Optimization of pump parameters for gain flattened Raman fiber amplifiers based on artificial fish school algorithm

Optics Communications 284 (2011) 5480–5483

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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m

Optimization of pump parameters for gain flattened Raman fiber amplifiers based on artificial fish school algorithm Hai Ming Jiang a,⁎, Kang Xie a, Ya Fei Wang b a b

School of Instrument Science and Opto-Electronic Engineering, Hefei University of Technology, No. 193 Tunxi Road, Hefei 230009, PR China School of Opto-Electronic Information, University of Electronic Science and Technology of China, No. 4 Section 2, North Jianshe Road, Chengdu 610054, PR China

a r t i c l e

i n f o

Article history: Received 21 March 2011 Received in revised form 29 July 2011 Accepted 30 July 2011 Available online 16 August 2011 Keywords: Raman fiber amplifiers Artificial fish school algorithm Gain spectrum Pump parameters

a b s t r a c t In this work, a novel metaheuristic named artificial fish school algorithm is introduced into the optimization of pump parameters for the design of gain flattened Raman fiber amplifiers for the first time. Artificial fish school algorithm emulates three simple social behaviors of a fish in a school, namely, preying, swarming and following, to optimize a target function. In this algorithm the pump wavelengths and power levels are mapped respectively to the state of a fish in a school, and the gain of a Raman fiber amplifier is mapped to the concentration of a food source for the fish school to search. Application of this algorithm to the design of a Cband gain flattened Raman fiber amplifier leads to an optimized amplifier that produces a flat gain spectrum with 0.63 dB in band ripple for given conditions. This result demonstrates that the artificial fish school algorithm is efficient for the optimization of pump parameters of gain flattened Raman fiber amplifiers. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Raman fiber amplifiers (RFAs) have been attracting much attention in the fields of WDM and long-haul optical fiber communication due to their inherent advantages [1–4]. A flat gain spectrum in the operation band is usually required for the RFAs used in these applications. There are two approaches to achieve this purpose in general. One is to use a fiber of inherently flat Raman gain efficiency as the gain media of the RFA [5–7]. The other is by simultaneously pumping a conventional silica-based fiber at appropriate wavelengths using multiple pumps of appropriate power levels [8–16]. In some applications, for example when upgrading the transmission bandwidth of an existing fiber link, the latter approach achieves flattening of gain spectrum by adding one or more pumps, therefore it enables one to maintain an old system with minimum cost and disturbance. It is more convenient and economical and in fact the only choice in such circumstance. In this situation, determining the set of appropriate power levels and wavelengths for the multiple pumps is a challenging work because of the complex and nonlinear nature of Raman amplification system. Several optimization algorithms have been developed to solve this problem so far [10–15]. In [16] a novel method was proposed by us for the design of gain-flattened Raman fiber amplifiers. In this method the solving of nonlinear Raman coupled equations and the search for

⁎ Corresponding author. Tel.: + 86 551 2901511; fax: + 86 551 2901508. E-mail address: [email protected] (H.M. Jiang). 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.07.074

appropriate wavelengths and power levels of the multiple pumps are respectively dealt with by the modified shooting algorithm and the improved particle swarm optimization (PSO). In the current work, a novel metaheuristic called artificial fish school algorithm (AFSA) is introduced into this research area by us for the first time. This algorithm is then developed to suit the design of gain flattened Raman fiber amplifiers, and is found very efficient and reliable in optimizing the pump parameters over a broad bandwidth. In the mean time the numerical solution of the nonlinear Raman coupled equations is dealt with by applying the average power analysis technique [17,18] to the system. The calculation efficiency of this technique is much higher than that of the direct integration method used in [15,16,19]. By incorporating the artificial fish school algorithm and the average power analysis technique into the design of gain-flattened Raman fiber amplifiers, the determination of appropriate wavelengths and power levels for the multiple pumps is accomplished automatically and efficiently for given conditions. And this enables the currently proposed design algorithm to be improved from that of [16] in calculation efficiency significantly. This method provides a new alternative for the optimization of pump parameters for gain flattened Raman fiber amplifiers. 2. Raman amplifier model The model of an RFA includes interactions between pumps and signals, between pumps, and between signals at different frequencies. It should also include Rayleigh scattering, amplified spontaneous emissions (ASE), and temperature dependencies. Here only the first three mechanisms are considered because the others have no big impact on the gain spectrum of an RFA [20]. In a steady state, the

H.M. Jiang et al. / Optics Communications 284 (2011) 5480–5483

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behaviors of Raman fiber amplifiers are governed by the following coupled set of equations [15,16]:

(6) the food concentration in this work is denoted by ρ = 1/Gripple, where Gripple is defined by Eqs. (2)–(4)


 gR vi −vj dPj ðzÞ =−αj Pj ðzÞ+ ∑
Pi ðzÞPj ðzÞ dz vi > vj Keff Aeff
 vj gR vj −vk Pj ðzÞPk ðzÞ; j = 1; 2⋯n − ∑ Keff Aeff vj > v k vk

ΔGmax = Gmax −Gt

ð2Þ

ΔGmin = Gmin −Gt

ð3Þ

ð1Þ

where Pj,Pi and Pk are the power levels of the jth, ith and kth optical channels respectively, and n is the total number of optical channels including pump and signal waves, “+” and “−” is respectively designated to the forwards and backwards traveling waves along the fiber, gR is the Raman gain coefficient of the fiber, νj, νi and νk are the frequencies of the optical signals in the jth, ith and kth channels respectively, αj is the absorption coefficient accounting for fiber loss at the frequency νj, Keff ≈ 2 is the polarization factor, Aeff is the effective overlap core area between waves of different optical channels. Without loss of generality, the channels are so numbered that the frequency is ascending from the nth channel to the first channel. Eq. (1) indicates that when light wave of frequency νj propagates along the fiber with waves of other frequencies, due to the stimulated Raman scattering, it receives power from light waves of frequency larger than νj, in the meantime it losses power to light waves of frequency smaller than νj. In general, Eq. (1) is dealt with numerically. The usual shooting algorithms [15,16,19] based on direct integration and the average power analysis technique [17,18] based on simple algebraic calculation can both be used to solve Eq. (1). In this work the average power analysis is adopted because it is more efficient than the method of direct integration. 3. Artificial fish school algorithm and its application to the optimization of pump parameters In a water area, fishes are most likely distributed around the region where foods are most abundant. A fish school completes its food foraging process by each fish functioning several simple social behaviors. From investigation, it is found that the three most common behaviors fishes will exercise in a school are (1) preying, i.e., fishes tend to head towards food; (2) swarming, gregarious fishes tend to concentrate towards each other while avoiding overcrowding; (3) following, the behavior of chasing the nearest buddy. The artificial fish school algorithm (AFSA) [21] emulates the above three basic social behaviors of a real fish. It is a novel metaheuristics based on the social habits and customs of fish to achieve optimization. AFSA has many advantages, including good global convergence, strong robustness, insensitivity to initial values, simplicity in implementation and so on. Since proposed AFSA has been widely used in many different applications such as neural network classifiers [22], signal processing [23], network combinatorial optimization [24], complex function optimization [25], multiuser detection in communication [26], etc. In this work the idea of AFSA is borrowed to construct an optimization scheme for the design of gain flattened Raman fiber amplifiers. Before applying the idea of AFSA to Raman fiber amplifiers, let's first introduce the following definitions: (1) the state of the ith fish Xi = (Xi1, Xi2, …, XiN) represents pump wavelengths and power levels, where i = 1, 2, … M, M is the number of artificial fishes, and N is the dimension of pump parameters including wavelengths and power levels; (2) the maximum visual distance of a fish is denoted by Dv; (3) Dstep represents the maximum step size a fish can make in one movement; (4) the distance between the ith and the jth fish is defined as the Euclidean norm of vector Xi − Xj, i.e., dij = ||Xi − Xj||; (5) the degree of congestion is represented by a pre-specified constant δ;

Gripple

8 < ΔGmax ; Gmax ≥Gt and Gmin ≥Gt = −ΔGmin ; Gmax < Gt and Gmin < Gt : ΔGmax −ΔGmin ; Gmax ≥Gt and Gmin < Gt :

ð4Þ

where Gt is the pre-specified target gain satisfying the design task, Gmax and Gmin are respectively the maximum and minimum signal gains obtained by solving Eq. (1) with the average power analysis method. Based on the idea of AFSA, the steps to optimize pump parameters for gain flattened Raman fiber amplifiers are set up as follows: Step 1 Initialize the states of M fishes and other relevant parameters stochastically in the pre-specified problem space. Record the best state Xbest among the M fishes and the corresponding maximum food concentration ρmax. Step 2 Judge if the criteria are met. If the answer is yes then stop the program and return with the values of Gripple = 1/ρmax and Xbest, otherwise proceed to Step 3. The criteria include the maximum allowed iteration loops and the desired level of Gripple. Step 3 Each fish in the school performs the following (a)–(c) actions once (a) Preying behavior: Suppose the current state of the ith fish is Xi. For prey purpose it attempts to take a new state X′i . A trial state within its maximum visual distance Dv is first derived from Eq. (5). If ρ(Xi) < ρ(X′i ) then the ith fish makes a real movement along the direction X′i − Xi by an amount given by Eq. (6); otherwise it makes another attempt to a different new state X′i according to Eq. (5). If the condition ρ(Xi) < ρ(X′i ) is not satisfied after number_try attempts, it makes a real movement according to Eq. (7). Xi′ = Xi + RandðÞ  Dv Xi′ = Xi + RandðÞ  Dstep 

ð5Þ X′i −Xi ‖ X i′−Xi ‖

Xi′ = Xi + RandðÞ  Dstep

ð6Þ ð7Þ

where number_try is a pre-specified constant integer. (b) Swarming behavior: Suppose the current state of the ith fish is Xi, the current fish population within the maximum visual distance Dv of the ith fish is nf and the population center is at Xc. If ρ(Xi) < ρ(Xc)/(δ · nf), which indicates that the population center is not overcrowded and there are more food available around, then the ith fish makes a real movement towards the population center by an amount given by Eq. (8); otherwise performs the preying behavior (a) instead. ″

Xi = Xi + RandðÞ  Dstep 

Xc −Xi ‖Xc −Xi ‖

ð8Þ

(c) Following behavior: Suppose the current state of the ith fish is Xi. Within its maximum visual distance Dv, the current fish population is nf and the state of its best mate is Xbetter. If ρ(Xi) < ρ(Xbetter)/(δ · nf), which indicates that the position of its best mate is not overcrowded and there are more food available around, then the ith fish makes a real movement

H.M. Jiang et al. / Optics Communications 284 (2011) 5480–5483

Raman gain coefficient gR /(10-14 m·W–1)

Loss/(dB·km-1)

5482

Wavelength/nm

Frequency shift/THz Fig. 1. Raman gain coefficient spectrum (measured at 1 μm pump wavelength) and loss spectrum (inset) of the single mode fiber used in the calculation.

towards its best mate by an amount given by Eq. (9); otherwise performs the preying behavior (a) instead. ‴

X i = Xi + RandðÞ  Dstep 

Xbetter −Xi ‖Xbetter −Xi ‖

ð9Þ

where Rand() in Eqs. (5)–(9) is a function that fetches a random real number between 0.0 and 1.0 at each call. Step 4 Pick out the maximum food concentration from ρ(X′i ), ρ(Xi″) and ρ(Xi‴) for ρimax, denote the state that possesses of ρimax by Xinext, assign the next state of the ith fish Xinext. Step 5 Denote the best Xinext and the best ρimax, i = 1, 2, …, M, respectively by Xbest_t and ρmax_t. If ρmax_t > ρmax update Xbest and ρmax to Xbest_t and ρmax_t respectively. Go to Step 2. 4. Numerical results and discussions

Gain /dB

Pump power/mW

The pump parameters for a gain-flattened Raman fiber amplifier in C-band are optimized using the proposed algorithm with the following parameters. The wavelengths of signals range from 1530 nm to 1565 nm in 1 nm steps. The power of each signal is 0.1 mW, and the fiber length is 20 km. The number of elemental amplifiers is set to 20 for average power analysis, and the effective core area is 80 μm 2. The wavelengths of two pumps are allowed to vary between 1420 nm and 1480 nm, and the power levels of pumps are allowed to vary between 50 mW and 500 mW. The Raman gain coefficient spectrum and the loss spectrum of the fiber are taken from [15] and are reproduced in Fig. 1. The parameters for artificial fish

school algorithm are set as follows. The number of artificial fishes is set to M = 20, with the congestion factor δ = 0.005. The number of attempts a fish will try in prey behavior is set to number_try = 3. The maximum visual distance of a fish is Dv = 40, and the maximum step size that a fish can make in one movement is Dstep = 6.0. The maximum allowed iteration loops for artificial fish school algorithm to run in the optimization process is set to 30. The optimization task is to find the appropriate pump wavelengths and power levels for the RFA that ensure a quasi-transparent transmission for all signals. In other words, the net gain (not on–off gain) of Raman amplifier is required to fully compensate for the fiber loss and Raman tilt within the specified C-band for all the 36 signal channels. In this work, Gt is set to zero and the allowed maximum in band gain ripple determined by Eqs. (2)–(4) is limited to 0.7 dB. The optimization target for the Raman fiber amplifier is reached when the wavelengths and power levels of pumps are optimized to 1435.4 nm, 1479.7 nm, and 109.9 mW, 166.1 mW, respectively. The optimized pump spectrum and the corresponding signal gain spectrum are plotted in Fig. 2. By the observation of Figs. 1 and 2, it is easy to find that the first and the second gain peaks are respectively attributed to the first and the second pumps. The overall gain of signals is the nonlinear summation of the impacts of the two pumps. It is confirmed from Fig. 2 that the gain fluctuates around the level of 0.0 dB, with an in-band ripple of 0.63 dB. This demonstrates that all signals transmit through the fiber transparently from input port to output port. In order to see the amplification effects of the RFA, the power levels of signal channels at the output port of the transmission fiber with and without optimized pumps are plotted in Fig. 3, where the dashed red line represents the power level of input signals. One can see from Fig. 3(a) that the signals suffer an attenuation of about 3.6 dB after a propagation distance of 20 km in the fiber when pumps are not in use. This is because the signals are approximately exponentially attenuated along the fiber due to material loss. Although the fiber loss increases from 1530 nm to 1565 nm as shown in the inset of Fig. 1, the Raman tilt in this signal band counteracts the effect of increasing fiber loss so that the attenuation curve of signals in Fig. 3(a) is approximately flat. Fig. 3(b) shows that when the optimized pumps are applied, the power level of output is pumped up to the level of input. It fluctuates around 0.1 mW with small ripples. This demonstrates that a transparent transmission of 20 km can be achieved with merely two pumps. When the proposed algorithm is compared with the algorithm in Ref. [15] for the gain-flattened characteristics of the same fiber parameters, it is found that both algorithms can deliver RFAs of similar performance. The calculation time the proposed algorithm takes to complete a design is about several dozens of seconds. On the other hand, the algorithm in [15] takes much longer to achieve a design that produces the same level of performance. This much slower design speed is due to its lower calculation efficiency of the old algorithm than that of the proposed algorithm. The dramatically improved

Wavelength/nm Fig. 2. The optimized pump spectrum and the corresponding signal gain spectrum.

H.M. Jiang et al. / Optics Communications 284 (2011) 5480–5483

(b)

Wavelength/nm

Wavelength/nm

Signal power/mW

Signal power/mW

(a)

5483

Fig. 3. The spectra of output signals. (a) Without pumps. (b) With optimized pumps. Dashed red line represents the power level of input signals.

Table 1 The pump parameters and gain ripples of several different designs.

Set # 1 Set # 2 Set # 3

Wavelength 1 (nm)

Wavelength 2 (nm)

Power 1 (mW)

Power 2 (mW)

Gain ripple (dB)

1425.3 1430.7 1436.6

1459.7 1466.3 1475.1

110.7 110.1 104.8

143.5 149.9 172.3

0.67 0.66 0.70

calculation efficiency of the proposed algorithm owes to the organic incorporation of the efficient AFSA and the efficient average power analysis technique. In this comparative study it is also found that, although both designs meet the target, i.e., satisfy the requirements in gain performance level, the two optimization algorithms do not converge to the same pump wavelengths and power levels. This is because the gain of an RFA is a multimodal function with respect to the pump parameters [11,12]. There exist many other appropriate sets of combinations for the pump wavelengths and power levels that produce similar gain performance for the RFAs. In other words, if the proposed algorithm is run several times, several different designs may result, with each design giving satisfactory gain performance. For the same fiber parameters as those used in the design of Fig. 2, three other sets of designs are obtained by the proposed algorithm in subsequent runs for example. They are listed in Table 1 together with the corresponding gain ripples. As one can see, they are different from each other but all meet the 0.7 dB target gain ripple. The algorithm in [15] does similar things. The chance that two of these designs coincide with each other is rare. In conclusion, both algorithms come up with working designs that satisfy the design criteria, but they do not match exactly in wavelengths and power levels. 5. Conclusion A novel design method for gain flattened Raman fiber amplifiers is proposed and demonstrated. This method is based on artificial fish school algorithm. In this algorithm the pump parameters including wavelengths and power levels are mapped to the state of a fish in a school, and the gain of a Raman fiber amplifier is mapped to the concentration of food source for the fish school to search respectively. A set of optimized wavelength and power levels are searched and a broadband flat gain Raman fiber amplifier is designed in the C-band.

The result demonstrates the reliability of the method. This efficient method provides an alternative for the optimization of pump parameters for gain flattened Raman fiber amplifiers. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (NSFC) under grants 60607005, 60877033, 60588502, the Science and Technology Bureau of Sichuan Province under grant 2006z02-010-3, the Youth Science and Technology Foundation of UESTC under grant JX0628, and the Fundamental Research Funds for the Central Universities under grant ZYGX2010J061. References [1] K.C. Reichmann, P.P. Iannone, X. Zhou, N.J. Frigo, B.R. Hemenway, IEEE Photon. Technol. Lett. 18 (2006) 328. [2] J. Bromage, J. Lightwave Technol. 22 (2004) 79. [3] H.M. Jiang, K. Xie, Y.F. Wang, J. Lightwave Technol. 28 (2010) 1932. [4] G.P. Agrawal, Nonlinear Fiber Optics, Elsevier Academic, San Diego, 1989. [5] H. Jiang, K. Xie, Y. Wang, Electron. Lett. 44 (2008) 796. [6] H.M. Jiang, K. Xie, Y.F. Wang, Sci. China Ser. E: Technol. Sci. 52 (2009) 2412. [7] H.M. Jiang, K. Xie, Y.F. Wang, Chin. Sci. Bull. 55 (2010) 555. [8] H. Kidorf, K. Rottwitt, M. Nissov, M. Ma, E. Rabarijaona, IEEE Photon. Technol. Lett. 11 (1999) 530. [9] Y. Emori, K. Tanaka, S. Namiki, Electron. Lett. 35 (1999) 1355. [10] X. Zhou, C. Lu, P. Shum, T.H. Cheng, IEEE Photon. Technol Lett. 13 (2001) 945. [11] X. Liu, J. Chen, C. Lu, X. Zhou, Opt. Express 12 (2004) 6053. [12] X. Liu, Y. Li, Opt. Commun. 230 (2004) 425. [13] M. Yan, J. Chen, W. Jiang, J. Li, J. Chen, X. Li, IEEE Photon. Technol. Lett. 13 (2001) 948. [14] J. Zhou, J. Chen, X. Li, G. Wu, Y. Wang, W. Jiang, J. Lightwave Technol. 24 (2006) 2362. [15] H.M. Jiang, K. Xie, Y.F. Wang, Opt. Commun. 283 (2010) 3348. [16] H.M. Jiang, K. Xie, Y.F. Wang, Opt. Express 18 (2010) 11033. [17] T.G. Hodgkinson, IEEE Photon. Technol. Lett. 3 (1991) 1082. [18] B. Min, W.J. Lee, N. Park, IEEE Photon. Technol. Lett. 12 (2000) 1486. [19] J. Ning, Q. Han, Z. Chen, J. Li, X. Li, Chin. Phys. Lett. 21 (2004) 2184. [20] X.M. Liu, B. Lee, Opt. Express 11 (2003) 2163. [21] X.L. Li, Z.J. Shao, J.X. Qian, Syst. Eng. Theory Pract. 22 (2002) 34. [22] M.F. Zhang, S. Cheng, F.C. Li, Proc. of IEEE International Conference on Mechatronics and Automation, 2006, p. 1598. [23] M.Y. Jiang, D.F. Yuan, Proc. of IEEE International Conference on Neural Networks and Brain, 2005, p. 569. [24] X.J. Shan, M.Y. Jiang, Proc. of IEEE the 6th World Congress on Intelligent Control and Automation, 2006, p. 3658. [25] J.M. Xiao, X.M. Zheng, X.H. Wang, Proc. of IEEE the 6th World Congress on Intelligent Control and Automation, 2006, p. 3456. [26] M.Y. Jiang, Y. Wang, S. Pfletschinger, M.A. Lagunas, Proc. of International Conference on Intelligent Computing, 2007, p. 1084.