Abstract

We propose a novel framework for the solution of a general fiber Raman amplifier problem by use of a closed integral form of a Raman equation. Treating the given problem as an adiabatic system and taking the Raman process as the perturbation parameter, we can seek the solution along the iteration axis rather than the fiber propagation axis, permitting an orders-of-magnitude increase for the product of convergence speed and spatial resolution in the numerical assessment.

© 2005 Optical Society of America

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References

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  1. M. N. Islam, J. Lightwave. Technol. 8, 548 (2002).
  2. H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
    [CrossRef]
  3. B. K. Min, W. J. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 12, 1486 (2000).
    [CrossRef]
  4. J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
    [CrossRef]
  5. V. E. Perlin and H. G. Winful, J. Lightwave. Technol. 20, 250 (2002).
    [CrossRef]
  6. K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IVA, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chapter 5, p. 217.

2004 (1)

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

2002 (2)

V. E. Perlin and H. G. Winful, J. Lightwave. Technol. 20, 250 (2002).
[CrossRef]

M. N. Islam, J. Lightwave. Technol. 8, 548 (2002).

2000 (1)

B. K. Min, W. J. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 12, 1486 (2000).
[CrossRef]

1999 (1)

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

Islam, M. N.

M. N. Islam, J. Lightwave. Technol. 8, 548 (2002).

Kidorf, H.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

Kim, P. H.

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

Lee, H. S.

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

Lee, W. J.

B. K. Min, W. J. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 12, 1486 (2000).
[CrossRef]

Ma, M.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

Min, B. K.

B. K. Min, W. J. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 12, 1486 (2000).
[CrossRef]

Nissov, M.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

Park, J. H.

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

Park, N. K.

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

B. K. Min, W. J. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 12, 1486 (2000).
[CrossRef]

Perlin, V. E.

V. E. Perlin and H. G. Winful, J. Lightwave. Technol. 20, 250 (2002).
[CrossRef]

Rabarijaona, E.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

Rottwitt, K.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IVA, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chapter 5, p. 217.

Stentz, A. J.

K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IVA, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chapter 5, p. 217.

Winful, H. G.

V. E. Perlin and H. G. Winful, J. Lightwave. Technol. 20, 250 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, IEEE Photon. Technol. Lett. 11, 530 (1999).
[CrossRef]

B. K. Min, W. J. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 12, 1486 (2000).
[CrossRef]

J. H. Park, P. H. Kim, J. H. Park, H. S. Lee, and N. K. Park, IEEE Photon. Technol. Lett. 16, 1649 (2004).
[CrossRef]

J. Lightwave. Technol. (2)

V. E. Perlin and H. G. Winful, J. Lightwave. Technol. 20, 250 (2002).
[CrossRef]

M. N. Islam, J. Lightwave. Technol. 8, 548 (2002).

Other (1)

K. Rottwitt and A. J. Stentz, in Optical Fiber Telecommunications IVA, I. P. Kaminow and T. Li, eds. (Academic, San Diego, Calif., 2002), Chapter 5, p. 217.

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Figures (3)

Fig. 1
Fig. 1

Flow diagram of the suggested adiabatic iteration algorithm along the iteration axis: Psig0th 0, 0th signal power at zk=0; PF-P0th 0, 0th forward pump power at zk=0; PB-P0th 0, 0th backward pump power at zk=0.

Fig. 2
Fig. 2

Raman on–off gain and signal power evolution at a wavelength of 1530–1600 nm (10-nm spacing) for three pumping configurations: (a) codirectional, (b) counterdirectional, and (c) bidirectional.

Fig. 3
Fig. 3

FRA noise at T=300 K in the counterpumping configuration: (a) forward ASE power, (b) double Rayleigh backscattered (DRS) signal power.

Equations (10)

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±dPidz=-αiPi+j=1M+NgjiPjPi,
Piz=Pi0expαiz±j=1M+Ngji0zPjζdζ.
0zPiζdζPi0=0zexpαiζ±j=1M+Ngji0ζPjξdξdζ.
Leff-iz=0zexpαiζ±j=1M+NgjiPj0Leff_jζdζ.
Leff_inthz=0zexpαiζ±j=1M+NgjiPjn-1th0×Leff_jn-1thζdζ.
Leff_inthzk=[exp(αizk±gjiPjn-1th0×L˜eff_Alln-1thzk]T˜trigΔz,
zk=0 Δz 2Δz 3Δz,,L-Δz L, Leff_inthzk=Leff_inth0  Leff_inthΔz,,Leff_inthL, gjiPjn-1th0=g1iP1n-1th0  g2iP2n-1th0,, gM+NiPM+Nn-1th0, L˜eff_Alln-1thzk=L˜eff_1n-1thzkL˜eff_2n-1thzkL˜eff_M+Nn-1thzkT˜trig=01/21/21/21/201/2111001/2110001/2100001/2.
Gi=10 logej=1M+NgjiLeff_jLPj0.
G=10 logeT˜×P,
T˜=g11Leff_1gM+N1Leff_M+Ng1M+NLeff_1gM+NM+NLeff_M+N, P=P10  P20PM+N0T.

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