Abstract

A novel analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pump lasers is derived taking into account pump-pump interactions. Validation against experimental data available in the literature with two and three pumps is performed. In order to test the limits of the approximated analytical solution, signal gain is numerically obtained by simulation for Raman amplifiers built with different types of fibers and covering bandwidths up to 100 nm. The results show that our analytical solution presents a good agreement with both numerical and experimental results in most of the practical situations. This allows the reduction of the computation time in several orders of magnitude when optimizing such amplifiers.

© 2009 IEEE

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  1. Y. Emori, K. Tanaka, S. Namiki, "100 nm bandwidth flat-gain Raman amplifiers pumped and gain-equalised by 12-wavelength-channel WDM laser diode unit," Electron. Lett. 35, 1355-1356 (1999).
  2. M. Nissov, C. R. Davidson, K. Rottwitt, R. Menges, P. C. Corbett, D. Innis, N. S. Bergano, "100 Gb/s (10$\, \times \,$10 Gb/s) WDM transmission over 7200 km using distributed Raman amplification," Proc. Eur. Conf. Opt. Commun. (ECOC) (1997) pp. 9-12.
  3. P. B. Hansen, L. Eskildsen, S. G. Grubb, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, D. J. DiGiovanni, "Capacity upgrades of transmission systems by Raman amplification," IEEE Photon. Technol. Lett. 9, 262-264 (1997).
  4. Raman Amplification in Fiber Optical Communication Systems (Elsevier Academic, 2005).
  5. Raman Amplifiers for Telecommunications 1—Physical Principles (Springer-Verlag, 2004).
  6. S. A. E. Lewis, S. V. Chernikov, J. R. Taylor, "Characterization of double Rayleigh scatter noise in Raman amplifiers," IEEE Photon. Technol. Lett. 12, 528-530 (2000).
  7. A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, S. Ten, "Analytical model for Raman noise figure in dispersion-managed fibers," IEEE Photon. Technol. Lett. 15, 30-32 (2003).
  8. X. Zhou, C. Lu, P. Shum, T. H. Cheng, "A simplified model and optimal design of a multiwavelength backward pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).
  9. S. Wang, C. Fan, "Distributed fiber Raman amplifiers: analytical expression of noise characteristics under complex conditions," Opt. Commun. 198, 65-70 (2001).
  10. W. Zhang, J. Peng, X. Liu, C. Fan, "An analytical expression of equivalent noise figure for distributed fiber Raman amplifiers with Rayleigh scattering," Opt. Commun. 199, 231-236 (2001).
  11. J. Zhou, J. Chen, X. Li, W. Jiang, "A novel algorithm for backward-pumped Raman amplifier," Fiber Integr. Opt. 24, 529-535 (2005).
  12. M. Santagiustina, "Exact integral solution of saturation and depletion in forward and backward optical fiber Raman amplifiers," Opt. Lett. 32, 3023-3025 (2007).
  13. S. P. Cani, M. Freitas, R. T. Almeida, L. C. Calmon, "Raman amplifier performance of dispersion compensating fibers," Proc. SBMO/IEEE MTT-S Int. Microw. Optoelectron. Conf. (IMOC03) (2003) pp. 553-558.
  14. M. Achtenhagen, T. G. Chang, B. Nyman, A. Hardy, "Analysis of a multiple-pump Raman amplifier," Appl. Phys. Lett. 78, 1322-1324 (2001).
  15. H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, E. Rabarijaona, "Pump interactions in a 100-nm bandwidth Raman amplifier," IEEE Photon. Technol. Lett. 11, 530-532 (1999).
  16. S. Namiki, Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Topics Quantum Electron. 7, 3-16 (2001).
  17. D. Dahan, G. Eisenstein, "Numerical comparison between distributed and discrete amplification in a point-to-point 40-Gb/s 40-WDM-based transmission system with three different modulation formats," J. Lightw. Technol. 20, 379-388 (2002).
  18. Y. Aoki, "Properties of fiber Raman amplifiers and their applicability to digital optical communication systems," J. Lightw. Technol. 6, 1225-1239 (1988).
  19. S. R. Chinn, "Analysis of counter-pumped small-signal fibre Raman amplifiers," Electron. Lett. 33, 607-608 (1997).
  20. A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, "Polarization dependence and gain tilt of Raman amplifiers for WDM systems," Proc. Opt. Fiber Commun. (OFC2001) (2001).
  21. C. R. S. Fludger, V. Handerek, R. J. Mears, "Pump to signal RIN transfer in Raman fiber amplifiers," Electron. Lett. 37, 15-17 (2001).
  22. V. E. Perlin, H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," J. Lightw. Technol. 20, 250-254 (2002).
  23. X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifier," J. Lightw. Technol. 21, 3446-3455 (2003).
  24. J. Bromage, "Raman amplification for fiber communications systems," J. Lightw. Technol. 22, 79-93 (2004).
  25. L. F. Shampine, M. W. Reichelt, J. Kierzenka, Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB With BVP4C ftp://ftp.mathworks.com/pub/doc/papers/bvp/..
  26. S. P. N. Cani, L. C. Calmon, C. A. D. Francisco, D. H. Spadoti, B. V. Borges, M. A. Romero, "Performance evaluation of simultaneous dispersion and Raman amplification using microstructured optical fibers," Proc. SBMO/IEEE MTT-S Int. Microw. Optoelectron. Conf. (IMOC05) (2005) pp. 546-549.
  27. M. Wandel, T. Veng, N. T. Le Quang, L. Grüner-Nielsen, "Dispersion compensating fiber with a high figure of merit," Proc. Eur. Conf. Opt. Commun. (ECOC) (2001) pp. 52-53.
  28. L. Gruner-Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Pálsdóttir, D. Jakobsen, "Dispersion-compensating fibers," J. Lightw. Technol. 23, 3566-3579 (2005).

2007

M. Santagiustina, "Exact integral solution of saturation and depletion in forward and backward optical fiber Raman amplifiers," Opt. Lett. 32, 3023-3025 (2007).

2005

J. Zhou, J. Chen, X. Li, W. Jiang, "A novel algorithm for backward-pumped Raman amplifier," Fiber Integr. Opt. 24, 529-535 (2005).

L. Gruner-Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Pálsdóttir, D. Jakobsen, "Dispersion-compensating fibers," J. Lightw. Technol. 23, 3566-3579 (2005).

2004

J. Bromage, "Raman amplification for fiber communications systems," J. Lightw. Technol. 22, 79-93 (2004).

2003

X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifier," J. Lightw. Technol. 21, 3446-3455 (2003).

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, S. Ten, "Analytical model for Raman noise figure in dispersion-managed fibers," IEEE Photon. Technol. Lett. 15, 30-32 (2003).

2002

D. Dahan, G. Eisenstein, "Numerical comparison between distributed and discrete amplification in a point-to-point 40-Gb/s 40-WDM-based transmission system with three different modulation formats," J. Lightw. Technol. 20, 379-388 (2002).

V. E. Perlin, H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," J. Lightw. Technol. 20, 250-254 (2002).

2001

C. R. S. Fludger, V. Handerek, R. J. Mears, "Pump to signal RIN transfer in Raman fiber amplifiers," Electron. Lett. 37, 15-17 (2001).

S. Namiki, Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Topics Quantum Electron. 7, 3-16 (2001).

M. Achtenhagen, T. G. Chang, B. Nyman, A. Hardy, "Analysis of a multiple-pump Raman amplifier," Appl. Phys. Lett. 78, 1322-1324 (2001).

X. Zhou, C. Lu, P. Shum, T. H. Cheng, "A simplified model and optimal design of a multiwavelength backward pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).

S. Wang, C. Fan, "Distributed fiber Raman amplifiers: analytical expression of noise characteristics under complex conditions," Opt. Commun. 198, 65-70 (2001).

W. Zhang, J. Peng, X. Liu, C. Fan, "An analytical expression of equivalent noise figure for distributed fiber Raman amplifiers with Rayleigh scattering," Opt. Commun. 199, 231-236 (2001).

2000

S. A. E. Lewis, S. V. Chernikov, J. R. Taylor, "Characterization of double Rayleigh scatter noise in Raman amplifiers," IEEE Photon. Technol. Lett. 12, 528-530 (2000).

1999

Y. Emori, K. Tanaka, S. Namiki, "100 nm bandwidth flat-gain Raman amplifiers pumped and gain-equalised by 12-wavelength-channel WDM laser diode unit," Electron. Lett. 35, 1355-1356 (1999).

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, E. Rabarijaona, "Pump interactions in a 100-nm bandwidth Raman amplifier," IEEE Photon. Technol. Lett. 11, 530-532 (1999).

1997

S. R. Chinn, "Analysis of counter-pumped small-signal fibre Raman amplifiers," Electron. Lett. 33, 607-608 (1997).

P. B. Hansen, L. Eskildsen, S. G. Grubb, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, D. J. DiGiovanni, "Capacity upgrades of transmission systems by Raman amplification," IEEE Photon. Technol. Lett. 9, 262-264 (1997).

1988

Y. Aoki, "Properties of fiber Raman amplifiers and their applicability to digital optical communication systems," J. Lightw. Technol. 6, 1225-1239 (1988).

Appl. Phys. Lett.

M. Achtenhagen, T. G. Chang, B. Nyman, A. Hardy, "Analysis of a multiple-pump Raman amplifier," Appl. Phys. Lett. 78, 1322-1324 (2001).

Electron. Lett.

S. R. Chinn, "Analysis of counter-pumped small-signal fibre Raman amplifiers," Electron. Lett. 33, 607-608 (1997).

Y. Emori, K. Tanaka, S. Namiki, "100 nm bandwidth flat-gain Raman amplifiers pumped and gain-equalised by 12-wavelength-channel WDM laser diode unit," Electron. Lett. 35, 1355-1356 (1999).

C. R. S. Fludger, V. Handerek, R. J. Mears, "Pump to signal RIN transfer in Raman fiber amplifiers," Electron. Lett. 37, 15-17 (2001).

Fiber Integr. Opt.

J. Zhou, J. Chen, X. Li, W. Jiang, "A novel algorithm for backward-pumped Raman amplifier," Fiber Integr. Opt. 24, 529-535 (2005).

IEEE J. Sel. Topics Quantum Electron.

S. Namiki, Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes," IEEE J. Sel. Topics Quantum Electron. 7, 3-16 (2001).

IEEE Photon. Technol. Lett.

P. B. Hansen, L. Eskildsen, S. G. Grubb, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, D. J. DiGiovanni, "Capacity upgrades of transmission systems by Raman amplification," IEEE Photon. Technol. Lett. 9, 262-264 (1997).

S. A. E. Lewis, S. V. Chernikov, J. R. Taylor, "Characterization of double Rayleigh scatter noise in Raman amplifiers," IEEE Photon. Technol. Lett. 12, 528-530 (2000).

IEEE Photon. Technol. Lett.

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, S. Ten, "Analytical model for Raman noise figure in dispersion-managed fibers," IEEE Photon. Technol. Lett. 15, 30-32 (2003).

X. Zhou, C. Lu, P. Shum, T. H. Cheng, "A simplified model and optimal design of a multiwavelength backward pumped fiber Raman amplifier," IEEE Photon. Technol. Lett. 13, 945-947 (2001).

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, E. Rabarijaona, "Pump interactions in a 100-nm bandwidth Raman amplifier," IEEE Photon. Technol. Lett. 11, 530-532 (1999).

J. Lightw. Technol.

Y. Aoki, "Properties of fiber Raman amplifiers and their applicability to digital optical communication systems," J. Lightw. Technol. 6, 1225-1239 (1988).

J. Lightw. Technol.

X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifier," J. Lightw. Technol. 21, 3446-3455 (2003).

J. Lightw. Technol.

J. Bromage, "Raman amplification for fiber communications systems," J. Lightw. Technol. 22, 79-93 (2004).

L. Gruner-Nielsen, M. Wandel, P. Kristensen, C. Jorgensen, L. V. Jorgensen, B. Edvold, B. Pálsdóttir, D. Jakobsen, "Dispersion-compensating fibers," J. Lightw. Technol. 23, 3566-3579 (2005).

V. E. Perlin, H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers," J. Lightw. Technol. 20, 250-254 (2002).

D. Dahan, G. Eisenstein, "Numerical comparison between distributed and discrete amplification in a point-to-point 40-Gb/s 40-WDM-based transmission system with three different modulation formats," J. Lightw. Technol. 20, 379-388 (2002).

Opt. Lett.

M. Santagiustina, "Exact integral solution of saturation and depletion in forward and backward optical fiber Raman amplifiers," Opt. Lett. 32, 3023-3025 (2007).

Opt. Commun.

S. Wang, C. Fan, "Distributed fiber Raman amplifiers: analytical expression of noise characteristics under complex conditions," Opt. Commun. 198, 65-70 (2001).

W. Zhang, J. Peng, X. Liu, C. Fan, "An analytical expression of equivalent noise figure for distributed fiber Raman amplifiers with Rayleigh scattering," Opt. Commun. 199, 231-236 (2001).

Other

Raman Amplification in Fiber Optical Communication Systems (Elsevier Academic, 2005).

Raman Amplifiers for Telecommunications 1—Physical Principles (Springer-Verlag, 2004).

M. Nissov, C. R. Davidson, K. Rottwitt, R. Menges, P. C. Corbett, D. Innis, N. S. Bergano, "100 Gb/s (10$\, \times \,$10 Gb/s) WDM transmission over 7200 km using distributed Raman amplification," Proc. Eur. Conf. Opt. Commun. (ECOC) (1997) pp. 9-12.

S. P. Cani, M. Freitas, R. T. Almeida, L. C. Calmon, "Raman amplifier performance of dispersion compensating fibers," Proc. SBMO/IEEE MTT-S Int. Microw. Optoelectron. Conf. (IMOC03) (2003) pp. 553-558.

A. Berntson, S. Popov, E. Vanin, G. Jacobsen, J. Karlsson, "Polarization dependence and gain tilt of Raman amplifiers for WDM systems," Proc. Opt. Fiber Commun. (OFC2001) (2001).

L. F. Shampine, M. W. Reichelt, J. Kierzenka, Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB With BVP4C ftp://ftp.mathworks.com/pub/doc/papers/bvp/..

S. P. N. Cani, L. C. Calmon, C. A. D. Francisco, D. H. Spadoti, B. V. Borges, M. A. Romero, "Performance evaluation of simultaneous dispersion and Raman amplification using microstructured optical fibers," Proc. SBMO/IEEE MTT-S Int. Microw. Optoelectron. Conf. (IMOC05) (2005) pp. 546-549.

M. Wandel, T. Veng, N. T. Le Quang, L. Grüner-Nielsen, "Dispersion compensating fiber with a high figure of merit," Proc. Eur. Conf. Opt. Commun. (ECOC) (2001) pp. 52-53.

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