Abstract

A theoretical investigation of bidirectionally dual-order pumped distributed Raman amplifiers is presented in detail, and comparisons with other Raman amplification schemes, i.e., bidirectional first-order pumping and Raman-plus-erbium-doped fiber hybrid amplification, are carried out, for the first time to the authors’ knowledge, at identical nonlinear phase shifts. The results show that symmetric bidirectional dual-order pumping can achieve the best optical signal-to-noise ratio performance by appropriate choice of the second-order pump wavelength and second-to-first-order pump power ratio for both short- and long-span conditions, which will be helpful for designing long-haul transmission systems.

© 2004 Optical Society of America

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  1. M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
    [CrossRef]
  2. V. E. Perlin and H. G. Winful, “Optimizing the noise performance of broadband WDM systems with distributed Raman amplification,” IEEE Photon. Technol. Lett. 14, 1199–1201 (2002).
    [CrossRef]
  3. J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
    [CrossRef]
  4. Z. Tong, H. Wei, and S. Jian, “Theoretical investigation and optimization of bidirectionally pumped broadband fiber Raman amplifiers,” Opt. Commun. 217, 401–413 (2003).
    [CrossRef]
  5. K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).
  6. J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
    [CrossRef]
  7. J. C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), symposium 3.04 (2002).
  8. M. D. Mermelstein, K. Brar, and C. Headley, “RIN transfer suppression technique for dual-order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 1354–1356 (2003).
    [CrossRef]
  9. Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
    [CrossRef]
  10. J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).
  11. Z. Tong, H. Wei, and S. Jian, “Comparison of different Raman amplification schemes in long-span fiber transmission systems with double Rayleigh backscattering,” IEEE Photon. Technol. Lett. 15, 1782–1784 (2003).
    [CrossRef]
  12. S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equaliazed by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
    [CrossRef]
  13. B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
    [CrossRef]
  14. R. L. Burden and J. D. Faires, Numerical Analysis (7th edition, Brooks-Cole, 2001), Chap. 10.
  15. R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
    [CrossRef]
  16. Z. Tong, H. Wei, and S. Jian, “Impacts of SPM/XPM on multi-span transmission systems using distributed Raman amplification at identical nonlinear phase shift,” IEEE Photon. Technol. Lett. 16, 933–935 (2004).
    [CrossRef]
  17. C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).
  18. M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
    [CrossRef]

2004 (1)

Z. Tong, H. Wei, and S. Jian, “Impacts of SPM/XPM on multi-span transmission systems using distributed Raman amplification at identical nonlinear phase shift,” IEEE Photon. Technol. Lett. 16, 933–935 (2004).
[CrossRef]

2003 (4)

Z. Tong, H. Wei, and S. Jian, “Theoretical investigation and optimization of bidirectionally pumped broadband fiber Raman amplifiers,” Opt. Commun. 217, 401–413 (2003).
[CrossRef]

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

M. D. Mermelstein, K. Brar, and C. Headley, “RIN transfer suppression technique for dual-order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 1354–1356 (2003).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Comparison of different Raman amplification schemes in long-span fiber transmission systems with double Rayleigh backscattering,” IEEE Photon. Technol. Lett. 15, 1782–1784 (2003).
[CrossRef]

2002 (3)

M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
[CrossRef]

V. E. Perlin and H. G. Winful, “Optimizing the noise performance of broadband WDM systems with distributed Raman amplification,” IEEE Photon. Technol. Lett. 14, 1199–1201 (2002).
[CrossRef]

R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
[CrossRef]

2001 (2)

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equaliazed by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[CrossRef]

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

2000 (1)

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[CrossRef]

1999 (2)

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
[CrossRef]

Antona, J. C.

C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).

Bayart, D.

C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).

Baynham, G.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Bouteiller, J. C.

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

J. C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), symposium 3.04 (2002).

Bouteiller, J.-C.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Brar, K.

M. D. Mermelstein, K. Brar, and C. Headley, “RIN transfer suppression technique for dual-order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 1354–1356 (2003).
[CrossRef]

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

J. C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), symposium 3.04 (2002).

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Bromage, J.

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Burden, R. L.

R. L. Burden and J. D. Faires, Numerical Analysis (7th edition, Brooks-Cole, 2001), Chap. 10.

Butler, D. L.

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

DiGiovanni, D. J.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Emori, Y.

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equaliazed by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[CrossRef]

Faires, J. D.

R. L. Burden and J. D. Faires, Numerical Analysis (7th edition, Brooks-Cole, 2001), Chap. 10.

Feder, K.

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

Fludger, C.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Goldhar, J.

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

Grüner-Nielsen, L.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Hadjifotiou, A.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Hainberger, R.

R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
[CrossRef]

Hansen, P.

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

Headley, C.

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

M. D. Mermelstein, K. Brar, and C. Headley, “RIN transfer suppression technique for dual-order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 1354–1356 (2003).
[CrossRef]

J. C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), symposium 3.04 (2002).

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Homan, J.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Hoshida, T.

R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
[CrossRef]

Islam, M. N.

M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
[CrossRef]

Jian, S.

Z. Tong, H. Wei, and S. Jian, “Impacts of SPM/XPM on multi-span transmission systems using distributed Raman amplification at identical nonlinear phase shift,” IEEE Photon. Technol. Lett. 16, 933–935 (2004).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Comparison of different Raman amplification schemes in long-span fiber transmission systems with double Rayleigh backscattering,” IEEE Photon. Technol. Lett. 15, 1782–1784 (2003).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Theoretical investigation and optimization of bidirectionally pumped broadband fiber Raman amplifiers,” Opt. Commun. 217, 401–413 (2003).
[CrossRef]

Joneckis, L. G.

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

Jones, M.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Jørgensen, L. V.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Kidorf, H. D.

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
[CrossRef]

Kim, J.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Klein, A.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Lee, W. J.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[CrossRef]

Lee, W. S.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Leeuwen, M. F. V.

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

Lingle, R. L.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Ma, M. X.

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
[CrossRef]

Martinelli, C.

C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).

Mermelstein, M. D.

M. D. Mermelstein, K. Brar, and C. Headley, “RIN transfer suppression technique for dual-order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 1354–1356 (2003).
[CrossRef]

Min, B.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[CrossRef]

Mongardien, D.

C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).

Namiki, S.

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equaliazed by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[CrossRef]

Nelson, L. E.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Nielson, T.

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

Nissov, M.

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
[CrossRef]

Onaka, H.

R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
[CrossRef]

Park, N.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[CrossRef]

Perlin, V. E.

V. E. Perlin and H. G. Winful, “Optimizing the noise performance of broadband WDM systems with distributed Raman amplification,” IEEE Photon. Technol. Lett. 14, 1199–1201 (2002).
[CrossRef]

Radic, S.

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

Rottwitt, K.

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
[CrossRef]

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

Scahill, C.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Shaw, B.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Simnneau, C.

C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).

Stentz, A.

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

Stulz, S.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Terahara, T.

R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
[CrossRef]

Thiele, H. J.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

Tong, Z.

Z. Tong, H. Wei, and S. Jian, “Impacts of SPM/XPM on multi-span transmission systems using distributed Raman amplification at identical nonlinear phase shift,” IEEE Photon. Technol. Lett. 16, 933–935 (2004).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Comparison of different Raman amplification schemes in long-span fiber transmission systems with double Rayleigh backscattering,” IEEE Photon. Technol. Lett. 15, 1782–1784 (2003).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Theoretical investigation and optimization of bidirectionally pumped broadband fiber Raman amplifiers,” Opt. Commun. 217, 401–413 (2003).
[CrossRef]

Walker, K.

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

Watley, D.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Wei, H.

Z. Tong, H. Wei, and S. Jian, “Impacts of SPM/XPM on multi-span transmission systems using distributed Raman amplification at identical nonlinear phase shift,” IEEE Photon. Technol. Lett. 16, 933–935 (2004).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Comparison of different Raman amplification schemes in long-span fiber transmission systems with double Rayleigh backscattering,” IEEE Photon. Technol. Lett. 15, 1782–1784 (2003).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Theoretical investigation and optimization of bidirectionally pumped broadband fiber Raman amplifiers,” Opt. Commun. 217, 401–413 (2003).
[CrossRef]

Wei, J. S.

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

Winful, H. G.

V. E. Perlin and H. G. Winful, “Optimizing the noise performance of broadband WDM systems with distributed Raman amplification,” IEEE Photon. Technol. Lett. 14, 1199–1201 (2002).
[CrossRef]

Zhu, Y.

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

Electron. Lett. (2)

Y. Zhu, W. S. Lee, C. Scahill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw, and A. Hadjifotiou, “1.28Tbit/s (32×40Gbit/s) transmission over 1000km NDSF employing distributed Raman amplification and active gain flattening,” Electron. Lett. 37, 43–45 (2001).
[CrossRef]

M. Nissov, K. Rottwitt, H. D. Kidorf, and M. X. Ma, “Rayleigh crosstalk in long cascades of distributed unsaturated Raman amplifiers,” Electron. Lett. 35, 997–998 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equaliazed by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron. 7, 3–16 (2001).
[CrossRef]

M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (8)

V. E. Perlin and H. G. Winful, “Optimizing the noise performance of broadband WDM systems with distributed Raman amplification,” IEEE Photon. Technol. Lett. 14, 1199–1201 (2002).
[CrossRef]

J. S. Wei, D. L. Butler, M. F. V. Leeuwen, L. G. Joneckis, and J. Goldhar, “Crosstalk bandwidth in backward pumped fiber Raman amplifiers,” IEEE Photon. Technol. Lett. 11, 1417–1419 (1999).
[CrossRef]

J. C. Bouteiller, K. Brar, J. Bromage, S. Radic, and C. Headley, “Dual-order Raman pump,” IEEE Photon. Technol. Lett. 15, 212–214 (2003).
[CrossRef]

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488 (2000).
[CrossRef]

M. D. Mermelstein, K. Brar, and C. Headley, “RIN transfer suppression technique for dual-order Raman pumping schemes,” IEEE Photon. Technol. Lett. 15, 1354–1356 (2003).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Comparison of different Raman amplification schemes in long-span fiber transmission systems with double Rayleigh backscattering,” IEEE Photon. Technol. Lett. 15, 1782–1784 (2003).
[CrossRef]

R. Hainberger, T. Hoshida, T. Terahara, and H. Onaka, “Comparison of span configurations of Raman-amplified dispersion-managed fibers,” IEEE Photon. Technol. Lett. 14, 471–473 (2002).
[CrossRef]

Z. Tong, H. Wei, and S. Jian, “Impacts of SPM/XPM on multi-span transmission systems using distributed Raman amplification at identical nonlinear phase shift,” IEEE Photon. Technol. Lett. 16, 933–935 (2004).
[CrossRef]

Opt. Commun. (1)

Z. Tong, H. Wei, and S. Jian, “Theoretical investigation and optimization of bidirectionally pumped broadband fiber Raman amplifiers,” Opt. Commun. 217, 401–413 (2003).
[CrossRef]

Other (5)

K. Rottwitt, A. Stentz, T. Nielson, P. Hansen, K. Feder, and K. Walker, “Transparent 80km bi-directionally pumped distributed Raman amplifier with second order pumping,” in Proc. European Conference on Optical Communication (ECOC’99, Institute of Electrical and Electronics Engineers, Nice, France), p. II-144 (1999).

J. C. Bouteiller, K. Brar, and C. Headley, “Quasi-constant signal power transmission,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), symposium 3.04 (2002).

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, J. Kim, A. Klein, G. Baynham, L. V. Jørgensen, L. Grüner-Nielsen, R. L. Lingle, and D. J. DiGiovanni, “High co-directional Raman gain for 200-km spans, enabling 40*10.66Gb/s transmission over 2400km,” in Optical Fiber Communication Conference (OFC), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2003), paper PD24-1 (2003).

C. Martinelli, D. Mongardien, J. C. Antona, C. Simnneau, and D. Bayart, “Analysis of bi-directional and second-order pumping in long-haul systems with distributed Raman amplification,” in Proc. European Conference on Optical Communication (ECOC’02, Institute of Electrical and Electronics Engineers, Copenhagen, Denmark), p. 3.30 (2002).

R. L. Burden and J. D. Faires, Numerical Analysis (7th edition, Brooks-Cole, 2001), Chap. 10.

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Figures (11)

Fig. 1.
Fig. 1.

Three span amplification configurations discussed in this paper. (a) Bi-directional dual order pumping (type 1). (b) Bi-directional first order pumping (type 2). (c) Raman+EDFA hybrid amplification structure (type 3).

Fig.2
Fig.2

Contour maps of output OSNR versus r 1 and rf · rb is 13dB for (a) and 20dB for (b). ‘+’ denotes the optimal OSNR value.

Fig.3
Fig.3

Optimized OSNR versus rf · KNL =0.072rad for (a), while KNL =0.16rad for (b). Symmetric pumping structure is used.

Fig. 4
Fig. 4

Optimized OSNR of three types against (a) KNL and (b) fiber loss.

Fig. 5
Fig. 5

Signal distribution curves of three pumping schemes

Fig. 6
Fig. 6

Contour maps of output OSNR versus r 1 and rf · rb is 13dB for (a) and 20dB for (b). ‘+’ denotes the optimal OSNR value. L=160km.

Fig.7
Fig.7

Calculated OSNR versus (a) rf and (b) second-order pump wavelength. Symmetric pumping scheme is used, and r=36dB in (b).

Fig.8
Fig.8

Calculated OSNR versus λ P2 when Rs=8× 10-5km-1 and span net gain is 4dB. The optimal λ P2 becomes 1400nm.

Fig.9
Fig.9

Signal and pump distribution of the BiDP scheme. The second-order pump wavelength is 1395nm, and rf is 4000:1.

Fig.10
Fig.10

Optimized (a) total OSNR, (b) corresponding OSNR with ASE only and (c) corresponding OSNR with DRB only of three types versus span length. KNL-ref=0.09rad.

Fig.11
Fig.11

Optimized OSNR of three types versus (a) KNL, (b) signal loss and (c) RS. Span span length is 200 km.

Equations (6)

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d P ± ( z , v ) dz = α ( v ) P ± ( z , v ) ± R s ( v ) P ( z , v ) ± P ± ( z , v ) · ξ > v g r ( v ξ ) K eff A eff ( ξ ) · [ P ± ( z , ξ ) + P ( z , ξ ) ]
± hv ξ > v g r ( v ξ ) A eff ( ξ ) [ P ± ( z , ξ ) + P ( z , ξ ) ] · [ 1 + 1 e h ( ξ v ) k T 1 ] Δ v
P ± ( z , v ) · ξ > v v ξ · g r ( v ξ ) A eff ( v ) K eff · [ P ± ( z , ξ ) + P ( z , ξ ) ]
2 hv P ± ( z , v ) · ξ < v g r ( v ξ ) A eff ( v ) · [ 1 + 1 e h ( v ζ ) j k T 1 ] Δ v ,
OSNR = P s ( 0 ) · G Raman · T [ P ASE ( L ) + P DRB ( L ) ] ,
OSNR = P s ( 0 ) · G Raman · G EDFA · T [ P ASE ( L ) + P DRB ( L ) ] · G EDFA + 2 h ν Δ ν · n s p · ( G EDFA 1 ) ,

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