Abstract

Double-clad fibers with a doped single-mode core and a noncylindrical multimode chaotic cladding are shown to provide optimal pump-power absorption in power amplifiers. Based on the chaotic dynamics of rays in such fibers, we propose a quantitative theory for the pump-absorption ratio and favorably compare the predictions of the theory with numerical results obtained through an adapted beam-propagation scheme.

© 2001 Optical Society of America

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References

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  1. E. Desurvire, Erbium-doped Fiber Amplifiers (Wiley Interscience, New York, 1994).
  2. E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.
  3. A. Liu and K. Ueda, Optics Commun. 132, 511 (1996).
    [CrossRef]
  4. R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.
  5. S. T. Jackson and T. A. King, Opt. Lett. 23, 1462 (2000).
    [CrossRef]
  6. V. Doya, “Du speckle aux scars: une expérience de chaos ondulatoire dans une fibre optique,” Ph.D dissertation (Université de Nice Sophia-Antipolis, Nice, France).
  7. H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge U. Press, Cambridge, 1999).
  8. R. L. Weaver and O. I. Lobkis, Phys. Rev. Lett. 84, 4942 (2000).
    [CrossRef] [PubMed]
  9. F. Mortessagne, O. Legrand, and D. Sornette, Chaos 3, 529 (1993).
    [CrossRef] [PubMed]
  10. S. Ree and L. E. Reichl, Phys. Rev. E 60, 1607 (1999).
    [CrossRef]
  11. L. A. Bunimovich, Commun. Math. Phys. 65, 295 (1979).
    [CrossRef]
  12. M. V. Berry, Eur. J. Phys. 2, 91 (1981).
    [CrossRef]
  13. M. V. Berry, J. Phys. A 10, 2083 (1977).
    [CrossRef]
  14. V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura are preparing a manuscript to be called “Speckle statistics in a chaotic multimode fiber.”
  15. F. Mortessagne, O. Legrand, and D. Sornette, J. Acoust. Soc. Am. 94, 154 (1993).
    [CrossRef]

2000 (2)

R. L. Weaver and O. I. Lobkis, Phys. Rev. Lett. 84, 4942 (2000).
[CrossRef] [PubMed]

S. T. Jackson and T. A. King, Opt. Lett. 23, 1462 (2000).
[CrossRef]

1999 (1)

S. Ree and L. E. Reichl, Phys. Rev. E 60, 1607 (1999).
[CrossRef]

1996 (1)

A. Liu and K. Ueda, Optics Commun. 132, 511 (1996).
[CrossRef]

1993 (2)

F. Mortessagne, O. Legrand, and D. Sornette, J. Acoust. Soc. Am. 94, 154 (1993).
[CrossRef]

F. Mortessagne, O. Legrand, and D. Sornette, Chaos 3, 529 (1993).
[CrossRef] [PubMed]

1981 (1)

M. V. Berry, Eur. J. Phys. 2, 91 (1981).
[CrossRef]

1979 (1)

L. A. Bunimovich, Commun. Math. Phys. 65, 295 (1979).
[CrossRef]

1977 (1)

M. V. Berry, J. Phys. A 10, 2083 (1977).
[CrossRef]

Berry, M. V.

M. V. Berry, Eur. J. Phys. 2, 91 (1981).
[CrossRef]

M. V. Berry, J. Phys. A 10, 2083 (1977).
[CrossRef]

Bunimovich, L. A.

L. A. Bunimovich, Commun. Math. Phys. 65, 295 (1979).
[CrossRef]

Clarkson, W. A.

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

Desurvire, E.

E. Desurvire, Erbium-doped Fiber Amplifiers (Wiley Interscience, New York, 1994).

Doya, V.

V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura are preparing a manuscript to be called “Speckle statistics in a chaotic multimode fiber.”

V. Doya, “Du speckle aux scars: une expérience de chaos ondulatoire dans une fibre optique,” Ph.D dissertation (Université de Nice Sophia-Antipolis, Nice, France).

Grudinin, A. B.

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

Hakimi, F.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

Hanna, D. C.

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

Hayward, R. A.

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

Jackson, S. T.

King, T. A.

Legrand, O.

F. Mortessagne, O. Legrand, and D. Sornette, Chaos 3, 529 (1993).
[CrossRef] [PubMed]

F. Mortessagne, O. Legrand, and D. Sornette, J. Acoust. Soc. Am. 94, 154 (1993).
[CrossRef]

V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura are preparing a manuscript to be called “Speckle statistics in a chaotic multimode fiber.”

Liu, A.

A. Liu and K. Ueda, Optics Commun. 132, 511 (1996).
[CrossRef]

Lobkis, O. I.

R. L. Weaver and O. I. Lobkis, Phys. Rev. Lett. 84, 4942 (2000).
[CrossRef] [PubMed]

McCollumn, B. C.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

Miniatura, Ch.

V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura are preparing a manuscript to be called “Speckle statistics in a chaotic multimode fiber.”

Mortessagne, F.

F. Mortessagne, O. Legrand, and D. Sornette, Chaos 3, 529 (1993).
[CrossRef] [PubMed]

F. Mortessagne, O. Legrand, and D. Sornette, J. Acoust. Soc. Am. 94, 154 (1993).
[CrossRef]

V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura are preparing a manuscript to be called “Speckle statistics in a chaotic multimode fiber.”

Nilsson, J.

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

Po, H.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

Ree, S.

S. Ree and L. E. Reichl, Phys. Rev. E 60, 1607 (1999).
[CrossRef]

Reichl, L. E.

S. Ree and L. E. Reichl, Phys. Rev. E 60, 1607 (1999).
[CrossRef]

Snitzer, E.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

Sornette, D.

F. Mortessagne, O. Legrand, and D. Sornette, Chaos 3, 529 (1993).
[CrossRef] [PubMed]

F. Mortessagne, O. Legrand, and D. Sornette, J. Acoust. Soc. Am. 94, 154 (1993).
[CrossRef]

Stöckmann, H.-J.

H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge U. Press, Cambridge, 1999).

Tumminelli, R.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

Turner, P. W.

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

Ueda, K.

A. Liu and K. Ueda, Optics Commun. 132, 511 (1996).
[CrossRef]

Weaver, R. L.

R. L. Weaver and O. I. Lobkis, Phys. Rev. Lett. 84, 4942 (2000).
[CrossRef] [PubMed]

Chaos (1)

F. Mortessagne, O. Legrand, and D. Sornette, Chaos 3, 529 (1993).
[CrossRef] [PubMed]

Commun. Math. Phys. (1)

L. A. Bunimovich, Commun. Math. Phys. 65, 295 (1979).
[CrossRef]

Eur. J. Phys. (1)

M. V. Berry, Eur. J. Phys. 2, 91 (1981).
[CrossRef]

J. Acoust. Soc. Am. (1)

F. Mortessagne, O. Legrand, and D. Sornette, J. Acoust. Soc. Am. 94, 154 (1993).
[CrossRef]

J. Phys. A (1)

M. V. Berry, J. Phys. A 10, 2083 (1977).
[CrossRef]

Opt. Lett. (1)

Optics Commun. (1)

A. Liu and K. Ueda, Optics Commun. 132, 511 (1996).
[CrossRef]

Phys. Rev. E (1)

S. Ree and L. E. Reichl, Phys. Rev. E 60, 1607 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

R. L. Weaver and O. I. Lobkis, Phys. Rev. Lett. 84, 4942 (2000).
[CrossRef] [PubMed]

Other (6)

R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, and D. C. Hanna, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 2000), paper CFH2.

E. Desurvire, Erbium-doped Fiber Amplifiers (Wiley Interscience, New York, 1994).

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollumn, in Optical Fiber Sensors, Vol. 2 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

V. Doya, “Du speckle aux scars: une expérience de chaos ondulatoire dans une fibre optique,” Ph.D dissertation (Université de Nice Sophia-Antipolis, Nice, France).

H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge U. Press, Cambridge, 1999).

V. Doya, O. Legrand, F. Mortessagne, and Ch. Miniatura are preparing a manuscript to be called “Speckle statistics in a chaotic multimode fiber.”

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Figures (2)

Fig. 1
Fig. 1

(a) Typical chaotic ray trajectory in the transverse section of a D-shaped fiber. (b) Typical specklelike near-field intensity actually measured at the output of an optical multimode fiber.

Fig. 2
Fig. 2

Pump-power decreases on a logarithmic scale along 20  m of a double-clad EDFA for three different geometries, indicated as insets. The two chaotic (truncated) geometries lead to nonsaturating absorption.

Equations (4)

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L=lαtanθ,
l=πAcladPcore
α=χlcoretanθ,
L-1=χAcoreAcladn1n0.

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