Use of a genetic algorithm to optimize multistage erbium-doped fiber-amplifier systems with complex structures Huai Wei, Zhi Tong, and Shuisheng Jian Institute of Lightwave Technology, Beijing Jiaotong University, Beijing, China
[email protected]
Abstract: We propose optimizing multifunctional multistage erbiumdoped fiber amplifiers (EDFAs) with complex structures by use of a genetic algorithm. With this method, we investigated optimum configurations of C- and L-band gain-flattened multistage EDFAs containing gain-flattening filters and high-loss interstage elements for dense wavelength-division multiplexing systems in detail and compared the amplifiers with various kinds of configurations under different design criteria. With the guidance of optimization results, the roles of all the factors such as pumping schemes, pump-power allocation, component position, and insertion loss in the optimization of EDFAs have been studied, and useful guidelines for optimizations have been provided. © 2004 Optical Society of America OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.2410) Fibers, erbium; (060.2360) Fiber optics links and subsystems.
References and links 1. K. Wundke, “Advanced amplifier design: physics and systems limitations,” in Optical Fiber Communication Conference (OFC 2003), Vol. 86 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003). 2. J. Lee, U.-C. Ryu, S. J. Ahn, and N. Park, “Enhancement of power conversion efficiency for an L-band EDFA with a secondary pumping effect in the unpumped EDF section,” IEEE Photon. Technol. Lett. 11, 42-44 (1999). 3. A. Yeniay and R. Gao, “Single stage high power L-band EDFA with multiple C-band seeds,” in Optical Fiber Communication Conference (OFC 2002), Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002). 4. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, New York, 1992). 5. C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9, 271-283 (1991). 6. T. G. Hodgkinson, “Improved average power analysis technique for erbium-doped fiber amplifiers,” IEEE Photon. Technol. Lett. 4, 1273-1275 (1992). 7. R. Lebref, B. Landousies, T. Georges, and E. Delevaque, “Theoretical study of the gain equalization of a stabilized gain EDFA for WDM applications,” J. Lightwave Technol. 15, 766-770 (1997). 8. Z. Tong, H. Wei, T. Li, and S. Jian, “Optimal design of L-band EDFAs with high-loss interstage elements,” Opt. Commun. 224, 63-72 (2003). 9. R. D. Muro, P. N. Kean, S. J. Wilson, and J. Mun, “Dependence of L-band amplifier efficiency on pump wavelength and amplifier design,” 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).
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(C) 2004 OSA
Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 531
1.
Introduction
The rapid development of optical fiber communications along with maturing large-capacity broadband transmission systems has led to the growth of erbium-doped fiber amplifiers (EDFAs) from simple gain block designs to complicated systems consisting of multiple functional elements. Many additional features such as the amplified spontaneous noise (ASE) filter, the gain-flattening filter (GFF), and the dispersion compensator are incorporated in the midsection of amplifiers [1]. Because the parameters of an amplifier’s structure have a great effect on the amplifier’s performance, an effective optimization method for designing EDFAs with a complex structure is necessary. In previous literature, most papers about EDFA design have focused on amplifiers with new structures [2, 3]; few papers touch on optimization methods. In this paper we describe the optimizations of multistage EDFAs by the genetic algorithm (GA) method. The paper is organized as follows. In Section 2, a procedure on how to realize the optimization is introduced in detail. There are two subsections in Section 3: the first presents optimizations for amplifiers with various configurations by use of the GA method. In the second, we systematically analyze the optimization results. Some useful guidelines for designing a multistage EDFA with high pump efficiency to satisfy the system’s requirements are also discussed in this subsection. 2.
Theory
As amplifiers’ structures become more complex, additional parameters must be concurrently optimized. Furthermore, the accurate analytic expression between the parameters of an EDFA’s structure and performance is often not available. Compared with conventional methods, the genetic algorithm (GA) has no requirement such as connectivity or convexity on searching space. It can efficiently search large and poorly understood searching space where expert knowledge is limited or inaccessible. And it has less probability of being trapped in a local optimum solution [4]. In the GA, an “individual” is a feasible solution that is described by a coded datum called a “chromosome” (in amplifier optimization, the coded datum contains amplifier information such as the length of the erbium-doped fiber (EDF), the pump power, and the position of optical components and pumps). After generating an initial population that contains a certain number of individuals, we perform a series of processes (selection, crossover, and mutation) on the population to generate the next generation circularly. The fittest individuals of any population tend to reproduce and survive into the next generation, thus improving successive generations. In amplifier optimization we should give a numerical value to represent the degree of satisfaction with the amplifier performance. Using the average inversion ratio iteration method or the average power analysis (APA) method based on the Giles model [5-7], we can simulate the amplifier in a static state. Because there are many optical components inserted into the EDFA, the numerical model should take them into consideration. Assuming that a component is located at z j , the optical power at the two ports of the component are PvL (z j ) and PvR (z j ). The relations between them are + + − − PνR (z j ) = PνL (z j ) F + (ν) , PνL (z j ) = PνR (z j ) F − (ν) .
(1)
F ± (ν) is used to denote the component’s property (ν is the frequency of the light, and +,- denote forward and backward direction, respectively; e.g., for an ideal optical isolator (OI) F + (ν) = 1, F - (ν) = 0]. Then the fitness value can be derived from the amplifier’s simulation result. For various optimization purposes, the evaluation function is different. Commonly, the optimized amplifier should have high gain, flattened gain profile, and low noise figure (NF), so the evaluation func#3539 - $15.00 US
(C) 2004 OSA
Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 532
tion can be calculated as follows: f = −α1 n f + α2 Gave − α3 u f ,
(2)
Out put (dBm)
Out put (dBm)
where α1 , α2 , α3 are weight factors; Gave is the average value of the amplifier’s gain; n f is the NF; and u f is the flatness of the amplifier’s gain profile. The weight factors are selected according to the requirements of amplifier performance. Simulated results have been compared with measurement results to validate the accuracy of the numerical model. Figure 1 shows the output spectrum profile of a signal stage C-band EDFA with –20-dBm input signal at 1550 nm [Fig. 1(a)], and a dual-stage L-band EDFA (Fig. 2) with –13-dBm input signal at 1580 nm [Fig. 1(b)]. The simulated results are consistent with the experimental results.
Wavelength (nm)
Wavelength (nm)
(a)
(b)
Fig .1 Comparison of simulated results with measurement results for C (a) and L-band (b) EDFA
Fig. 1. Comparison of simulated results with measurement results for C- (a) and L-band (b) EDFA.
2m
L1
23m
L2
DCM
980nm 100mw
12dB loss
980nm 340mw
Fig .2 Structure of L-band EDFA
Fig. 2. Structure of L-band EDFA.
The effectiveness of the GA method has also been verified. Figure 3 gives the relationship between average gain and fitness value to L1 , L2 of an L-band multistage EDFA (Fig. 2) [we assume that the pump power and the position of the dispersion-compensation module (DCM) are fixed to make the optimization a comparatively simple problem that is easy to express with three-dimensional graphics). From Fig. 3 we can see that the optimization problem is a multiple-peaked problem with discontinuous properties. These properties seriously limited the application of conventional optimization methods. Although we can use the enumeration algorithm to find the global optimum solution by computing all the feasible solutions, the large amount of calculation makes the enumeration algorithm inefficient. It takes 326 min. for us with a Pentium IV 2-GHz computer to find the optimum solution in this simple example that has only two parameters to be optimized. When the searching space is large, it is impractical to compute all the feasible solutions. With the genetic method, setting the population to be 40, after 50 generations of evolution, we get the optimum solution that is the same as we derived #3539 - $15.00 US
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 533
Fitness value
Average gain (dB)
L1 (m)
L1 (m)
L2 (m)
L2 (m)
(a)
(b)
Fig .3 The relationship between average gain (a) and fitness value (b) to L1, L2 for an L-band multi stage EDFA
Fig. 3. Relationship between average gain (a) and fitness value (b) to L1 , L2 for an L-band multistage EDFA.
Fitness value
with the enumeration algorithm. Figure 4 shows the trace of the optimization. It indicates that 20 generations of evolution are sufficient for obtaining the optimum solution, with a computing time of 39 min.
Generation Fig .44.The trace ofoptimization. the optimization Fig. Trace of the
3. 3.1.
Applications and discussion Applications for EDFA optimization
We derive the optimal parameters for EDFAs with different structures by the GA method and then compare the optimized EDFAs to find the one with best performance under certain conditions. Optimizations for both C- and L-band EDFA have been performed. First, we optimized a C-band EDFA pumped with two laser diodes. The amplifier is composed of EDF (Table 1, conventional EDF for C-band), pump units [laser diode (LD) and wavelength-division multiplexing (WDM) coupler], a gain-flattening filter (GFF) and a DCM (with 12-dB loss for pump and signal power). We use the GFF [made of fiber Bragg grating (FBG) and OI] to keep the flatness of the gain for all the channels less than ±0.4 dB. The DCM is inserted into the EDFA to derive better system performance. There are 40 input wavelength channels on the International #3539 - $15.00 US
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 534
Telecommunication Union (ITU) grid with 100-GHz spacing, between 1528.77 and 1559.79 nm. The signal power is –17 dBm/channel. The sum power of the amplifier’s two pumps is fixed at 380 mW, whereas the power ratio of two pumps can be selected. The goal of optimization is assembling the components to form an EDFA with optimized structure (Fig. 5). The optimized amplifier should have the highest gain, with a gain flatness lower than ±0.4 dB, and at the same time a NF lower than a certain request value. The parameters used in the optimizations are shown in Tables 1 and 2. Table 1. Parameters of the EDF used in this paper. Conventional EDF
Numerical aperture
for C-band EDFA 0.24
High concentration EDF for L-band EDFA 0.24
Cut-off wavelength
917 nm
910 nm
Mode field diameter
6.2um
5.32µm
Background loss@1550nm
6.3dB/km
13.47dB/km
Peak absorption coefficient@980nm
4.2dB/m
15 dB/m
Peak absorption coefficient@1530nm
6.4dB/m
21 dB/m
Peak emission coefficient@1530nm
6.0dB/m
19.4dB/m
Parameters
Table 2. Other parameters used in the optimizations.
Signal wavelengths (C-band)
Input signal power
1528.77 ~1559.79nm, 40 channels with 0.8nm spacing 1571.24~ 1602.74nm, 40 channels with 0.8nm spacing -17dBm per channel
Pump/signal coupler loss@1580nm
0.3dB
OI Isolator loss@1580nm
0.5dB
Isolation of the isolator
50dB
Fiber fusing loss for standard single-mode fiber (SMF) and conventional EDF Fiber fusing loss for SMF and high concentration EDF Extra insertion loss of GFF@1550
0.1dB
Signal wavelengths (L-band)
0.2dB 1.0dB
A series of optimizations for different kinds of EDFA under various requests on NF (NF < 5.8–10 dB) have been carried out. Six kinds of pumping schemes have been taken into consideration: the forward–backward (FB) pumping and dual-forward (FF) pumping-direction schemes; and for each pumping-direction scheme there are three kinds of pump wavelength configurations: 980 nm + 1480 nm, 980 nm + 980 nm, and 1480 nm + 1480 nm. We compared the #3539 - $15.00 US
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 535
EDF
DCM
GFF
GA method to assemble the components to form EDFAs with optimized structure Fig. 5. Use of theFig.5 GAUsemethod to assemble the components to form EDFAs with optimized (IO module is for L-band EDFA and GFF is for C-band EDFA only ) structure (IO module is for L-band EDFA, and GFF is for C-band EDFA only).
optimized configuration for each structure (Fig. 6) to find which pumping scheme has the best performance. The L-band EDFAs with six kinds of pumping schemes have been optimized under different allowed NF requests by the GA method in the same manner as we used for the C-band EDFAs. The structures for L-band EDFAs [Figs. 5, 6(c), and 6(d)] are not the same as those of C-band. To derive a higher pump-utilization ratio, an OI unit with pump path (composed of two pumpsignal WDM couplers) is used to restrain the backward ASE, and the pump power (include backward pumping) is coupled into the high-concentration EDF (Table 1) at a selected position to utilize the enhancement of power conversion efficiency with the secondary pumping effect [2, 8]. The GFF used in the C-band is not needed in the L-band EDFA because it has a flat gain profile.
DCM
GFF
DCM
GFF (b)
(a)
DCM
DCM
(c)
(d)
Fig. 6. Some structures forSome C-band (a,forb) and(a,b) L-band (c, d) Fig.6 structures C-band and L-band (c,d)EDFA EDFA (input and output OI have and output OI have not been included in the figure) not been included in the(input figure).
In the L-band EDFA optimizations, the sum power of the two-pump LDs is 440 mW, and there are 40 input channels with 100-GHz spacing (–17 dBm/channel, 1571.24–1602.74 nm). The optimized amplifiers should have the highest possible gain. The gain flatness of the amplifiers should be lower than ±1.5 dB for all 40 channels and less than ±0.8 dB for the channels between 1574 and 1598 nm; at the same time, the NF of the optimized EDFAs should be lower than requirements (NF < 5.8–10dB). The optimization results such as the output characteristics of some optimized EDFAs, gain performance for amplifiers with various configurations under different allowed NF, and amplifier structures are given in Figs. 7, 8, and 9, respectively. Figure 7 shows the output optical spectra, gain, and NF of the optimized EDFAs. The results indicate that the optimized EDFAs can surely satisfy the requirements, so the optimizations are confirmed to be effective. The performance of the optimized EDFAs is shown in Fig. 8(a) (C-band) and Fig. 8(b) (L-
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 536
Output (dBm)
Output (dBm)
Wavelength (nm) (b)
Gain and NF (dB)
Gain and NF (dB)
Wavelength (nm) (a)
Wavelength (nm) (c)
Wavelength (nm) (d)
Fig. 7 Output optical spectra, gain and NF of the optimized C-band (a, c)(FB 980+1480nm pumped) Fig. 7.and Output spectra, gain, and NFpumped) of the with optimized C-band (a, c) (FB 980 nm L-bandoptical (b, d) EDFA(FB dual-1480nm 12dB inter-stage loss(NF60%) for the allowed NF < 5.5 dB, but when we take the loss into account, the PCE decreases to 42% even for the allowed NF of 6.5 dB. The configurations for the EDFAs with different DCM loss are also analyzed (Figs. 16 and 17). When the loss of DCM becomes higher, the NF of the amplifier increases, and it cannot satisfy the requirement; then the structure of the amplifier needs to be adjusted (P1 /P should be larger, and components should be moved toward output end) to have better noise performance at the expense of decrease in gain. 3.2.4.
Summary
Selecting proper pumping wavelength is the most important issue in designing an EDFA, and it should be done as the first step. In the C band, the 980 nm + 1480 nm pumping scheme has advantages over other pumping schemes for a wide range of allowed NF, whereas the dual1480-nm pumping scheme is quite suitable for L-band amplification.
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 542
Average gain (dB )
Average gain (dB )
Allowed noise figure (dB) (a)
Allowed noise figure (dB) (b)
Fig.15 Gain for optimized EDFA with and with out insertion loss of components ((a)C-
Average gain (dB )
Position of components
Fig. 15. band Gain980+1480FB for optimized EDFAscheme) with and with out insertion loss of components [(a) pumping ((b)L-band 1480+1480FB pumping scheme) C-band 980+1480FB pumping scheme, (b) L-band 1480 + 1480 FB pumping scheme].
Loss of DCM (dB) (a)
Loss of DCM (dB) (b)
Average gain (dB )
Position of components
Fig.16gain Average gain(a) and optimized position of components(b) optimizedC-band CFig. 16. Average (a) and optimized position of components (b) forfor optimized EDFA FF pumping scheme) withDCM different EDFA (980 nmband + 1480 nm (980+1480nm FF pumping scheme) with different loss.DCM loss
Loss of DCM (a)
Loss of DCM (dB) (b)
Average gain(a) optimized positionofofcomponents components(b) L-band Fig. 17. Fig.17 Average gain (a) and and optimized position (b)for foroptimized optimized L-band EDFA(1480+1480nm FF pumping scheme) with different DCM loss EDFA (1480 nm + 1480 nm FF pumping scheme) with different DCM loss.
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 543
Compared with pumping wavelength, the pumping direction of the amplifier’s rear stage has a lesser effect. Although the dual-forward pumping scheme is slightly more suitable for the situation of low allowed NF, and the forward–backward pumped EDFA can provide higher gain when the allowed NF is high, the difference between these two kinds of pumping schemes is very small. A compromise between the noise and gain performance is the main issue in EDFA optimization; choosing the pump-power allocation and component position for multistage EDFA is key to the compromise. The components, especially the DCM, GFF, and setup for use of unpumped EDF, should be placed properly according to the allowed noise and gain performance under the guidance that we have introduced. Insertion loss of components and splicing loss of different kinds of fibers can degrade the performance of multistage EDFAs greatly. Therefore, minimizing the insertion loss is very important to get EDFA with good performance. 4.
Conclusions
For multistage EDFAs with complex structures, many factors such as the pumping schemes, pump-power allocation, components position, and insertion loss determine the performance of EDFA jointly. GA is an effective method for optimizing EDFAs, taking all those factors into consideration. Using the GA method, we have done a series of optimizations; then under the guidance of optimization results, a systematic account of the subtle relations between amplifiers’ performance and all those factors have been derived. Acknowledgments This research was supported by the National Hi-tech Research 863 Project of China (No. 2001AA122012).
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Received 16 December 2003; revised 28 January 2004; accepted 2 February 2004
23 February 2004 / Vol. 12, No. 4 / OPTICS EXPRESS 544
