IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 15, AUGUST 1, 2012

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Gain Ripple Decrement of S-Band Raman Amplifiers Farzin Emami and Majid Akhlaghi, Member, IEEE

Abstract— Using the fuzzy adaptive modified particle swarm optimization method, an optimized gain ripple for S-band Raman fiber amplifiers is found. In this simulation, a special fiber with minimum loss at the water peak is used. Index Terms— Fuzzy adaptive modified particle swarm optimization (FAMPSO), gain, Raman fiber amplifier.

I. I NTRODUCTION

R

AMAN amplification has been a powerful amplification mechanism in optical fibers during the last decade [1]. In long-haul optical communication systems, these structures can be used to send the optical signals which are attenuated by fiber losses. In the minimum loss region of optical fibers, data transmission can be done in three different frequency bands; C-, L- and S-bands. Some of the optical amplifiers such as erbium doped fiber amplifiers (EDFAs) are utilized for C- and L-bands [1]. In these bands, there are many reports for optimized EDFAs in the literature [2], [3]. In the S-band region the Raman amplifiers (RAs) are the best optical amplifiers which can be operated in low loss operation and hence they can be used as wide-band amplifiers [1]. There are two types of optimization reported in the literature to optimize the Raman gain. In the first approach, the gain is optimized in some new structures such as photonic crystals (PCs) which have a flat Raman gain inherently excite by just one pump. In the second approach, optimization for silica fiber by multiple pumps is considered. In the first method, a PC fiber is used and a single pump is derived with minimized gain ripple for some interval of the operating wavelengths [4]. The use of various methods such as particle swarm optimization (PSO) algorithm with shooting method [5], modified PSO (MPSO), Lagrangian multiplier method, artificial fish school algorithm, variational method and traditional genetic algorithm, it is possible to optimize multiple pump Raman gain ripples. In the reported work, gain optimization is performed in C and L-bands. In this letter, a more powerful algorithm the fuzzy adaptive modified particle swarm optimization (FAMPSO) is applied to find the pump powers and the pump wavelengths with a minimum gain ripple in the S-band. Manuscript received May 6, 2012; revised June 1, 2012; accepted June 2, 2012. Date of publication June 8, 2012; date of current version July 10, 2012. This work was supported in part by the Optoelectronic Research Center, Electronic Department, Shiraz University of Technology, Shiraz, Iran. The authors are with the Opto-Electronic Research Center, Electronic Department, Shiraz University of Technology, Shiraz 7183754435, Iran (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2012.2203591

II. T HEORY AND O PERATION A. Theory Generally the following equations can be applied to the pump and signal powers along the direction of propagation z [5]:  gμv   d Pv± = ∓αν Pv± + Pv± Pμ+ + Pμ− dz A μ μ>ν  v gμv   −Pv± Pμ+ + Pμ− . (1) μ A μ μ<ν Where P is the optical signal power, ± represents the forward or backward signal, ν and μ are the optical signal frequencies, αν is the attenuation factor, A is the effective cross section of the optical signal and g is the Raman gain. In a wide-band RA, the gain widths and the peak gain ripple are two parameters that must be chosen accurately. Hence, there have been efforts in the literature to find an optimized Raman gain structure. Genetic algorithm (GA) is a very popular method for the gain flatness. If a standard single mode fiber in the simulations for S-band region is used, the achieved pump wavelengths are laid around the water-peak region of the loss curve and hence the pump powers will be increased [6]. Therefore to have the smaller loss, a True Wave Reach Low Water Peak Fiber is used. B. Particle Swarm Optimization (PSO) Classical PSO: This algorithm is an optimization procedure inspired by a colony such as birds which can improve its behaviors. Any element of this colony called a particle move in an n-dimensional space and correct its trajectory based on the previous actions of itself and of the neighboring particles [7]. For each particle, the velocity and displacement were updated based on the following relations:     (2) v ik+1 = w v ik + c1r1 pik − x ik + c2 r2 pgk − x ik x ik+1 = x ik + v ik+1 , i = 1, . . . , n.

(3)

Where k is the current iteration number, n is the particles number, w is the inertia weight, c1 and c2 are acceleration parameters and finally r1 and r2 are random parameters between 0 and 1. The best position for the i-th particle so far stored is represented as: Pki = [ p1k , pik , . . . , pnk ]T Pik

(4)

(p_best) are evaluated by using fitness function. All the The best particle among all p_best is represented as pgk

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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 15, AUGUST 1, 2012

(Gbest_best_value). Which for minimization problems pgk is the smallest member of the Pik vector and for maximization problems it is the largest member of Pik . Modified PSO (MPSO): To increase the population diversity and PSO performance, mutation is applied to the classical PSO [8]. Application of the mutation in PSO algorithm generates a new population and prevents early convergence to a local optimum point. This new population is found from random selection of three non-equal initial populations, X z1 , X z2 , X z3 , with the following definition [9]:

Fig. 1.

Xmut = Xz1 + β ∗ (Xz2 − Xz3 ) .

TABLE I F UZZY RULES OF THE I NPUT AND O UTPUT VARIABLES [9]

Usual crossover is selected as 0.1
−1 G_best_value n . (7) c1,2 = 1 + 1 + exp − G0 We chose n = 2 and G 0 as the G_best_value in the first iteration. D. Fuzzy Formulation for Tuning of the Weighing Factor w The parameter w determines the effect of former velocity on the new one. The proper selection of this parameter generates a balance between the local and global searches. It is usually considered to be a constant or with linear variations. With these values one generally cannot find the global optimum. Therefore the best selection to tune w is based on the G_best_value calculations using fuzzy logic. In the fuzzy method the inputs are NFV and w, whereas the output is w. In this method, NFV is defined as [10]: (8)

Where FV is the best response at each step, FV min is the FV at the first iteration and F Vmax is a very large number greater than any acceptable feasible solution [10]. Since 0.4
w

w

(5)

Where β ∗ is the mutation constant with the value of 0.93< β ∗ <1. Using this idea, the previous vector can be mutated and the following new vector is generated:  Xmut,i , i f (r and < cr ossover) Xnew,i = i = 1, 2, . . . , n Xi , Other wi se (6)

(F V − F Vmin ) . N FV = (F Vmax − F Vmin )

Membership functions.

NFV

S M L

S

M

L

ZE PE PE

NE ZE ZE

NE NE NE

the positive and negative corrections should be used. Therefore, the variations between −0.1 to 0.1 is selected here. The output variable of this system is a correction for the weighing factor in the form of [10]: wk+1 = wk + w.

(9)

The membership functions for input and output are displayed in Fig. 1. [10]. For simplicity, triangular membership functions were chosen. Each input variable can be medium (M), small (S) or large (L), whereas the output variable may become positive (PE), negative (NE) or zero (ZE). The fuzzy rules are shown in Table I suggested by [10]. There are nine rules to correct the weighing factor and each of them describes a plan from the input to the output space. As an example, if the weighing factor w for an identifying variable is medium (M) with small (S) NFV, w will be negative. All the fuzzy rules are driven in the same way. III. N UMERICAL R ESULTS The PSO and FAMPSO methods are applied and a broadband gain- flattened Raman amplifier with 8 backward pumps is designed in the S-band with a bandwidth of 80-nm. The wavelengths of signal range from 1460nm to 1530nm in 5nm steps are selected. The power of each signal is 10mW and the fiber length is 100 km. To find the pump powers, we used the shooting method proposed in [11]. Indeed, the pump-topump and pump-to-signal interactions were included for an eight-pump backward structure and the related equations were solved by Runge-Kutta method. Our goal is to minimize the gain ripple by optimizing sixteen parameters; eight pump powers and eight pump wavelengths with the following criteria: P1 − P8 ∈ (0 − 70mW ) & λ1 −λ8 ∈ (1360 − 1450nm) . (10) Such minimization must be done around a predefined average gain g0 . In other words, our procedure should be minimized by the following function: Max {Abs [gai n (λs1 ) − g0 , gai n(λs2 ) −g0 , . . . , gai n(λs16) − g0 ]} .

(11)

EMAMI AND AKHLAGHI: GAIN RIPPLE DECREMENT OF S-BAND RAs

4.5

Gain around 4dB

10

Gain ripple ~ 0.41

9

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TABLE II O PTIMIZATION R ESULTS FOR E IGHT-P UMPS F IBER RA

Gain around 9dB

4

8 3.5 1460

1480

1500

1520

Gain ripple ~ 1.27

7 1460

1480

Wavelength (nm) Fig. 2.

1500

FAMPSO Gain around 9(dB)

Gain ripple ∼ 0.32

1520

Gain ripple ∼ 0.136

10

Gain around 4dB

Gain around 9dB

9.5

4.1

1.5

9

4

8.5

3.9 1460

Gain ripple ~ 0.136 1480

1500

1520

(a)

8 1460

1480

1500

1520

0.5

Wavelength (nm)

Gain ripple (dB)

0.14

5

10

15

20

0.13 0

5

10

15

20

Fig. 5. Gain ripples versus the number of the independent algorithm running in (a) PSO method and (b) FAMPSO method. PSO FAMPSO

algorithms running. As it is seen, our method is more reliable than the classical PSO.

2

0 0

(b)

Optimization around 4(dB)

4

1

Optimization around 4dB

0.15

Gain optimization by using the FAMPSO method.

3

0.16

1

Gain ripple ~ 0.32

0

Fig. 3.

Pp: 39.9 19.6 32.1 21.3 19.6 12 19.8 18.8 λp: 1359.1 1422.8 1371.7 1427.7 1425.7 1434.6 1386.9 1399.9

FAMPSO Gain about 4(dB)

Gain optimization by using the classical PSO method.

4.2

Pp: 40.7 67.3 2.3 60.7 34.7 55.1 57.8 0 λp: 1438.7 1422.8 1368.9 1441.2 1421.7 1396.6 1381

Optimization around 4dB

IV. C ONCLUSION 100 200 Number of iteration

300

Fig. 4. Gain ripples versus the number of iteration for the standard PSO and the proposed FAMPSO.

Applying the classical PSO algorithm to optimize the onoff gain ripple of a Raman amplifier will lead to the results plotted in Fig. 2. An important advantage of this method in comparison with the proposed genetic algorithm [12] that exists here is possible to optimize the high value of the Raman gain ripples. Our efficient FAMPSO algorithm is proposed to optimize and design the flattened Raman gain in the S-band region. In our simulations, the number of particles is considered to be three times of the optimization parameters (3 × 16 parameters). The Increase of the number of particles can improve the convergence speed initially, whereas it will be reduced the accuracy and convergence speed for more iterations. As shown in Fig. 3, FAMPSO is much more powerful than PSO algorithm (note that PSO algorithm is usually trapped in some local minimum). In Table II, the optimization results for the eight-pump fiber Raman amplifier are shown. Based on the results of this table, we could optimize the gain ripple using the maximum pump powers of less than 70 mW. The convergence characteristic of the proposed method is compared with that of PSO and the results are shown in Fig. 4. As shown in Fig. 4, FAMPSO algorithm is performing better than PSO in term of accuracy and convergence speed. As a final result, Fig. 5 shows the distribution of the minimum gain ripples obtained by PSO and FAMPSO for 23 independent

An optimized algorithm based on PSO optimization method was proposed to find a minimum ripple for on-off Raman S-band gain. To find the global answer instead of the local minima to in which the classical optimization methods usually converge, we utilized a combinational algorithm called FAMPSO for optimizing the Raman gain ripple and found the proper pump powers and operating wavelengths. The proposed method was applied by a backward eight-pump Raman amplifier in a True Wave Reach Low Water Peak fiber. This fiber has a lower loss around the water peak which is compared by a standard fiber. It was found that the proposed algorithm can give fewer ripples for Raman gain and hence uniform gain in the related bandwidth with less iterations and higher accuracy. This method can be used in L- and C-bands. R EFERENCES [1] M. N. Islam, “Raman amplifiers for telecommunications,” IEEE J. Sel. Topics Quantum Electron., vol. 8, no. 3, pp. 548–559, May/Jun. 2002. [2] A. Mowla and N. Granpayeh, “A novel design approach for erbiumdoped fiber amplifiers by particle swarm optimization,” Progress Electromagn. Res., vol. 3, pp. 103–118, 2008. [3] L. Mescia, A. Giaquinto, G. Fornarelli, G. Acciani, M. De Sario, and F. Prudenzano, “Particle swarm optimization for the design and characterization of silica-based photonic crystal fiber amplifiers,” J. NonCryst. Solids, vol. 357, nos. 8–9, pp. 1851–1855, 2011. [4] H. Jiang, K. Xie, and Y. Wang, “Photonic crystal fiber for use in fiber Raman amplifiers,” Electron. Lett., vol. 44, no. 13, pp. 796–798, 2008. [5] H. M. Jiang, K. Xie, and Y. F. Wang, “Flat gain spectrum design of Raman fiber amplifiers based on particle swarm optimization and average power analysis technique,” Opt. Lasers Eng., vol. 50, no. 2, pp. 226–230, 2012. [6] J. Fiuza, F. Mizutani, and M. A. G. Martinez, “Analysis of distributed Raman amplification in the S-band over a 100 km fiber span,” J. Microw. Optoelect., vol. 6, pp. 323–334, Jun. 2007.

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IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 15, AUGUST 1, 2012

[10] P. Bajpai and S. N. Singh, “Fuzzy adaptive particle swarm optimization for biddinrg strategy in uniform price spot market,” IEEE Trans. Power Syst., vol. 22, no. 4, pp. 2152–2160, Nov. 2007. [11] Z. L. Dashtestani, F. Korushavi, and M. H. Rahmani, “An efficient shooting method for fiber amplifiers and lasers,” J. Opt. Laser Technol., vol. 40, no. 8, pp. 1041–1046, 2008. [12] G. C. M. Ferreira, S. P. N. Cani, M. J. Pontes, and M. E. V. Segatto, “Optimization of distributed Raman amplifiers using a hybrid genetic algorithm with geometric compensation technique,” IEEE Photon. J., vol. 3, no. 3, pp. 390–399, Jun. 2011.