Abstract

We present a vector theory of Raman amplification and use it to discuss the effect of polarization-mode dispersion (PMD) on the Raman gain process inside the optical fiber used for stimulated Raman scattering. We show that the PMD induces large fluctuations in the amplified signal and reduces the average value of the amplifier gain. In the case of forward pumping, fluctuations are expected to be more than 15% under typical operating conditions and can exceed 50% for fiber with a relatively low value of the PMD parameter. The PMD effects are much less severe in the case of backward pumping. Signal fluctuations reduce to less than 1% in this case when the PMD parameter exceeds 0.05 ps/km.

© 2002 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. R. Hellwarth, J. Cherlow, and T. Yang, Phys. Rev. B 11, 964 (1975).
    [CrossRef]
  5. R. H. Stolen, IEEE J. Quantum Electron. QE-15, 1157 (1979).
    [CrossRef]
  6. D. J. Dougherty, F. X. Kärtner, H. A. Haus, and E. P. Ippen, Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  7. H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 15.
  8. S. Popov, E. Vanin, and G. Jacobsen, Opt. Lett. 27, 848 (2002).
    [CrossRef]
  9. P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weid, F. Prieto, and C. W. Zimmer, J. Lightwave Technol. 16, 757 (1998).
    [CrossRef]
  10. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed. (Springer, New York, 1985).

2002 (1)

2001 (1)

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

1998 (1)

1995 (1)

1979 (1)

R. H. Stolen, IEEE J. Quantum Electron. QE-15, 1157 (1979).
[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]

Ciprut, P.

Dougherty, D. J.

Emori, Y.

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

Gardiner, C. W.

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

Gisin, B.

Gisin, N.

Haus, H. A.

Hellwarth, R.

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

Ippen, E. P.

Jacobsen, G.

Jopson, R. M.

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 15.

Kärtner, F. X.

Kogelnik, H.

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 15.

Namiki, S.

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

Nelson, L. E.

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 15.

Passy, R.

Popov, S.

Prieto, F.

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.

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.

Stolen, R. H.

R. H. Stolen, IEEE J. Quantum Electron. QE-15, 1157 (1979).
[CrossRef]

Vanin, E.

Von der Weid, J. P.

Yang, T.

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

Zimmer, C. W.

IEEE J. Quantum Electron. (1)

R. H. Stolen, IEEE J. Quantum Electron. QE-15, 1157 (1979).
[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)

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).

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chap. 15.

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.

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Figures (2)

Fig. 1
Fig. 1

Average Raman gain as a function of PMD parameters at two pump powers. The solid and dashed curves correspond to the cases in which the pump and signal at the input end are copolarized and orthogonally polarized, respectively. Other parameters are given in the text.

Fig. 2
Fig. 2

Fluctuations in the amplified signal power as a function of PMD parameter in the case of forward pumping at three pump powers. The solid curves show the copolarized case and the dashed curves represent the case of orthogonal polarizations initially. All other parameters are the same as in Fig. 1.

Equations (13)

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ηdPdz= -αpP-ωp2ωsgRP0S+S0P+ωpβ+γpWpNL×P,
dSdz= -αsS+12gRS0P+P0S+ωsβ+γsWsNL×S,
ηdP0dz= -ωp2ωsgRS0+αpP0-ωp2ωsgRP·S,
dS0dz= 12gRP0-αsS0+12gRP·S.
bz=0,  bz1bz2=13Dp2Iδz2-z1,
dS0dz=12gRPin exp-αpzPˆ·S,
dSdz= 12gRPin exp-αpzS0Pˆ-ΩRb×S-8γs9P×S,
Gav=S0LS00,  σs2=S02L-S0L2S0L2.
dS0dz= 12gRPin exp-αpzS0 cos θ,
dS0 cos θdz= 12gRPin exp-αpzS0-13Dp2ΩR2S0 cos θ,
dS02dz= gRPin exp-αpzS02 cos θ,
dS02 cos θdz= -13Dp2ΩR2S02 cos θ+12gRPin×exp-αpzS02+S02cos2 θ,
dS02 cos θdz= -Dp2ΩR2S02 cos2 θ+13Dp2ΩR2S02+gRPin exp-αpzS02 cos θ.

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