Abstract

We develop a low complexity computational model for the gain profile and amplified spontaneous emission noise for broadband counter-pumped Raman fiber amplifiers. The proposed model is based on two adjustment parameters used to account for the interactions between the pumps. The obtained results show a good agreement between experimental measurements and detailed numerical simulations, for different combinations of pump wavelengths and pump powers, with a processing time several times lower than the time taken by a detailed numerical model.

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  1. A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
    [CrossRef]
  2. F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.
  3. K. Manousakis, K. Christodoulopoulos, E. Kamitsas, I. Tomkos, and E. Varvarigos, “Offline impairment-aware routing and wavelength assignment algorithms in translucent WDM optical networks,” J. Lightwave Technol., vol. 27, no. 12, pp. 1866–1877, 2009.
    [CrossRef]
  4. J. Bromage, “Raman amplification for fiber communications systems,” J. Lightwave Technol., vol. 22, no. 1, pp. 79–93, 2004.
    [CrossRef]
  5. C. Headley and G. Agrawal, Raman Amplification in Fiber Optical Communication Systems. Academic Press, 2005.
  6. M. Zirngibl, “Analytical model of Raman gain effects in massive wavelength division multiplexed transmission systems,” Electron. Lett., vol. 34, no. 8, pp. 789–790, 1998.
    [CrossRef]
  7. S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron., vol. 7, no. 1, pp. 3–16, 2001.
    [CrossRef]
  8. S. Chinn, “Analysis of counter-pumped small-signal fibre Raman amplifiers,” Electron. Lett., vol. 33, no. 7, pp. 607–608, 1997.
    [CrossRef]
  9. A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
    [CrossRef]
  10. X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
    [CrossRef]
  11. S. Cani, L. de Calazans Calmon, M. Pontes, M. Ribeiro, M. Segatto, and A. Cartaxo, “An analytical approximated solution for the gain of broadband Raman amplifiers with multiple counter-pumps,” J. Lightwave Technol., vol. 27, no. 7, pp. 944–951, 2009.
    [CrossRef]
  12. J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
    [CrossRef]
  13. M. Santagiustina, “Exact, implicit, integral solution of depletion and saturation in Raman and Brillouin fiber amplifiers,” in European Conf. on Lasers and Electro-Optics, and the Int. Quantum Electronics Conf., CLEOE-IQEC 2007, 2007.
  14. B. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1486–1488, 2000.
    [CrossRef]
  15. M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
    [CrossRef]
  16. J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
    [CrossRef]
  17. J. Park and P. Kim, “Gain and noise figure spectrum control algorithm for fiber Raman amplifiers,” IEEE Photon. Technol. Lett., vol. 18, no. 10, pp. 1125–1127, 2006.
    [CrossRef]
  18. M. Fugihara and A. Pinto, “Low-cost Raman amplifier for CWDM systems,” Microwave Opt. Technol. Lett., vol. 50, no. 2, pp. 297–301, 2008.
    [CrossRef]
  19. J. Ferreira, M. Fugihara, and A. Pinto, “Transient response and control of pump-reflecting Raman fiber amplifiers,” Fiber Integr. Opt., vol. 29, no. 1, pp. 44–61, 2010.
  20. J. Ferreira, R. Nogueira, P. Monteiro, and A. Pinto, “Raman amplifier undepleted pump model customization to include pump-to-pump interactions,” in IEEE Int. Conf. on Computer as a Tool (EUROCON), 2011.
  21. C. Fludger, V. Handerek, N. Jolley, and R. Mears, “Fundamental noise limits in broadband Raman amplifiers,” in Optical Fiber Communication Conf., 2001, MA5.
  22. N. Muga, M. Fugihara, M. Ferreira, and A. Pinto, “Non-Gaussian ASE noise in Raman amplification systems,” J. Lightwave Technol., vol. 27, no. 16, pp. 3389–3398, 2009.
    [CrossRef]

2010 (1)

J. Ferreira, M. Fugihara, and A. Pinto, “Transient response and control of pump-reflecting Raman fiber amplifiers,” Fiber Integr. Opt., vol. 29, no. 1, pp. 44–61, 2010.

2009 (3)

2008 (2)

A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
[CrossRef]

M. Fugihara and A. Pinto, “Low-cost Raman amplifier for CWDM systems,” Microwave Opt. Technol. Lett., vol. 50, no. 2, pp. 297–301, 2008.
[CrossRef]

2006 (1)

J. Park and P. Kim, “Gain and noise figure spectrum control algorithm for fiber Raman amplifiers,” IEEE Photon. Technol. Lett., vol. 18, no. 10, pp. 1125–1127, 2006.
[CrossRef]

2005 (1)

J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
[CrossRef]

2004 (3)

M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

J. Bromage, “Raman amplification for fiber communications systems,” J. Lightwave Technol., vol. 22, no. 1, pp. 79–93, 2004.
[CrossRef]

2003 (1)

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

2001 (2)

X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
[CrossRef]

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron., vol. 7, no. 1, pp. 3–16, 2001.
[CrossRef]

2000 (1)

B. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1486–1488, 2000.
[CrossRef]

1998 (1)

M. Zirngibl, “Analytical model of Raman gain effects in massive wavelength division multiplexed transmission systems,” Electron. Lett., vol. 34, no. 8, pp. 789–790, 1998.
[CrossRef]

1997 (1)

S. Chinn, “Analysis of counter-pumped small-signal fibre Raman amplifiers,” Electron. Lett., vol. 33, no. 7, pp. 607–608, 1997.
[CrossRef]

Agrawal, G.

C. Headley and G. Agrawal, Raman Amplification in Fiber Optical Communication Systems. Academic Press, 2005.

Bayart, D.

F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.

Brogard, N.

A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
[CrossRef]

F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.

Bromage, J.

Cani, S.

Cartaxo, A.

Chen, J.

J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
[CrossRef]

Cheng, T.

X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
[CrossRef]

Chinn, S.

S. Chinn, “Analysis of counter-pumped small-signal fibre Raman amplifiers,” Electron. Lett., vol. 33, no. 7, pp. 607–608, 1997.
[CrossRef]

Christodoulopoulos, K.

de Calazans Calmon, L.

Emori, Y.

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron., vol. 7, no. 1, pp. 3–16, 2001.
[CrossRef]

Ferreira, J.

J. Ferreira, M. Fugihara, and A. Pinto, “Transient response and control of pump-reflecting Raman fiber amplifiers,” Fiber Integr. Opt., vol. 29, no. 1, pp. 44–61, 2010.

J. Ferreira, R. Nogueira, P. Monteiro, and A. Pinto, “Raman amplifier undepleted pump model customization to include pump-to-pump interactions,” in IEEE Int. Conf. on Computer as a Tool (EUROCON), 2011.

Ferreira, M.

Fludger, C.

C. Fludger, V. Handerek, N. Jolley, and R. Mears, “Fundamental noise limits in broadband Raman amplifiers,” in Optical Fiber Communication Conf., 2001, MA5.

Fugihara, M.

J. Ferreira, M. Fugihara, and A. Pinto, “Transient response and control of pump-reflecting Raman fiber amplifiers,” Fiber Integr. Opt., vol. 29, no. 1, pp. 44–61, 2010.

N. Muga, M. Fugihara, M. Ferreira, and A. Pinto, “Non-Gaussian ASE noise in Raman amplification systems,” J. Lightwave Technol., vol. 27, no. 16, pp. 3389–3398, 2009.
[CrossRef]

M. Fugihara and A. Pinto, “Low-cost Raman amplifier for CWDM systems,” Microwave Opt. Technol. Lett., vol. 50, no. 2, pp. 297–301, 2008.
[CrossRef]

Giudice, G.

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

Handerek, V.

C. Fludger, V. Handerek, N. Jolley, and R. Mears, “Fundamental noise limits in broadband Raman amplifiers,” in Optical Fiber Communication Conf., 2001, MA5.

Headley, C.

C. Headley and G. Agrawal, Raman Amplification in Fiber Optical Communication Systems. Academic Press, 2005.

Honzátko, P.

M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
[CrossRef]

Jiang, W.

J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
[CrossRef]

Jolley, N.

C. Fludger, V. Handerek, N. Jolley, and R. Mears, “Fundamental noise limits in broadband Raman amplifiers,” in Optical Fiber Communication Conf., 2001, MA5.

Kamitsas, E.

Kanka, J.

M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
[CrossRef]

Karásek, M.

M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
[CrossRef]

Kim, P.

J. Park and P. Kim, “Gain and noise figure spectrum control algorithm for fiber Raman amplifiers,” IEEE Photon. Technol. Lett., vol. 18, no. 10, pp. 1125–1127, 2006.
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

Kobyakov, A.

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

Lee, H.

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

Lee, W.

B. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1486–1488, 2000.
[CrossRef]

Leplingard, F.

A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
[CrossRef]

F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.

Li, X.

J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
[CrossRef]

Lu, C.

X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
[CrossRef]

Manousakis, K.

Mears, R.

C. Fludger, V. Handerek, N. Jolley, and R. Mears, “Fundamental noise limits in broadband Raman amplifiers,” in Optical Fiber Communication Conf., 2001, MA5.

Min, B.

B. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1486–1488, 2000.
[CrossRef]

Monteiro, P.

J. Ferreira, R. Nogueira, P. Monteiro, and A. Pinto, “Raman amplifier undepleted pump model customization to include pump-to-pump interactions,” in IEEE Int. Conf. on Computer as a Tool (EUROCON), 2011.

Morea, A.

A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
[CrossRef]

F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.

Muga, N.

Namiki, S.

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron., vol. 7, no. 1, pp. 3–16, 2001.
[CrossRef]

Nogueira, R.

J. Ferreira, R. Nogueira, P. Monteiro, and A. Pinto, “Raman amplifier undepleted pump model customization to include pump-to-pump interactions,” in IEEE Int. Conf. on Computer as a Tool (EUROCON), 2011.

Park, J.

J. Park and P. Kim, “Gain and noise figure spectrum control algorithm for fiber Raman amplifiers,” IEEE Photon. Technol. Lett., vol. 18, no. 10, pp. 1125–1127, 2006.
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

Park, N.

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

B. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1486–1488, 2000.
[CrossRef]

Peterka, P.

M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
[CrossRef]

Pinto, A.

J. Ferreira, M. Fugihara, and A. Pinto, “Transient response and control of pump-reflecting Raman fiber amplifiers,” Fiber Integr. Opt., vol. 29, no. 1, pp. 44–61, 2010.

N. Muga, M. Fugihara, M. Ferreira, and A. Pinto, “Non-Gaussian ASE noise in Raman amplification systems,” J. Lightwave Technol., vol. 27, no. 16, pp. 3389–3398, 2009.
[CrossRef]

M. Fugihara and A. Pinto, “Low-cost Raman amplifier for CWDM systems,” Microwave Opt. Technol. Lett., vol. 50, no. 2, pp. 297–301, 2008.
[CrossRef]

J. Ferreira, R. Nogueira, P. Monteiro, and A. Pinto, “Raman amplifier undepleted pump model customization to include pump-to-pump interactions,” in IEEE Int. Conf. on Computer as a Tool (EUROCON), 2011.

Pontes, M.

Ribeiro, M.

Santagiustina, M.

M. Santagiustina, “Exact, implicit, integral solution of depletion and saturation in Raman and Brillouin fiber amplifiers,” in European Conf. on Lasers and Electro-Optics, and the Int. Quantum Electronics Conf., CLEOE-IQEC 2007, 2007.

Segatto, M.

Shum, P.

X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
[CrossRef]

Ten, S.

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

Tomkos, I.

Tsuda, S.

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

Varvarigos, E.

Vasilyev, M.

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

Zami, T.

A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
[CrossRef]

F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.

Zhou, J.

J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
[CrossRef]

Zhou, X.

X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
[CrossRef]

Zirngibl, M.

M. Zirngibl, “Analytical model of Raman gain effects in massive wavelength division multiplexed transmission systems,” Electron. Lett., vol. 34, no. 8, pp. 789–790, 1998.
[CrossRef]

Compt. Rend. (1)

A. Morea, F. Leplingard, T. Zami, and N. Brogard, “New transmission systems enabling transparent network perspectives,” Compt. Rend., vol. 9, no. 9–10, pp. 985–1001, 2008.
[CrossRef]

Electron. Lett. (2)

S. Chinn, “Analysis of counter-pumped small-signal fibre Raman amplifiers,” Electron. Lett., vol. 33, no. 7, pp. 607–608, 1997.
[CrossRef]

M. Zirngibl, “Analytical model of Raman gain effects in massive wavelength division multiplexed transmission systems,” Electron. Lett., vol. 34, no. 8, pp. 789–790, 1998.
[CrossRef]

Fiber Integr. Opt. (2)

J. Zhou, J. Chen, X. Li, and W. Jiang, “A novel algorithm for backward-pumped Raman amplifier,” Fiber Integr. Opt., vol. 24, no. 6, pp. 529–535, 2005.
[CrossRef]

J. Ferreira, M. Fugihara, and A. Pinto, “Transient response and control of pump-reflecting Raman fiber amplifiers,” Fiber Integr. Opt., vol. 29, no. 1, pp. 44–61, 2010.

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

S. Namiki and Y. Emori, “Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes,” IEEE J. Sel. Top. Quantum Electron., vol. 7, no. 1, pp. 3–16, 2001.
[CrossRef]

IEEE Photon. Technol. Lett. (5)

J. Park, P. Kim, J. Park, H. Lee, and N. Park, “Closed integral form expansion of Raman equation for efficient gain optimization process,” IEEE Photon. Technol. Lett., vol. 16, no. 7, pp. 1649–1651, 2004.
[CrossRef]

J. Park and P. Kim, “Gain and noise figure spectrum control algorithm for fiber Raman amplifiers,” IEEE Photon. Technol. Lett., vol. 18, no. 10, pp. 1125–1127, 2006.
[CrossRef]

A. Kobyakov, M. Vasilyev, S. Tsuda, G. Giudice, and S. Ten, “Analytical model for Raman noise figure in dispersion-managed fibers,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 30–32, 2003.
[CrossRef]

X. Zhou, C. Lu, P. Shum, and T. Cheng, “A simplified model and optimal design of a multiwavelength backward-pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 945–947, 2001.
[CrossRef]

B. Min, W. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equations with average power analysis,” IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1486–1488, 2000.
[CrossRef]

Int. J. Numer. Model. (1)

M. Karásek, J. Kaňka, P. Honzátko, and P. Peterka, “Time-domain simulation of power transients in Raman fibre amplifiers,” Int. J. Numer. Model., vol. 17, no. 2, pp. 165–176, 2004.
[CrossRef]

J. Lightwave Technol. (4)

Microwave Opt. Technol. Lett. (1)

M. Fugihara and A. Pinto, “Low-cost Raman amplifier for CWDM systems,” Microwave Opt. Technol. Lett., vol. 50, no. 2, pp. 297–301, 2008.
[CrossRef]

Other (5)

F. Leplingard, T. Zami, A. Morea, N. Brogard, and D. Bayart, “Determination of the impact of a quality of transmission estimator margin on the dimensioning of an optical network,” in Optical Fiber Communication Conf., 2008, OWA–6.

M. Santagiustina, “Exact, implicit, integral solution of depletion and saturation in Raman and Brillouin fiber amplifiers,” in European Conf. on Lasers and Electro-Optics, and the Int. Quantum Electronics Conf., CLEOE-IQEC 2007, 2007.

J. Ferreira, R. Nogueira, P. Monteiro, and A. Pinto, “Raman amplifier undepleted pump model customization to include pump-to-pump interactions,” in IEEE Int. Conf. on Computer as a Tool (EUROCON), 2011.

C. Fludger, V. Handerek, N. Jolley, and R. Mears, “Fundamental noise limits in broadband Raman amplifiers,” in Optical Fiber Communication Conf., 2001, MA5.

C. Headley and G. Agrawal, Raman Amplification in Fiber Optical Communication Systems. Academic Press, 2005.

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Figures (7)

Fig. 1
Fig. 1

On/Off gain measurements and comparison with numerical models for a counter-pumped RFA with four pumps and a total pump power of 745 mW: experimental measurements (crosses), detailed numerical results (full line), undepleted pump model (dotted line), linear regression of the detailed numerical model (dashed line), linear regression of the undepleted pump model (dash–dot line). The inset refers to the pump wavelengths and pump powers of the RFA.

Fig. 2
Fig. 2

On/Off gain measurements and comparison with numerical models for a counter-pumped RFA with four pumps and a total pump power of 745 mW: experimental measurements (crosses), detailed numerical results (full line), weighted undepleted pump model (dotted line), linear regression of the detailed numerical model (dashed line), linear regression of the weighted undepleted pump model (dash–dot line), when adjusting (a) the tilt and (b) the tilt and offset.

Fig. 3
Fig. 3

On/Off gain measurements and comparison with numerical models for a counter-pumped RFA with four pumps and a total pump power of 745 mW: experimental measurements (crosses); detailed numerical results (full line); WAE (dotted line); linear regression of the detailed numerical model (dashed line); linear regression of the WAE (dash–dot line).

Fig. 4
Fig. 4

On/Off gain measurements and comparison with numerical models for a counter-pumped RFA in (a) configuration 2 with a total pump power of 612 mW and (b) configuration 3 with a pump power of 760 mW: experimental measurements (crosses); detailed numerical results (full line); undepleted pump model (dotted line); weighted undepleted pump model based on comparison with experimental or detailed numerical simulation, WBC (dashed line); weighted undepleted pump model based on analytical expressions, WAE (dash–dot line). The inset refers to the pump wavelengths and pump powers of the RFA.

Fig. 5
Fig. 5

MAE of the On/Off gain for the different models for configurations 1, 2 and 3, when compared with experimental results.

Fig. 6
Fig. 6

MAE between the On/Off gain obtained with the undepleted pump model, WBC and WAE, and the detailed numerical model for different total input pump powers for configurations 1 and 4; see Table I.

Fig. 7
Fig. 7

(a) ASE noise measured and estimated based on the undepleted pump model and on the WAE for the amplifier of configuration 1; (b) OSNR measurements and estimation based on the undepleted pump model and based on the WAE for configuration  1.

Tables (2)

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Table I Pump Wavelengths and Input Pump Powers of RFA Configurations

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Table II Processing Times (ms) of the Models in an Intel T5500 Processor at 1.66 GHz With 2 GB of RAM

Equations (20)

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Ps(L)=Ps(0)expCs,pPp(L)LeffαsL,
Ci,j=gR(νjνi)2Aeffif νjνi0,νiνjgR(νiνj)2Aeffif νjνi<0,
Ps(L)=Ps(0)expi=1NCs,iPi(L)Leff,iαsL,
GdB,s=10log10Ps,On(L)Ps,Off(L),
Ps(L)=Ps(0)expi=1NCs,iPiSRSLeff,iαsL,
PiSRS=Pi(L)expj=1NCi,jPj(L)1exp(αjDint)αj,
Gs=Ps,On(L)Ps,Off(L)=expi=1NCs,iPiSRSLeff,i,
ln(Gs)Leffi=1NCs,iPi(L)expLeffj=1NCi,jPj(L),
ln(Gs)Leffi=1NCs,iPiLeffi=1Nj=1NCs,iCi,jPiPj.
Dintln(Gs)Li=1NCs,iPiLi=1Nj=1NCs,iCi,jPiPj.
Ps(L)=Ps(0)expi=1NCs,iPiSRSLeff,iαsL,
Leff,i=1exp((αi+αSRS)L)αi+αSRS,
ΔGs=expi=1NCs,iPiSRSLeff,iexpi=1NCs,iPiSRSLeff,i.
Leff,i=ΔGsi=1N(Cs,iPiSRS)+Leff,i.
αSRS=1ΔGsi=1NCs,iPiSRS+1αiαi.
DintN1Ptotalj=2N|C1,j|,
αSRS10Llog10P1SRSP1(L),
G=exp(αsignalsL)igi,
PASE(L)=hνB0iEiln(gi)iln(gi)1+αLeffexp(αL)iln(gi)G1+αLeffiln(gi),
Ei=1+1exphΔνikT1,