Abstract

A mid-point shooting algorithm using the Newton–Raphson method is adopted for solving nonlinear coupled equations describing bidirectionally pumped broadband Raman amplifiers. A series of novel backward-differentiation methods are constructed for the first time to our knowledge. Their combination can form a powerful solution for fiber amplifiers. Numerical results show that the approach can solve Raman amplifier propagation equations on various conditions including co-, counter-, and bidirectionally pumped cases. The computation speed of the present methods is about four times that of the backward-differentiation methods previously adopted.

© 2004 Optical Society of America

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References

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ECOC???2001 (1)

Y. Chen et al., �??Bi-directionally pumped broadband Raman Amplifier,�?? ECOC�??2001, Tu.L.3.4.

Electron. Lett. (1)

Y. Zhu et al., �??Experimental comparison of all-Raman and Raman/EDFA hybrid amplifications using 40 Gbit/s-based transmissions over 400 km TW-RS fibre,�?? Electron. Lett. 38, 893�??895 (2002).
[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]

IEEE Photon. Technol. Lett. (3)

X. M. Liu, H. Y. Zhang, and Y. L. Guo, �??A novel method for Raman amplifier propagation equations,�?? IEEE Photon. Technol. Lett. 15, 392�??394 (2003).
[CrossRef]

X. M. Liu, �??Corrections to: a novel method for Raman amplifier propagation equations,�?? IEEE Photon. Technol. Lett. 15, 1321�??1321 (2003).
[CrossRef]

A. Pizzinat, M. Santagiustina, and C. Schivo, �??Impact of hybrid EDFA-distributed Raman amplification on a 4 x 40-Gb/s WDM optical communication system,�?? IEEE Photon. Technol. Lett. 15, 341�??343 (2003).
[CrossRef]

J. Lightwave Technol. (3)

OFC 2000 (1)

C. R. S. Fludger and V. Handerek, �??Fundamental noise limits in broadband Raman amplifiers,�?? in Optical Fiber Communication Conference (OFC 2000), Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D. C., 2000), paper MA-5

Opt. Commun. (3)

H. H. Lee et al., �??A gain-clamped-semiconductor-optical-amplifier combined with a distributed Raman-fiber-amplifier: a good candidate as an inline amplifier for WDM networks,�?? Opt. Commun. 229, 249�??252 (2004).
[CrossRef]

X. M. Liu and Y. H. Li, �??Optimizing the bandwidth and noise performance of distributed multi-pump Raman amplifiers,�?? Opt. Commun. 230, 425�??431 (2004)
[CrossRef]

Z. Tong, H. Wei, and S. S. Jian, �??Theoretical investigation and optimization of bi-directionally pumped broadband fiber Raman amplifiers,�?? Opt. Commun. 217, 401�??413 (2003).
[CrossRef]

Opt. Express (4)

Other (2)

<a href= "http://www.nr.com.">http://www.nr.com</a>

H. B. Keller, Numerical Methods for Two-Point Boundary-Value Problems (Blaisdell, Waltham, Mass., 1968) pp. 192.

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Figures (1)

Fig. 1.
Fig. 1.

Power evolution of pumps and signals along the fiber position, where for (a) 1st iteration (i.e., estimated values), (b) 2nd iteration, (c) 3rd iteration, and (d) 4th iteration.

Tables (1)

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Table 1. Coefficients of Eq. (3) up to order 6

Equations (11)

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d P v ± dz = α v P v ± ± η v P v ± P v ± μ > v g μ v Γ A eff [ P μ + + P μ ]
± h v i μ > v g μ v A eff [ P μ + + P μ ] [ 1 + ( e h ( μ v ) KT 1 ) 1 ] Δ v
P v ± μ > v v μ g μ v Γ A eff [ P μ + + P μ ] 2 h v i P v ± μ > v v μ g μ v A eff [ 1 + ( e h ( v μ ) KT 1 ) 1 ] Δ v ,
d P i ( z ) dz = P i ( z ) f i ( z , P 1 , P 2 , P N ) , ( i = 1 , 2 , , N ) .
B 1 j ( z 1 , P 1 , P 2 , P N ) = 0 , ( j = 1 , 2 , , n 1 ) ,
B 2 k ( z 2 , P 1 , P 2 , P N ) = 0 , ( k = 1 , 2 , , n 2 ) .
ln ( P t ) = j = 1 k α j ln ( P t j ) + Δ z β f ( z t , P t ) ,
P t = ( j = 1 k P t j α j ) · exp ( Δ z β f ( z t , P t ) ) .
g ( P t ) = P t ( j = 1 k P t j α j ) · exp ( Δ z β f ( z t , P t ) ) = 0 .
P t n + 1 = P t n ( I A · Δ z β · f P t n ) 1 ( P t n A )
A = ( j = 1 k P t j α j ) · exp ( Δ z β f ( z t , P t n ) ) ,

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