Abstract

The pumping scheme of multipumped distributed fiber Raman amplifiers is optimized by a powerful method called particle swarm optimization. By use of particle swarm optimization, we optimize both pump powers and frequencies of multipumped Raman amplifiers with a high number of pumps. Particle swarm optimization is a fast and effective method, and it surpasses other optimization methods, such as the genetic algorithm, for optimizing fiber amplifiers. It is shown that the computational efficiency of particle swarm optimization is significantly better than that of the genetic algorithm, reducing the time of computation to one third, and its implementation is more straightforward. A gain bandwidth of 92.1nm and a gain variation of 0.49dB in the range of 1524.51616.6nm are obtained by this method, using ten backward pumps in a 60-km-long amplifier. The gain variation reduction is due to the inclusion of pump frequencies in the optimization process.

© 2008 Optical Society of America

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References

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  1. C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier Academic Press, 2005), pp. 33-163.
  2. J. Bromage, “Raman amplification for fiber communications systems,” J. Lightwave Technol. 22, 79-93 (2004).
    [Crossref]
  3. 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. 7, 3-16 (2001).
    [Crossref]
  4. X. Liu and B. Lee, “A fast and stable method for Raman amplifier propagation equations,” Opt. Express 11, 2163-2176 (2003).
    [Crossref] [PubMed]
  5. X. Liu and B. Lee, “Effective shooting algorithm and its application to fiber amplifiers,” Opt. Express 11, 1452-1461 (2003).
    [Crossref] [PubMed]
  6. X. Liu and Y. Li, “Optimizing the bandwidth and noise performance of distributed multipump Raman amplifiers,” Opt. Commun. 230, 425-431 (2004).
    [Crossref]
  7. X. Liu and B. Lee, “Optimal design for ultra-broad-band amplifier,” J. Lightwave Technol. 21, 3446-3455 (2003).
    [Crossref]
  8. X. Liu, “Optimization for various schemes of distributed fiber Raman amplifiers,” J. Opt. A, Pure Appl. Opt. 6, 1017-1026 (2004).
    [Crossref]
  9. J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks (IEEE, 1995), pp. 1942-1948.
    [Crossref]
  10. R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
    [Crossref]
  11. J. Kennedy and R. C. Eberhart, Swarm Intelligence (Morgan Kaufmann, 2001), Chap. 7.
  12. M. N. Islam, Raman Amplifiers for Telecommunications I (Springer, 2004).
  13. A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence (Wiley, 2005), Chap. 16.

2004 (3)

J. Bromage, “Raman amplification for fiber communications systems,” J. Lightwave Technol. 22, 79-93 (2004).
[Crossref]

X. Liu and Y. Li, “Optimizing the bandwidth and noise performance of distributed multipump Raman amplifiers,” Opt. Commun. 230, 425-431 (2004).
[Crossref]

X. Liu, “Optimization for various schemes of distributed fiber Raman amplifiers,” J. Opt. A, Pure Appl. Opt. 6, 1017-1026 (2004).
[Crossref]

2003 (3)

2001 (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. 7, 3-16 (2001).
[Crossref]

Agrawal, G. P.

C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier Academic Press, 2005), pp. 33-163.

Bromage, J.

Eberhart, R. C.

J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks (IEEE, 1995), pp. 1942-1948.
[Crossref]

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

J. Kennedy and R. C. Eberhart, Swarm Intelligence (Morgan Kaufmann, 2001), Chap. 7.

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. 7, 3-16 (2001).
[Crossref]

Engelbrecht, A. P.

A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence (Wiley, 2005), Chap. 16.

Headley, C.

C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier Academic Press, 2005), pp. 33-163.

Islam, M. N.

M. N. Islam, Raman Amplifiers for Telecommunications I (Springer, 2004).

Kennedy, J.

J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks (IEEE, 1995), pp. 1942-1948.
[Crossref]

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

J. Kennedy and R. C. Eberhart, Swarm Intelligence (Morgan Kaufmann, 2001), Chap. 7.

Lee, B.

Li, Y.

X. Liu and Y. Li, “Optimizing the bandwidth and noise performance of distributed multipump Raman amplifiers,” Opt. Commun. 230, 425-431 (2004).
[Crossref]

Liu, X.

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. 7, 3-16 (2001).
[Crossref]

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. 7, 3-16 (2001).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. A, Pure Appl. Opt. (1)

X. Liu, “Optimization for various schemes of distributed fiber Raman amplifiers,” J. Opt. A, Pure Appl. Opt. 6, 1017-1026 (2004).
[Crossref]

Opt. Commun. (1)

X. Liu and Y. Li, “Optimizing the bandwidth and noise performance of distributed multipump Raman amplifiers,” Opt. Commun. 230, 425-431 (2004).
[Crossref]

Opt. Express (2)

Other (6)

C. Headley and G. P. Agrawal, Raman Amplification in Fiber Optical Communication Systems (Elsevier Academic Press, 2005), pp. 33-163.

J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks (IEEE, 1995), pp. 1942-1948.
[Crossref]

R. C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” in Proceedings of the Sixth International Symposium on Micro Machine and Human Science (IEEE, 1995), pp. 39-43.
[Crossref]

J. Kennedy and R. C. Eberhart, Swarm Intelligence (Morgan Kaufmann, 2001), Chap. 7.

M. N. Islam, Raman Amplifiers for Telecommunications I (Springer, 2004).

A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence (Wiley, 2005), Chap. 16.

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Figures (7)

Fig. 1
Fig. 1

Propagating diagram of signal powers and copropagating (CO) and counterpropagating (CT) pump powers [2].

Fig. 2
Fig. 2

Dispersion-shifted fiber’s (a) Raman gain efficiency and (b) attenuation coefficient used in the computer DFRA model [12].

Fig. 3
Fig. 3

Comparison of basic flow charts of PSO and GA.

Fig. 4
Fig. 4

Output signal powers of DFRA for (a) six- and ten-BiD-pumped and (b) six- and ten-BW-pumped 60 km fiber amplifiers.

Fig. 5
Fig. 5

Signal gains of DFRA for (a) six BW pumps and (b) ten BW pumps, considering and ignoring frequencies in optimization.

Fig. 6
Fig. 6

ASE and DRBS noises for a 60 km BiD amplifier: (a) backward noise powers and (b) forward noise powers propagating through the amplifier.

Fig. 7
Fig. 7

Comparison of GA and PSO speeds of convergence to the global solutions by plotting the fitness mean values versus the normalized time.

Tables (5)

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Table 1 Parameters of Distributed Fiber Raman Amplifier Used for Optimization by PSO

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Table 2 Optimized Pump Powers for 60 km Six-BW-Pumped and Six-BiD-Pumped DFRAs Considering F obj 1

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Table 3 Optimized Pump Powers for 60 km Ten-BW-Pumped and Ten-BiD-Pumped DFRAs Considering F obj 1

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Table 4 Optimized Pump Powers and Frequencies for 60 km Six-BW-Pumped DFRAs Considering F obj 2

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Table 5 Optimized Pump Powers and Frequencies for 60 km Ten-BW-Pumped DFRAs Considering F obj 2

Equations (6)

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± d P i ± d z = α i P i ± + γ i P i + P i ± ν j > ν i g j i Γ A eff [ P j + + P j ] P i ± ν j < ν i ν i ν j g i j Γ A eff [ P j + + P j ] 2 h ν i P i ± ν j < ν i ν i ν j g i j Γ A eff [ 1 + ( e [ h ( ν i ν j ) ] K T 1 ) 1 ] Δ ν + 2 h ν i ν j > ν i g j i Γ A eff [ P j + + P j ] [ 1 + ( e [ h ( ν j ν i ) ] K T 1 ) 1 ] Δ ν ,
υ i ( k ) = φ υ i ( k 1 ) + ρ 1 C f ( x Sbest i x i ( k ) ) + ρ 2 C f ( x Gbest i x i ( k ) ) ,
φ = 1 0.7 1 k 1 k max ,
x i ( k ) = x i ( k 1 ) + υ i ( k ) .
F obj 1 = k = 1 : n s P s k ( 0 ) P s k ( L ) ,
F obj 2 = Max 10 × log ( P s k ( L ) P s k ( 0 ) ) + α k = 1 : n s 10 × log ( P s k ( L ) P s k ( 0 ) ) ,

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