Abstract

A hybrid genetic algorithm (HGA) assisted by stochastic perturbation and the adaptive technique is proposed. Compared with our previous reports, the proposed HGA can exploit better solutions and greatly shorten the amount of run time. An example shows that the design of multipump Raman amplifiers involves the multimodal function optimization problem with multiple variables. With the new HGA, relationships of the optimal signal bandwidth with the span length and the ON-OFF Raman gain are obtained. A movie demonstrates the detailed interaction in pump-to-signal and signal-to-signal procedures. The corresponding optical signal-to-noise ratio of optimal results is obtained.

© 2004 Optical Society of America

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References

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IEEE Photon. Technol. Lett. (7)

S. Faralli and E. Di Pasquale, �??Impact of double Rayleigh scattering noise in distributed higher order Raman pumping schemes,�?? IEEE Photon. Technol. Lett. 15, 804-806 (2003).
[CrossRef]

P. B. Hansen L. Eskilden, A. J. Stentz, T. A. Strasser, J. Judkins, J. J. DeMarco, R. Pedrazzani, and D. J. DiBiovanni, �??Rayleigh scattering limitations in distributed Raman pre-amplifiers,�?? IEEE Photon. Technol. Lett. 10, 159-161 (1998).
[CrossRef]

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. 15, 206-208 (2003).
[CrossRef]

M. Yan et al., �??Automatic design scheme for optical-fiber Raman amplifiers backward-pumped with multiple laser diode pumps,�?? IEEE Photon. Technol. Lett. 13, 948�??950 (2001).
[CrossRef]

X. Zhou, C. Lu, P. Shum, and T. H. Cheng, �??A simplified model and optimal design of a multiwavelength backward-pumped Raman amplifier,�?? IEEE Photon. Technol. Lett. 13, 945�??947 (2001).
[CrossRef]

X. M. Liu and B. Lee, �??Optimal design of fiber Raman amplifier based on hybrid genetic algorithm,�?? IEEE Photon. Technol. Lett. 16, (to be published).

H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, and E. Rabarijaona, �??Pump interactions in a 100-nm bandwidth Raman amplifier,�?? IEEE Photon. Technol. Lett. 11, 530-532 (1999).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Commun. (2)

Y. Hadjar et al., �??Enhanced double Rayleigh backscattering in second order Raman amplification and system performance implications,�?? Opt. Commun. 229, 419-423 (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]

Opt. Express (6)

X. M. Liu, �??Powerful solution for simulating nonlinear coupled equations describing bidirectionally pumped broadband Raman amplifiers,�?? Opt. Express. (this issue).

X. M. Liu and B. Lee, �??A fast and stable method for Raman amplifier propagation equations,�?? Opt. Express 11, 2163�??2176 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2163">.http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2163</a>
[CrossRef] [PubMed]

X. Liu and Y. Li, �??Optimal design of DFG-based wavelength conversion based on hybrid genetic algorithm,�?? Opt. Express 11, 1677-1688 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1677">.http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-14-1677</a>
[CrossRef] [PubMed]

X. M. Liu and B. Lee, �??Effective shooting algorithm and its application to fiber amplifiers,�?? Opt. Express 11, 1452-1461 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1452">.http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-12-1452</a>
[CrossRef] [PubMed]

M. Tang, P. Shum, and Y. D. Gong, �??Design of double-pass discrete Raman amplifier and the impairments induced by Rayleigh backscattering,�?? Opt. Express 11, 1887-1893 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-16-1887">.http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-16-1887</a>
[CrossRef] [PubMed]

A. A. B. Tio, P. Shum, and Y. D. Gong, �??Wide bandwidth flat gain Raman amplifier by using polarization-independent interferometric filter,�?? Opt. Express 11, 2991-2996 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-2991">.http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-2991</a>
[CrossRef] [PubMed]

Other (2)

S. W. Mahfoud, �??Niching methods for genetic algorithms,�?? Ph.D. dissertation (University of Illinois, Urbana, Ill., 1995).

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

Supplementary Material (1)

» Media 1: AVI (1745 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Contour of optimal signal bandwidth Δλ with pump wavelengths λ 2 and λ 3 in the four-pump Raman amplifier, where wavelengths of two other pumps are specified as λ 1=1434.72 and λ 4=1497.75 nm. (b) Magnification of the white dash frame in (a). The color scale in the inset of Fig. 1 illustrates the distribution of Δλ. n j (j=1, 2, …, 7) denote the center of seven clusters for simulating Fig. 3. D is the normalized niche radius. The global maximum Δλ=82.5 nm.

Fig. 2.
Fig. 2.

Distribution of wavelength λ and power P of four pumps, where the y coordinate represents pump power and abscissa denotes the pump wavelength.

Fig. 3.
Fig. 3.

Signal spectra of centers of seven clusters based on the proposed HGA.

Fig. 4.
Fig. 4.

Relationship of optimal signal bandwidth Δλ versus span length L. Circles are the optimized global maxima based on the new HGA, and the red solid curve is their fitted line.

Fig. 5.
Fig. 5.

Relationship of optimal signal bandwidth Δλ versus ON-OFF Raman gain G ON-OFF. Circles are the optimized global maxima based on the new HGA, and the red solid curve is their fitted line.

Fig. 6.
Fig. 6.

(1745 KB) Movie showing the procedure of all channels transmitting along the fiber.

Fig. 7.
Fig. 7.

Corresponding OSNR of L=40 and 50 km in Fig. 4 versus wavelength.

Tables (2)

Tables Icon

Table 1. Power, wavelength, and bandwidth of the optimal results in Fig. 3.

Tables Icon

Table 2. Power, wavelength and bandwidth of the optimal results at L=80 km in Fig. 4.

Equations (5)

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± d P k dz = [ α k + j = 1 k 1 g R ( v j v k ) Γ A eff P j j = k + 1 n + m v k v j g R ( v k v j ) Γ A eff P j ] P k , ( k = 1 , 2 , , n + m ) .
± d P ASE , k ± dz = α k P ASE , k ± + γ k P ASE , k
+ P ASE , k ± j = 1 k 1 g R ( v j v k ) Γ A eff P j ± [ 1 + 2 h v k P ASE , k ± ( 1 + ( e h ( v j v k ) k B T 1 ) 1 ) Δ v ] ,
P ASE , k ± j = k + 1 n + m v k v j g R ( v k v j ) Γ A eff [ P j ± + 4 h v k ( 1 + ( e h ( v k v j ) k B T 1 ) 1 ) Δ v ]
d ij = k = 1 4 ( λ k ( i ) λ k ( j ) λ fa ) 2 .

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