Abstract

Traditional heuristic algorithms are time consuming in searching the pump configuration to obtain a wide-band flat-gain fiber Raman amplifier (FRA). In this paper, two methods are proposed to deal with this problem. One is called combined generic algorithm (CGA). By using the quadratic programming algorithm instead of generic algorithm (GA) to solve the pump integral, the search space dimension is reduced by half, and obviously, this method will converge faster. Based on a linear time-invariant (LTI) system model, another method is also presented under the assumption that the effective area of fiber is weakly dependent on stokes wave. Then, the amplifier gain can be viewed as the output of a special LTI system, which characterizes the normalized Raman gain profile as its unit impulse response and the pump power integral impulse sequence in frequency domain as its input. By using the nonnegative constraint least-square error (LSE) and clustering technique, we will solve this problem quickly. Numerical simulations shows that the total computation time will be halved at the cost of a slight deterioration in gain flatness.

© 2005 IEEE

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  1. P. B. Hansen, L. Eskildsen, S. G. Grubb, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani and D. J. DiGiovanni, "Capacity upgrades of transmission systems by Raman amplification", IEEE Photon. Technol. Lett., vol. 9, no. 2, pp. 262-264, Feb. 1997.
  2. A. Carena, V. Curri and P. Poggiolini, "On the optimization of hybrid Raman/erbium-doped fiber amplifiers", IEEE Photon. Technol. Lett., vol. 13, no. 11, pp. 1170-1172, Nov. 2001.
  3. P. C. Reeves-Hall, D. A. Chestnut, C. J. S. De Matos and J. R. Taylor, "Dual wavelength pumped L-and U-band Raman amplifier", Electron. Lett., vol. 37, no. 14, pp. 883-884, 2001.
  4. Y. Emori and S. Namiki, "100 nm bandwidth flat gain Raman amplifiers pumped and gain-equalized by 12-wavelength-channel WDM high power laser diodes", presented at the Optical Fiber Communication Conf., 1999, Paper PD19.
  5. H. Kidorf, K. Rottwitt, M. Nissov, M. Ma and E. Rabarijaona, "Pump interactions in a 100-nm bandwidth Raman amplifier", IEEE Photon. Technol. Lett., vol. 11, no. 5, pp. 530-532, May 2001.
  6. T. Terahara, T. Hoshida, J. Kumasako and H. Onaka, "128 x 10.66 Gbit/s transmission over 840-km standard SMF with 140-km optical repeater spacing (30.4-dB loss) employing dual-band distributed Raman amplification", presented at the Optical Fiber Communication Conf., 2000, Paper PD28.
  7. Y. Zhu, W. S. Lee, C. Scanhill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw and A. Hadjifotiou, "1.28 Tbit/s (32 x 40 Gbit/s) transmission over 1000 km with only 6 spans", presented at the Eur. Conf. Optical Communication, 2000,Postdeadline paper 1.4.
  8. L. L. Wang, J. Yu, V. Milner, I. Aherne, K. Kojima, O. Mizuhar and V. Swarninithan, "Error-free repeaterless transmission over 300 km of SSMF with DML's, APD receivers and all-Raman amplification", Electron. Lett., vol. 39, no. 1, pp. 90-91, 2003.
  9. J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, R. Boncek, J. Kim, A. Klein, G. Baynham, L. V. Jrgensen, L. Gruner-Nielsen, R. L. Lingle and D. J. DiGiovanni, "WDM transmission over multiple long spans with bidirectional Raman pumping", J. Lightw. Tech., vol. 22, no. 1, pp. 225-232, Jan. 2004.
  10. J. Bromage, "Raman amplification for fiber communications systems", J. Lightw. Tech., vol. 22, no. 1, pp. 79-93, Jan. 2004.
  11. R. P. Espindola, K. L. Bacher, K. Kojima, N. Chand, S. Srinivasan, G. C. Cho, F. Jin, C. Fuchs, V. Millner and W. C. Dautremont-Smith, "High-power, low RIN, spectrally broadened 14xx DFB pump for application in co-pumped Raman amplification", presented at the Eur. Conf. Optical Communications, 2001,Paper PD.F.1.7.
  12. M. D. Mermelstein, C. Horn, Z. Huang, M. Luvalle, J.-C. Bouteiller, C. Headley and B. J. Eggleton, "Configurability of a three-wavelength Raman fiber laser for gain ripple minimization and power partitioning", presented at the Optical Fiber Communication Conf. 2002, 2002, Paper TuJ2.
  13. S. Kado, Y. Emori and S. Namiki, "Gain and noise tilt control in multiwavelength bi-directionally pumped Raman amplifier", presented at the Optical Fiber Communication Conf. 2002 ,, Paper TuJ4.
  14. M. Sobe and Y. Yano, "Automatic pump power adjustment for gain-flattened multiwavelength pumped Raman amplifier", presented at the Optical Fiber Communication Conf. 2002 , Mar. 2002, Paper TuJ5.
  15. W. Zhang, X. Feng, J. Peng and X. Liu, "A simple algorithm for gain spectrum adjustment of backward pumped distributed fiber Raman amplifiers", IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 69-71, Jan. 2004.
  16. M. Muktoyuk, S. Gray and A. Evans, "A method for progressive optimization of pump power and wavelengths for Raman amplification", IEEE Photon. Technol. Lett., vol. 16, no. 5, pp. 1283-1285, May 2004.
  17. 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, Jul. 2004.
  18. S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes", IEEE J. Sel. Topics Quantum Electron., vol. 7, no. 1, pp. 3-16, Jan./Feb. 2001.
  19. X. Zhou, C. Lu, P. Shum and T. H. 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, Sep. 2001.
  20. M. Yan, J. Chen, W. Jiang, J. Li, J. Chen and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps", IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 948-950, Sep. 2001.
  21. V. E. Perlin and H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers", J. Lightw. Tech., vol. 20, no. 2, pp. 250-254, Feb. 2002.
  22. P. C. Xiao, Q. J. Zeng, J. Huang and J. M. Liu, "A new optimal algorithm for multipump sources of distributed fiber Raman amplifier", IEEE Photon. Technol. Lett., vol. 15, no. 2, pp. 206-208, Feb. 2003.
  23. X. Liu and B. Lee, "Optimal design for ultra-broad-band amplifier", J. Lightw. Technol., vol. 21, no. 12, pp. 3446-3455, Dec. 2003.
  24. J.-C. Bouteiller, J. Bromage, H.-J. Thiele, L. E. Nelson, K. Brar and S. Stulz, "An optimization process for Raman-amplified long-span transmission", IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 326-328, Jan. 2004.
  25. I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in single-mode optical fiber", IEEE Photon. Technol. Lett., vol. 15, no. 12, pp. 1704-1706, Dec. 2003.
  26. J. Nocedal and S. J. Wright, Numerical Optimization, New York: Springer-Verlag, 1999.

Other

P. B. Hansen, L. Eskildsen, S. G. Grubb, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani and D. J. DiGiovanni, "Capacity upgrades of transmission systems by Raman amplification", IEEE Photon. Technol. Lett., vol. 9, no. 2, pp. 262-264, Feb. 1997.

A. Carena, V. Curri and P. Poggiolini, "On the optimization of hybrid Raman/erbium-doped fiber amplifiers", IEEE Photon. Technol. Lett., vol. 13, no. 11, pp. 1170-1172, Nov. 2001.

P. C. Reeves-Hall, D. A. Chestnut, C. J. S. De Matos and J. R. Taylor, "Dual wavelength pumped L-and U-band Raman amplifier", Electron. Lett., vol. 37, no. 14, pp. 883-884, 2001.

Y. Emori and S. Namiki, "100 nm bandwidth flat gain Raman amplifiers pumped and gain-equalized by 12-wavelength-channel WDM high power laser diodes", presented at the Optical Fiber Communication Conf., 1999, Paper PD19.

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma and E. Rabarijaona, "Pump interactions in a 100-nm bandwidth Raman amplifier", IEEE Photon. Technol. Lett., vol. 11, no. 5, pp. 530-532, May 2001.

T. Terahara, T. Hoshida, J. Kumasako and H. Onaka, "128 x 10.66 Gbit/s transmission over 840-km standard SMF with 140-km optical repeater spacing (30.4-dB loss) employing dual-band distributed Raman amplification", presented at the Optical Fiber Communication Conf., 2000, Paper PD28.

Y. Zhu, W. S. Lee, C. Scanhill, C. Fludger, D. Watley, M. Jones, J. Homan, B. Shaw and A. Hadjifotiou, "1.28 Tbit/s (32 x 40 Gbit/s) transmission over 1000 km with only 6 spans", presented at the Eur. Conf. Optical Communication, 2000,Postdeadline paper 1.4.

L. L. Wang, J. Yu, V. Milner, I. Aherne, K. Kojima, O. Mizuhar and V. Swarninithan, "Error-free repeaterless transmission over 300 km of SSMF with DML's, APD receivers and all-Raman amplification", Electron. Lett., vol. 39, no. 1, pp. 90-91, 2003.

J. Bromage, J.-C. Bouteiller, H. J. Thiele, K. Brar, L. E. Nelson, S. Stulz, C. Headley, R. Boncek, J. Kim, A. Klein, G. Baynham, L. V. Jrgensen, L. Gruner-Nielsen, R. L. Lingle and D. J. DiGiovanni, "WDM transmission over multiple long spans with bidirectional Raman pumping", J. Lightw. Tech., vol. 22, no. 1, pp. 225-232, Jan. 2004.

J. Bromage, "Raman amplification for fiber communications systems", J. Lightw. Tech., vol. 22, no. 1, pp. 79-93, Jan. 2004.

R. P. Espindola, K. L. Bacher, K. Kojima, N. Chand, S. Srinivasan, G. C. Cho, F. Jin, C. Fuchs, V. Millner and W. C. Dautremont-Smith, "High-power, low RIN, spectrally broadened 14xx DFB pump for application in co-pumped Raman amplification", presented at the Eur. Conf. Optical Communications, 2001,Paper PD.F.1.7.

M. D. Mermelstein, C. Horn, Z. Huang, M. Luvalle, J.-C. Bouteiller, C. Headley and B. J. Eggleton, "Configurability of a three-wavelength Raman fiber laser for gain ripple minimization and power partitioning", presented at the Optical Fiber Communication Conf. 2002, 2002, Paper TuJ2.

S. Kado, Y. Emori and S. Namiki, "Gain and noise tilt control in multiwavelength bi-directionally pumped Raman amplifier", presented at the Optical Fiber Communication Conf. 2002 ,, Paper TuJ4.

M. Sobe and Y. Yano, "Automatic pump power adjustment for gain-flattened multiwavelength pumped Raman amplifier", presented at the Optical Fiber Communication Conf. 2002 , Mar. 2002, Paper TuJ5.

W. Zhang, X. Feng, J. Peng and X. Liu, "A simple algorithm for gain spectrum adjustment of backward pumped distributed fiber Raman amplifiers", IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 69-71, Jan. 2004.

M. Muktoyuk, S. Gray and A. Evans, "A method for progressive optimization of pump power and wavelengths for Raman amplification", IEEE Photon. Technol. Lett., vol. 16, no. 5, pp. 1283-1285, May 2004.

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, Jul. 2004.

S. Namiki and Y. Emori, "Ultrabroad-band Raman amplifiers pumped and gain-equalized by wavelength-division-multiplexed high-power laser diodes", IEEE J. Sel. Topics Quantum Electron., vol. 7, no. 1, pp. 3-16, Jan./Feb. 2001.

X. Zhou, C. Lu, P. Shum and T. H. 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, Sep. 2001.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen and X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps", IEEE Photon. Technol. Lett., vol. 13, no. 9, pp. 948-950, Sep. 2001.

V. E. Perlin and H. G. Winful, "Optimal design of flat-gain wide-band fiber Raman amplifiers", J. Lightw. Tech., vol. 20, no. 2, pp. 250-254, Feb. 2002.

P. C. Xiao, Q. J. Zeng, J. Huang and J. M. Liu, "A new optimal algorithm for multipump sources of distributed fiber Raman amplifier", IEEE Photon. Technol. Lett., vol. 15, no. 2, pp. 206-208, Feb. 2003.

X. Liu and B. Lee, "Optimal design for ultra-broad-band amplifier", J. Lightw. Technol., vol. 21, no. 12, pp. 3446-3455, Dec. 2003.

J.-C. Bouteiller, J. Bromage, H.-J. Thiele, L. E. Nelson, K. Brar and S. Stulz, "An optimization process for Raman-amplified long-span transmission", IEEE Photon. Technol. Lett., vol. 16, no. 1, pp. 326-328, Jan. 2004.

I. Mandelbaum and M. Bolshtyansky, "Raman amplifier model in single-mode optical fiber", IEEE Photon. Technol. Lett., vol. 15, no. 12, pp. 1704-1706, Dec. 2003.

J. Nocedal and S. J. Wright, Numerical Optimization, New York: Springer-Verlag, 1999.

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