Abstract

An efficient and robust shooting algorithm for the design of bidirectionally pumped Raman fiber amplifiers is proposed. First, a parameter S, new to our knowledge, called scaling vector, is introduced. This parameter is used in combination with the physical picture of stimulated Raman scattering to generate accurate initial guesses for the powers of backward pumps in the bidirectionally pumped Raman fiber amplifiers. Second, a modified Newton–Raphson method is developed. With an appropriate restriction for the adjustment of increments of initial guess attached, the modified Newton–Raphson method is used to correct the initial guesses to approach the true solution of the problem. By combining the method of initial value determination and the correction mechanism, 14 types of bidirectionally pumped Raman fiber amplifiers are designed. The simulation results show that the proposed shooting algorithm is more efficient and stable than most of the existing ones. Comparison with three other relevant methods reported in the literature is made to reveal the advantages of the new method.

© 2011 Optical Society of America

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References

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  1. C. Headly and G. P. Agarwal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. X. Liu, “Optimization for various schemes of distributed fibre Raman amplifiers,” J. Opt. A 6, 1017–1026 (2004).
    [CrossRef]
  6. Z. Lalidastjerdi, F. Kroushavi, and M. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” Opt. Laser Technol. 40, 1041–1046 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEE Proc. J. 132, 58–63(1985).
    [CrossRef]
  16. T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 1082–1084 (1991).
    [CrossRef]
  17. B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equation with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488(2000).
    [CrossRef]

2010

2008

Z. Lalidastjerdi, F. Kroushavi, and M. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” Opt. Laser Technol. 40, 1041–1046 (2008).
[CrossRef]

2006

2004

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

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

X. Liu, J. Chen, C. Lu, and X. Zhou, “Optimizing gain profile and noise performance for distributed fiber Raman amplifiers,” Opt. Express 12, 6053–6066 (2004).
[CrossRef] [PubMed]

X. Liu, “Optimization for various schemes of distributed fibre Raman amplifiers,” J. Opt. A 6, 1017–1026 (2004).
[CrossRef]

2003

2002

M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
[CrossRef]

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. 13, 945–947(2001).
[CrossRef]

2000

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equation with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488(2000).
[CrossRef]

1991

T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 1082–1084 (1991).
[CrossRef]

1985

M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEE Proc. J. 132, 58–63(1985).
[CrossRef]

Adams, M. J.

M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEE Proc. J. 132, 58–63(1985).
[CrossRef]

Agarwal, G. P.

C. Headly and G. P. Agarwal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).

Bromage, J.

Chen, J.

Chen, Z.

Q. Han, J. Ning, H. Zhang, and Z. Chen, “Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers,” J. Lightwave Technol. 24, 1946–1952 (2006).
[CrossRef]

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

Cheng, T. H.

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. 13, 945–947(2001).
[CrossRef]

Collins, J. V.

M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEE Proc. J. 132, 58–63(1985).
[CrossRef]

Han, Q.

Q. Han, J. Ning, H. Zhang, and Z. Chen, “Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers,” J. Lightwave Technol. 24, 1946–1952 (2006).
[CrossRef]

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

Headly, C.

C. Headly and G. P. Agarwal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).

Henning, I. D.

M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEE Proc. J. 132, 58–63(1985).
[CrossRef]

Hodgkinson, T. G.

T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 1082–1084 (1991).
[CrossRef]

Islam, M. N.

M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
[CrossRef]

Jiang, H.

Kroushavi, F.

Z. Lalidastjerdi, F. Kroushavi, and M. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” Opt. Laser Technol. 40, 1041–1046 (2008).
[CrossRef]

Lalidastjerdi, Z.

Z. Lalidastjerdi, F. Kroushavi, and M. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” Opt. Laser Technol. 40, 1041–1046 (2008).
[CrossRef]

Lee, B.

Lee, W. J.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equation with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488(2000).
[CrossRef]

Li, J.

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

Li, X.

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

Liu, X.

Lu, C.

X. Liu, J. Chen, C. Lu, and X. Zhou, “Optimizing gain profile and noise performance for distributed fiber Raman amplifiers,” Opt. Express 12, 6053–6066 (2004).
[CrossRef] [PubMed]

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. 13, 945–947(2001).
[CrossRef]

Min, B.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equation with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488(2000).
[CrossRef]

Ning, J.

Q. Han, J. Ning, H. Zhang, and Z. Chen, “Novel shooting algorithm for highly efficient analysis of fiber Raman amplifiers,” J. Lightwave Technol. 24, 1946–1952 (2006).
[CrossRef]

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

Park, N.

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equation with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488(2000).
[CrossRef]

Rahmani, M.

Z. Lalidastjerdi, F. Kroushavi, and M. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” Opt. Laser Technol. 40, 1041–1046 (2008).
[CrossRef]

Roberts, S. M.

S. M. Roberts and J. S. Shipman, Two-point Boundary Value Problems: Shooting Methods (American Elsevier, 1972), Chap. 6, pp. 111–114.

Shipman, J. S.

S. M. Roberts and J. S. Shipman, Two-point Boundary Value Problems: Shooting Methods (American Elsevier, 1972), Chap. 6, pp. 111–114.

Shum, P.

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. 13, 945–947(2001).
[CrossRef]

Wang, Y.

Xie, K.

Zhang, H.

Zhou, X.

X. Liu, J. Chen, C. Lu, and X. Zhou, “Optimizing gain profile and noise performance for distributed fiber Raman amplifiers,” Opt. Express 12, 6053–6066 (2004).
[CrossRef] [PubMed]

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. 13, 945–947(2001).
[CrossRef]

Chin. Phys. Lett.

J. Ning, Q. Han, Z. Chen, J. Li, and X. Li, “A powerful simple shooting method for designing multi-pumped fibre Raman amplifiers,” Chin. Phys. Lett. 21, 2184–2187 (2004).
[CrossRef]

IEE Proc. J.

M. J. Adams, J. V. Collins, and I. D. Henning, “Analysis of semiconductor laser optical amplifiers,” IEE Proc. J. 132, 58–63(1985).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Top. Quantum Electron. 8, 548–559 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

T. G. Hodgkinson, “Average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 3, 1082–1084 (1991).
[CrossRef]

B. Min, W. J. Lee, and N. Park, “Efficient formulation of Raman amplifier propagation equation with average power analysis,” IEEE Photon. Technol. Lett. 12, 1486–1488(2000).
[CrossRef]

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. 13, 945–947(2001).
[CrossRef]

J. Lightwave Technol.

J. Opt. A

X. Liu, “Optimization for various schemes of distributed fibre Raman amplifiers,” J. Opt. A 6, 1017–1026 (2004).
[CrossRef]

Opt. Commun.

H. Jiang, K. Xie, and Y. Wang, “Shooting algorithm and particle swarm optimization based Raman fiber amplifiers gain spectra design,” Opt. Commun. 283, 3348–3352 (2010).
[CrossRef]

Opt. Express

Opt. Laser Technol.

Z. Lalidastjerdi, F. Kroushavi, and M. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” Opt. Laser Technol. 40, 1041–1046 (2008).
[CrossRef]

Other

C. Headly and G. P. Agarwal, Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).

S. M. Roberts and J. S. Shipman, Two-point Boundary Value Problems: Shooting Methods (American Elsevier, 1972), Chap. 6, pp. 111–114.

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Figures (4)

Fig. 1
Fig. 1

Raman gain coefficient (measured at 1 μm pump wavelength) and (inset) loss spectrum of a single-mode fiber.

Fig. 2
Fig. 2

Evolutions of the second pump power for different initial guesses and final solution in simulation of the four-pump RFA in Case II of Table 3.

Fig. 3
Fig. 3

Evolutions of the fourth pump power for different initial guesses and final solution in simulation of the four-pump RFA in Case II of Table 3.

Fig. 4
Fig. 4

Comparison of gain profiles of a four- pump RFA generated by four different numerical methods for Case I of Table 4.

Tables (5)

Tables Icon

Table 1 Parameters Used in Simulations of Four-Pump RFAs

Tables Icon

Table 2 Simulation Results of Four-Pump RFAs with One Forward Pump and Three Backward Pumps

Tables Icon

Table 3 Simulation Results of Four-Pump RFAs with Two Forward and Two Backward Pumps

Tables Icon

Table 4 Simulation Results of Four-Pump RFAs with Three Forward Pumps and One Backward Pump

Tables Icon

Table 5 Calculation Time of Different Methods in Case I of Table 4

Equations (5)

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

± d P i d z = j = 1 , j i n 1 + n 2 + m g ( v j , v i ) P j P i α i P i , ( i = 1 , 2 , , n 1 + n 2 + m ) ,
P I = ( P I 1 , P I 2 , , P I n 1 ) = S · P I t = ( P I 1 t / S 1 , P I 2 t / S 2 , , P I n 1 t / S n 1 )
P I ( k ) = P I ( k 1 ) + α Δ P I ,
Δ P I = J 1 · D ,
J = [ J 11 J 12 J 1 n 1 J 21 J 22 J 2 n 1 J n 1 1 J n 1 2 J n 1 n 1 ] ,

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