossRef]

M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
[CrossRef]

S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

1994 (3)

Y. T. Chieng, G. J. Cowle, Electron. Lett. 30, 1419 (1994).
[CrossRef]

L. Rahman, H. G. Winful, IEEE J. Quantum Electron. 30, 1405 (1994).
[CrossRef]

J. K. Kringlebotn, J.-L. Archambault, L. Reekie, D. N. Payne, Opt. Lett. 19, 2101 (1994).
[CrossRef] [PubMed]

1993 (2)

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
[CrossRef]

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

1992 (1)

R. Schatz, IEEE J. Quantum Electron. 28, 1443 (1992).
[CrossRef]

1991 (1)

1989 (1)

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

1985 (1)

W. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

1982 (1)

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

1979 (1)

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Archambault, J.-L.

Asobe, M.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
[CrossRef]

Asseh, A.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Cada, M.

S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Chieng, Y. T.

Y. T. Chieng, G. J. Cowle, Electron. Lett. 30, 1419 (1994).
[CrossRef]

Christodoulides, D. N.

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Cooperman, G. D.

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

Cowle, G. J.

Y. T. Chieng, G. J. Cowle, Electron. Lett. 30, 1419 (1994).
[CrossRef]

Edwall, G.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Francois, P. L.

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

Garmire, E.

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

He, J.

S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Hübner, J.

M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
[CrossRef]

Itoh, H.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
[CrossRef]

Jackson, K. R.

Janz, S.

S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Kanamori, T.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
[CrossRef]

Kringlebotn, J. K.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

J. K. Kringlebotn, J.-L. Archambault, L. Reekie, D. N. Payne, Opt. Lett. 19, 2101 (1994).
[CrossRef] [PubMed]

Kristensen, M.

M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
[CrossRef]

Laming, R. I.

W. H. Loh, R. I. Laming, Electron. Lett. 31, 1440 (1995).
[CrossRef]

Le Boudec, P.

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

Loh, W. H.

W. H. Loh, R. I. Laming, Electron. Lett. 31, 1440 (1995).
[CrossRef]

Marburger, J. H.

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Margulis, W.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Martijn de Sterke, C.

Miyazawa, T.

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
[CrossRef]

Payne, D. N.

Rahman, L.

L. Rahman, H. G. Winful, IEEE J. Quantum Electron. 30, 1405 (1994).
[CrossRef]

Reekie, L.

Robert, B. D.

Rozzi, T. E.

K. A. Shore, T. E. Rozzi, in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, San Diego, Calif., 1988), pp. 417–433.

Sahlgren, B.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Sanchez, F.

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

Sandgren, S.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Schatz, R.

R. Schatz, IEEE J. Quantum Electron. 28, 1443 (1992).
[CrossRef]

Seijka, M.

M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
[CrossRef]

Shore, K. A.

K. A. Shore, T. E. Rozzi, in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, San Diego, Calif., 1988), pp. 417–433.

Stephan, G.

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

Storoy, H.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Stubbe, R.

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

Varming, P.

M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
[CrossRef]

Wasilewski, Z. R.

S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

Winful, H. G.

L. Rahman, H. G. Winful, IEEE J. Quantum Electron. 30, 1405 (1994).
[CrossRef]

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

Winful, W. G.

W. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 13.

Appl. Phys. Lett. (4)

H. G. Winful, J. H. Marburger, E. Garmire, Appl. Phys. Lett. 35, 379 (1979).
[CrossRef]

S. Janz, J. He, Z. R. Wasilewski, M. Cada, Appl. Phys. Lett. 67, 1051 (1995).
[CrossRef]

H. G. Winful, G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).
[CrossRef]

W. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

Electron. Lett. (5)

A. Asseh, H. Storoy, J. K. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, Electron. Lett. 31, 969 (1995).
[CrossRef]

W. H. Loh, R. I. Laming, Electron. Lett. 31, 1440 (1995).
[CrossRef]

M. Seijka, P. Varming, J. Hübner, M. Kristensen, Electron. Lett. 31, 1445 (1995).
[CrossRef]

M. Asobe, H. Itoh, T. Miyazawa, T. Kanamori, Electron. Lett. 29, 1966 (1993).
[CrossRef]

Y. T. Chieng, G. J. Cowle, Electron. Lett. 30, 1419 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Schatz, IEEE J. Quantum Electron. 28, 1443 (1992).
[CrossRef]

L. Rahman, H. G. Winful, IEEE J. Quantum Electron. 30, 1405 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Phys. Rev. A (1)

F. Sanchez, P. Le Boudec, P. L. Francois, G. Stephan, Phys. Rev. A 48, 2220 (1993).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[CrossRef] [PubMed]

Other (2)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 13.

K. A. Shore, T. E. Rozzi, in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, San Diego, Calif., 1988), pp. 417–433.

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Figures (4)

Fig. 1
Fig. 1

Spatial profile of cavity photon density for a silica-based uniform DFB fiber laser with κL = 8.5, L = 2 cm, g0L = 0.5.

Fig. 2
Fig. 2

(a) Antiphase self-pulsation at κL = 8.5, g0L = 0.28 for a high-n2 DFB fiber laser (at z = L). (b) Output of the last 50 ns at z = L (solid curve) and z = 0 (dotted curve). (c) Spatiotemporal evolution of photon density in the last 50 ns.

Fig. 3
Fig. 3

Spatiotemporal evolution of photon density of in-phase self-pulsation; g0L = 0.305, κL = 8.5, and time interval 5 ns.

Fig. 4
Fig. 4

Symmetric and asymmetric photon-density profiles at κL= 2.0 for g0L = 5.0 (solid curve), g0L = 5.3 (dotted curve), and g0L = 5.5 (dashed–dotted curve).

Equations (7)

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

E = E F ( z , t ) exp [ i ( β z - ω t ) ] + E B ( z , t ) × exp [ - i ( β z + ω t ) ] ,
n ( z ) = n 0 + n 1 cos ( 2 β 0 z ) .
Δ n = ½ n 2 E 2 .
g = g 0 1 + E 2 E s 2 ,
n 0 c E F t + E F z = i κ E B exp ( - i 2 Δ β z ) + g E F + i γ ( E F 2 + 2 E B 2 ) E F + K sp ,
n 0 c E B t E B z = i κ E F exp ( i 2 Δ β z ) + g E B + i γ ( E B 2 + 2 E F 2 ) E B + K sp ,
Δ β L = Δ β 0 L + 3 2 γ L E 2 .

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