Abstract

Self-similarity techniques are used to study pulse propagation in a normal-dispersion optical fiber amplifier with an arbitrary longitudinal gain profile. Analysis of the nonlinear Schrödinger equation that describes such an amplifier leads to an exact solution in the high-power limit that corresponds to a linearly chirped parabolic pulse. The self-similar scaling of the propagating pulse in the amplifier is found to be determined by the functional form of the gain profile, and the solution is confirmed by numerical simulations. The implications for achieving chirp-free pulses after compression of the amplifier output are discussed.

© 2000 Optical Society of America

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References

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  1. G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge U. Press, Cambridge, 1996).
  2. A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
    [CrossRef]
  3. S. An and J. E. Sipe, Opt. Lett. 16, 1478 (1991).
    [CrossRef] [PubMed]
  4. C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
    [CrossRef] [PubMed]
  5. T. M. Monro, P. D. Millar, L. Poladian, and C. M. de Sterke, Opt. Lett. 23, 268 (1998).
    [CrossRef]
  6. M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000); S. Sears, M. Soljacic, M. Segev, D. Krylov, and K. Bergman, Phys. Rev. Lett. 84, 1902 (2000).
    [CrossRef] [PubMed]
  7. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
    [CrossRef] [PubMed]
  8. D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, J. Opt. Soc. Am. B 10, 1185 (1993).
    [CrossRef]
  9. K. Tamura and M. Nakazawa, Opt. Lett. 21, 68 (1996).
    [CrossRef] [PubMed]
  10. A. Galvanauskas and M. E. Fermann, in Conference on Lasers and Electro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), postdeadline paper CPD 3-1.
  11. B. Deutsch and Th. Pfeiffer, Electron. Lett. 28, 303–304 (1992).
    [CrossRef]
  12. P. A. Bélanger, L. Gagnon, and C. Paré, Opt. Lett. 14, 943 (1989).
    [CrossRef]

2000 (2)

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000); S. Sears, M. Soljacic, M. Segev, D. Krylov, and K. Bergman, Phys. Rev. Lett. 84, 1902 (2000).
[CrossRef] [PubMed]

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

1998 (1)

1996 (1)

1993 (1)

1992 (2)

B. Deutsch and Th. Pfeiffer, Electron. Lett. 28, 303–304 (1992).
[CrossRef]

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

1991 (2)

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

S. An and J. E. Sipe, Opt. Lett. 16, 1478 (1991).
[CrossRef] [PubMed]

1989 (1)

Afanas’ev, A. A.

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

An, S.

Anderson, D.

Barenblatt, G. I.

G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge U. Press, Cambridge, 1996).

Bélanger, P. A.

de Sterke, C. M.

Desaix, M.

Deutsch, B.

B. Deutsch and Th. Pfeiffer, Electron. Lett. 28, 303–304 (1992).
[CrossRef]

Dudley, J. M.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Fermann, M. E.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

A. Galvanauskas and M. E. Fermann, in Conference on Lasers and Electro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), postdeadline paper CPD 3-1.

Gagnon, L.

Galvanauskas, A.

A. Galvanauskas and M. E. Fermann, in Conference on Lasers and Electro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), postdeadline paper CPD 3-1.

Harvey, J. D.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Jakyte, R.

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

Karlsson, M.

Kruglov, V. I.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

Levi, D.

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Lisak, M.

Menyuk, C. R.

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000); S. Sears, M. Soljacic, M. Segev, D. Krylov, and K. Bergman, Phys. Rev. Lett. 84, 1902 (2000).
[CrossRef] [PubMed]

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Millar, P. D.

Monro, T. M.

Nakazawa, M.

Paré, C.

Pfeiffer, Th.

B. Deutsch and Th. Pfeiffer, Electron. Lett. 28, 303–304 (1992).
[CrossRef]

Poladian, L.

Quiroga-Teixeiro, M. L.

Samson, B. A.

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

Segev, M.

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000); S. Sears, M. Soljacic, M. Segev, D. Krylov, and K. Bergman, Phys. Rev. Lett. 84, 1902 (2000).
[CrossRef] [PubMed]

Sipe, J. E.

Soljacic, M.

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000); S. Sears, M. Soljacic, M. Segev, D. Krylov, and K. Bergman, Phys. Rev. Lett. 84, 1902 (2000).
[CrossRef] [PubMed]

Tamura, K.

Thomsen, B. C.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

Volkov, V. M.

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

Winternitz, P.

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Electron. Lett. (1)

B. Deutsch and Th. Pfeiffer, Electron. Lett. 28, 303–304 (1992).
[CrossRef]

J. Mod. Opt. (1)

A. A. Afanas’ev, V. I. Kruglov, B. A. Samson, R. Jakyte, and V. M. Volkov, J. Mod. Opt. 38, 1189 (1991).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. E (1)

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000); S. Sears, M. Soljacic, M. Segev, D. Krylov, and K. Bergman, Phys. Rev. Lett. 84, 1902 (2000).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett. 84, 6010 (2000).
[CrossRef] [PubMed]

C. R. Menyuk, D. Levi, and P. Winternitz, Phys. Rev. Lett. 69, 3048 (1992).
[CrossRef] [PubMed]

Other (2)

A. Galvanauskas and M. E. Fermann, in Conference on Lasers and Electro-Optics, 2000 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), postdeadline paper CPD 3-1.

G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics (Cambridge U. Press, Cambridge, 1996).

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Figures (3)

Fig. 1
Fig. 1

Evolution of a Gaussian pulse toward a parabolic pulse for three different gain distributions. Top, intensity profiles on a logarithmic scale; bottom, normalized intensity profiles on a linear scale. The profiles are shown in 1-m increments.

Fig. 2
Fig. 2

Evolution of effective pulse width τpz (top) and peak amplitude Az,0 (bottom) for (a) increasing gain, (b) constant gain, and (c) decreasing gain. Solid curves, simulation results; circles, theoretical predictions for z>2.5 m.

Fig. 3
Fig. 3

Top, intensity (left axes) and chirp (right axes) of the amplifier output obtained from NLSE simulations (solid curves) compared with theoretical predictions (circles), for three different gain profiles. Bottom, the corresponding spectra.

Equations (10)

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

izΨ=β222τ2Ψ-γΨ2Ψ+igz2Ψ,
Uz=Uz0expz0zgzdz,
Az,τ=fzFϑ,
Φz,τ=φz+Czτ2.
dfdz=β2Cf+g2f,
2β2C2-dCdz1f6UzUz02ϑ2-1f2dφdz=-γF2,
Az,τ=3Uz/4τpz1/21-τ/τpz21/2,  ττpz,
φz=φz0+3γ/4z0zUz/τpzdz,
Cz=-2β2-1d/dzln τpz,
d2τpdz2=32β2γUzτp2,

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