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Efficient algorithm and optimization for broadband Raman amplifiers

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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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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)

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

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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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