Abstract

We develop an analytic model for finding the statistics of polarization-dependent gain (PDG) in fiber-based Raman amplifiers. We use it to find an analytic form for the probability distribution of PDG and study how the mean PDG and the variance of PDG fluctuations depend on the PMD parameter. We show that mean PDG as well as PDG fluctuations are reduced by approximately a factor of 30 in the case of backward pumping.

© 2003 Optical Society of America

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References

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  1. S. Namiki and Y. Emori, IEEE Sel. Top. Quantum Electron. 7, 3 (2001).
    [CrossRef]
  2. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).
  3. K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IV A, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 5.
  4. P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.
  5. S. Popov, E. Vanin, and G. Jacobsen, Opt. Lett. 27, 848 (2002).
    [CrossRef]
  6. R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
    [CrossRef]
  7. D. J. Dougherty, F. X. Kartner, H. A. Haus, and E. P. Ippen, Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  8. B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quan. Electron. 6, 317 (2000).
    [CrossRef]
  9. A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
    [CrossRef]
  10. G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
    [CrossRef]
  11. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer, New York, 1985).

2002 (2)

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
[CrossRef]

S. Popov, E. Vanin, and G. Jacobsen, Opt. Lett. 27, 848 (2002).
[CrossRef]

2001 (1)

S. Namiki and Y. Emori, IEEE Sel. Top. Quantum Electron. 7, 3 (2001).
[CrossRef]

2000 (1)

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quan. Electron. 6, 317 (2000).
[CrossRef]

1995 (1)

1991 (1)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

1975 (1)

R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).

Cherlow, J.

R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Dougherty, D. J.

Ebrahimi, P.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Emori, Y.

S. Namiki and Y. Emori, IEEE Sel. Top. Quantum Electron. 7, 3 (2001).
[CrossRef]

Foschini, G. J.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer, New York, 1985).

Geiser, C.

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quan. Electron. 6, 317 (2000).
[CrossRef]

Gisin, N.

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quan. Electron. 6, 317 (2000).
[CrossRef]

Gurkan, D.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Hauer, M. C.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Haus, H. A.

Hellwarth, R.

R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Huttner, B.

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quan. Electron. 6, 317 (2000).
[CrossRef]

Ippen, E. P.

Jacobsen, G.

Kartner, F. X.

Khosravani, R.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Kim, D. W.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Lee, D. W.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Mecozzi, A.

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
[CrossRef]

Namiki, S.

S. Namiki and Y. Emori, IEEE Sel. Top. Quantum Electron. 7, 3 (2001).
[CrossRef]

Poole, C. D.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Popov, S.

Rottwitt, K.

K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IV A, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 5.

Shtaif, M.

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
[CrossRef]

Stentz, A. J.

K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IV A, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 5.

Vanin, E.

Willner, A. E.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

Yang, T.

R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Yu, Q.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

IEEE J. Sel. Top. Quan. Electron. (1)

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Sel. Top. Quan. Electron. 6, 317 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
[CrossRef]

IEEE Sel. Top. Quantum Electron. (1)

S. Namiki and Y. Emori, IEEE Sel. Top. Quantum Electron. 7, 3 (2001).
[CrossRef]

J. Lightwave Technol. (1)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
[CrossRef]

Other (4)

C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer, New York, 1985).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001).

K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IV A, I. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 5.

P. Ebrahimi, M. C. Hauer, Q. Yu, R. Khosravani, D. Gurkan, D. W. Kim, D. W. Lee, and A. E. Willner, in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), p. 143.

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Figures (3)

Fig. 1
Fig. 1

Probability distribution of PDG as a function of Dp for a 10-km Raman amplifier pumped with 0.3 W of power in the forward direction.

Fig. 2
Fig. 2

Mean PDG as a function of PMD parameter, normalized to the average Raman gain. The inset shows the same data plotted as a function of 1/Dp.

Fig. 3
Fig. 3

Same as Fig. 2 expect that the rms value of PDG is plotted as a function of the PMD parameter.

Equations (16)

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

±dPdz=-αpP-ωp2ωsgRP0S+S0P+ωpβ+γpWpNL×P,
dSdz=-αsS+12gRS0P+P0S+ωsβ+γsWsNL×S,
dS/dz=-αsS+12gRS0P+P0S-ΩRb×S,
bz=0,  bz1bz2=13Dp2Iδz2-z1,
dΔdz= gRΔ2 cothΔ2aP-P·ΔˆΔˆ+agRP·ΔˆΔˆ-ΩRb×Δ.
dΔ/dzagRP-ΩRb×Δ,
Δz=agRRz0zR-1zPzdz,
dΔ/dz=-ηΔ+agRPine-αpzPˆ,
dΔ2/dz=2agRPine-αpzPˆ·Δ,
dC/dz=-3ηC+ηΔ2I-ΔΔ,
Δ= agRPinPˆη-αp1-αpLeff-e-ηL,
Δ2= 2agRPin2η2-αp21-αpLeffe-ηL-1+Leffαp+η1-αpLeff/2,
pΔ= 2π-3/2σσ2×exp-Δ1-Δ022σ2-Δ22+Δ322σ2,
pΔ= Δ2σσexp-Δ2r-1-rΔ02/2σ2×erfΔr-1+rΔ0/2σ+erfΔr-1-rΔ0/2σ,
Δ4agRPinπDpΩRLeff1-αpLeff/21/2.
σΔ3π/8-1Δ0.422Δ.

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