Abstract

In this paper, we propose an efficient and accurate method that combines the Genetic Algorithm (GA) with the Nelder-Mead method in order to obtain the gain optimization of distributed Raman amplifiers. By using these two methods together, the advantages of both are combined: the convergence of the GA and the high accuracy of the Nelder-Mead. To enhance the convergence of the GA, several features were examined and correlated with fitting errors. It is also shown that when the right moment to switch between methods is chosen, the computation time can be reduced by a factor of two.

© 2007 Optical Society of America

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References

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  1. C. Headley, G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems, (San Diego, CA: Academic, 2005), chap. 3.
  2. H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
    [CrossRef]
  3. J. Bromage, "Raman amplification for fiber communication systems," J. Lightwave Technol. 1, 79-93 (2004).
    [CrossRef]
  4. X. Liu, "Powerful solution for simulating nonlinear coupled equations describing bidirectionally pumped broadband Raman amplifiers," Opt. Express 4, 545-550 (2004).
    [CrossRef]
  5. Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
    [CrossRef]
  6. B. Min, W. J. Lee, N. Park, "Efficient formulation of Raman amplifier propagation equation with average power analysis," IEEE Photon. Technol Lett. 11, 1486-1488 (2000).
  7. 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. 2, 206-208 (2003).
    [CrossRef]
  8. M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).
  9. 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. 9, 945-947 (2001).
    [CrossRef]
  10. J. Zhou, J. Chen, X. Li, "A novel method to optimize optical-fiber Raman amplifiers using equally spaced low-power laser diode pumps," Microwave Opt. Technol. Lett. 2, 124-127 (2004).
    [CrossRef]
  11. X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifer," J. Lightwave Technol. 12, (2003).
  12. Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
    [CrossRef]
  13. M. Mitchell, An Introduction to Genetic Algorithms (Massachusetts: MIT Press co, 1998), Chap. 5.
  14. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Massachusetts, Addison-Wesley Co, 1989).
  15. B. Neto, S. StevanJr, A. Teixeira, P. André, "Efficient simulation of Raman ampliers propagation equations using optimization techniques," in Proceedings of 11th European Conference on Netwoks & Optical Communication - NOC 2006, (2006), pp. 381-386.

2006

Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
[CrossRef]

2004

J. Bromage, "Raman amplification for fiber communication systems," J. Lightwave Technol. 1, 79-93 (2004).
[CrossRef]

X. Liu, "Powerful solution for simulating nonlinear coupled equations describing bidirectionally pumped broadband Raman amplifiers," Opt. Express 4, 545-550 (2004).
[CrossRef]

J. Zhou, J. Chen, X. Li, "A novel method to optimize optical-fiber Raman amplifiers using equally spaced low-power laser diode pumps," Microwave Opt. Technol. Lett. 2, 124-127 (2004).
[CrossRef]

2003

X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifer," J. Lightwave Technol. 12, (2003).

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. 2, 206-208 (2003).
[CrossRef]

2001

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (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. 9, 945-947 (2001).
[CrossRef]

2000

B. Min, W. J. Lee, N. Park, "Efficient formulation of Raman amplifier propagation equation with average power analysis," IEEE Photon. Technol Lett. 11, 1486-1488 (2000).

1999

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

1998

Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
[CrossRef]

Bromage, J.

J. Bromage, "Raman amplification for fiber communication systems," J. Lightwave Technol. 1, 79-93 (2004).
[CrossRef]

Chen, J.

J. Zhou, J. Chen, X. Li, "A novel method to optimize optical-fiber Raman amplifiers using equally spaced low-power laser diode pumps," Microwave Opt. Technol. Lett. 2, 124-127 (2004).
[CrossRef]

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).

Chen, Z.

Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
[CrossRef]

Cheng, T. H.

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. 9, 945-947 (2001).
[CrossRef]

Han, Q.

Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
[CrossRef]

Huang, J.

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. 2, 206-208 (2003).
[CrossRef]

Jiang, W.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).

Kirdof, H.

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

Lagarias,

Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
[CrossRef]

Lee, B.

X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifer," J. Lightwave Technol. 12, (2003).

Lee, W. J.

B. Min, W. J. Lee, N. Park, "Efficient formulation of Raman amplifier propagation equation with average power analysis," IEEE Photon. Technol Lett. 11, 1486-1488 (2000).

Li, J.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).

Li, X.

J. Zhou, J. Chen, X. Li, "A novel method to optimize optical-fiber Raman amplifiers using equally spaced low-power laser diode pumps," Microwave Opt. Technol. Lett. 2, 124-127 (2004).
[CrossRef]

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).

Liu, J. M.

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. 2, 206-208 (2003).
[CrossRef]

Liu, X.

X. Liu, "Powerful solution for simulating nonlinear coupled equations describing bidirectionally pumped broadband Raman amplifiers," Opt. Express 4, 545-550 (2004).
[CrossRef]

X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifer," J. Lightwave Technol. 12, (2003).

Lu, C.

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. 9, 945-947 (2001).
[CrossRef]

Ma, M.

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

Min, B.

B. Min, W. J. Lee, N. Park, "Efficient formulation of Raman amplifier propagation equation with average power analysis," IEEE Photon. Technol Lett. 11, 1486-1488 (2000).

Ning, J.

Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
[CrossRef]

Nissov, M.

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

Park, N.

B. Min, W. J. Lee, N. Park, "Efficient formulation of Raman amplifier propagation equation with average power analysis," IEEE Photon. Technol Lett. 11, 1486-1488 (2000).

Reeds, J. A.

Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
[CrossRef]

Ribarijaona, E.

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

Rottwitt, K.

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

Shum, P.

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. 9, 945-947 (2001).
[CrossRef]

Wright, M. H.

Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
[CrossRef]

Wright, P. E.

Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
[CrossRef]

Xiao, P. C.

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. 2, 206-208 (2003).
[CrossRef]

Yan, M.

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (2001).

Zeng, Q. J.

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. 2, 206-208 (2003).
[CrossRef]

Zhang, H.

Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
[CrossRef]

Zhou, J.

J. Zhou, J. Chen, X. Li, "A novel method to optimize optical-fiber Raman amplifiers using equally spaced low-power laser diode pumps," Microwave Opt. Technol. Lett. 2, 124-127 (2004).
[CrossRef]

Zhou, X.

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. 9, 945-947 (2001).
[CrossRef]

IEEE Photon Technol. Lett.

H. Kirdof, K. Rottwitt, M. Nissov, M. Ma, E. Ribarijaona, "Pump amplification in a 100 nm bandwidth Raman amplifier," IEEE Photon Technol. Lett. 11, 530-532 (1999).
[CrossRef]

IEEE Photon. Technol Lett.

B. Min, W. J. Lee, N. Park, "Efficient formulation of Raman amplifier propagation equation with average power analysis," IEEE Photon. Technol Lett. 11, 1486-1488 (2000).

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. 2, 206-208 (2003).
[CrossRef]

M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, "Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps," IEEE Photon. Technol Lett. 9, 948-950 (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. 9, 945-947 (2001).
[CrossRef]

J. Lightwave Technol.

J. Bromage, "Raman amplification for fiber communication systems," J. Lightwave Technol. 1, 79-93 (2004).
[CrossRef]

Q. Han, J. Ning, H. Zhang, Z. Chen, "Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers," J. Lightwave Technol. 4, 1946-1952 (2006).
[CrossRef]

X. Liu, B. Lee, "Optimal design for ultra-broad-band amplifer," J. Lightwave Technol. 12, (2003).

Microwave Opt. Technol. Lett.

J. Zhou, J. Chen, X. Li, "A novel method to optimize optical-fiber Raman amplifiers using equally spaced low-power laser diode pumps," Microwave Opt. Technol. Lett. 2, 124-127 (2004).
[CrossRef]

Opt. Express

X. Liu, "Powerful solution for simulating nonlinear coupled equations describing bidirectionally pumped broadband Raman amplifiers," Opt. Express 4, 545-550 (2004).
[CrossRef]

SIAM J. Optim.

Lagarias, J.C. , J. A. Reeds, M. H. Wright, P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM J. Optim. 9, 112-147(1998).
[CrossRef]

Other

M. Mitchell, An Introduction to Genetic Algorithms (Massachusetts: MIT Press co, 1998), Chap. 5.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Massachusetts, Addison-Wesley Co, 1989).

B. Neto, S. StevanJr, A. Teixeira, P. André, "Efficient simulation of Raman ampliers propagation equations using optimization techniques," in Proceedings of 11th European Conference on Netwoks & Optical Communication - NOC 2006, (2006), pp. 381-386.

C. Headley, G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems, (San Diego, CA: Academic, 2005), chap. 3.

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of the implemented setup in the 5 pumps scenario.

Fig. 2.
Fig. 2.

Optimized ripples at the end of the GA and the hybrid GA for different number of generations for a population size of 50 individuals. The line is the exponential interpolation.

Fig. 3.
Fig. 3.

Relative Nelder-Mead time and the corresponding ripple variation. The lines are visual guides.

Fig. 4.
Fig. 4.

The GA, the Nelder-Mead and the total simulation times for a hybrid GA against the number of generations for a population size of 50 individuals. The lines are visual guides.

Tables (5)

Tables Icon

Table 1. Optimised pumps wavelengths and powers.

Tables Icon

Table 2. Optimized ripples (means and standard deviations) obtained in 10 trials at the end of the first generation for population sized with 25, 50, 75 and 100 individuals.

Tables Icon

Table 3. Optimized ripples (means and standard deviations) obtained in 10 trials for different types of selection methods at the end of 10 generations.

Tables Icon

Table 4. Optimized ripples (means and standard deviations) obtained in 10 trials for different types of crossover methods at the end of 10 generations.

Tables Icon

Table 5. Optimized ripples (means and standard deviations) obtained in 10 trials for different types of mutation methods at the end of 10 generations.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

± d P i ± d z = [ α i + j = 1 i 1 g ji ( P j + + P j ) j = i + 1 m υ i υ j g ij ( P j + + P j ) 2 h υ i j = i + 1 m g ij Γ ( 1 + η ij ) Δ υ ] P i ±
+ γ i P i + h υ i j = 1 i 1 g ij Γ ( P j + + P j ) ( 1 + η ji ) Δ υ
η ij = { exp [ h ( υ i υ j ) k T ] 1 } 1
g ij = g R ( υ i υ j ) Γ A eff

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