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Performance optimization of EDFA–Raman hybrid optical amplifier using genetic algorithm
Optics & Laser Technology 68 (2015) 89–95
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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Performance optimization of EDFA–Raman hybrid optical amplifier using genetic algorithm Simranjit Singh a,n, R.S. Kaler b a b
Department of Electronics and Communication Engineering, Punjabi University, Patiala, Punjab 147002, India Department of Electronics and Communication Engineering, Thapar University, Patiala, Punjab 147004, India
art ic l e i nf o
a b s t r a c t
Article history: Received 12 June 2014 Received in revised form 10 October 2014 Accepted 14 October 2014
For the first time, a novel net gain analytical model of EDFA–Raman hybrid optical amplifier (HOA) is designed and optimized the various parameters using genetic algorithm. Our method has shown to be robust in the simultaneous analysis of multiple parameters, such as Raman length, EDFA length and its pump powers, to obtained highest possible gain. The optimized HOA is further investigated and characterized on system level in the scenario of 100 10 Gbps dense wavelength division multiplexed (DWDM) system with 25 GHz interval. With an optimized HOA, a flat gain of 418 dB is obtained from frequency region 187 to 189.5 THz with a gain variation of less than 1.35 dB without using any gain flattened technique. The obtained noise figure is also the lowest value ( o2 dB/channel) ever reported for proposed hybrid optical amplifier at reduced channel spacing with acceptable bit error rate. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Hybrid optical amplifiers DWDM system Genetic algorithm
1. Introduction The hybrid optical amplifiers (HOAs), combination of Raman and erbium doped fiber amplifiers (EDFA), have emerged as a promising solution in extending the span and transmission capacity of DWDM system [1]. It is attractive because of their abilities to tailor the gain profile, compensate fiber dispersion/loss, and suppress the spontaneous noise [2,3]. Hasan et al. [4] proposed the various configurations of Raman and EDFA. After comparison it was observed that the EDFA–Raman HOA provides better results as compared to other with cost effective solution. Although Ramanonly amplifiers have demonstrated the capability to improve the system BER performance [5] but still the configuration of EDFA and Raman have been found to be comparatively more power-efficient and cost-effective [6]. However, a drawback with Raman amplifier is that the nonlinear effects such as stimulated Brillouin scattering, self-phase modulation, cross-phase modulation, and four-wave mixing degrade the signals when the amplifiers have large output powers [7]. On the other hand, the non-uniform gain spectrum in conjunction with the saturation effects of EDFAs cause increase in signal power levels and decrease in the optical signal-to-noise ratio to unacceptable values in systems [8]. Therefore, both the amplifiers and their applied systems must be carefully designed if we wish to install the HOA in DWDM system at reduced channel spacing.
n
Corresponding author. E-mail address: [email protected] (S. Singh).
http://dx.doi.org/10.1016/j.optlastec.2014.10.011 0030-3992/& 2014 Elsevier Ltd. All rights reserved.
So it is mandatory to optimize the important parameters (such as Raman length, EDFA length and pump power etc.) before the HOA is deployed. In literature, various optimization techniques are used to optimize the parameters of HOAs to improve the system performance. Carena et al. [9] presented the mathematical optimization to yield the optimal configuration of hybrid Raman/EDFA HOA for given target optical signal to noise ratio. It was reported that span distance is around 30 km when only EDFAs are used, while it is increased to 50–60 km in the case of HOA. Kaler [10] investigated the simulation based DWDM system to optimize the Raman–EDFA HOA. Unfortunately, this investigation is based on single/local parameter optimization (i.e. at single time only one parameter of HOA is varied). In previous research papers published [11–13], various global optimization techniques (such as genetic algorithm, hybrid genetic algorithm, neural network learning etc.) are presented to optimize the Raman and EDFA individually. Till now no global optimization technique is applied to optimize the EDFA– Raman HOA in optical communication system. As the mathematical model of HOA is concerned, according to Refs. [9,14,15] the total gain is the multiplication/addition of individual gain of cascaded amplifiers. But for the better precision, the net gain model of HOA has to be calculated, which is not done in literature. Recently, we have proposed various combinations of the optical amplifiers and investigates the impact of the reduced channel spacing at high bit rates [16]. It was observed that Raman–EDFA HOA is the best combination to achieve better results. In Refs. [14,17], to take the advantage of Raman–EDFA, we have further
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improved our previous scheme and address the various problems to achieve better performance in term of crosstalk and gain flatness without using any other costly components. But in these investigations the optimization of HOA has not been done. In this paper, we extend the previous reported results in Refs. [4,10–18] by designing the net gain mathematical model and to optimize the cost effective EDFA–Raman HOA using genetic algorithm for better performance. This paper is organized as follows. After this introductory part, the gain model of EDFA–Raman HOA is described in Section 2. In Sections 3 and 4, the proposed genetic algorithm and its analog to optical system is presented to provide the optimal parameters. The system setup and results are described in Section 4. Section 5 summarizes the conclusions.
P Pout R ¼ e αp z P Pin R i.e.
P PR ¼ P Pout R ¼ P Pin R exp αp z
ð4Þ
Substituting value of PPR (also called PPout-R) from Eq. (4) in Eq. (1), dP SR g ¼ αS P SR þ R P SR P Pin R expð αP z Þ dz αP
ð5Þ
On left hand side of Eq. (5), the distribution of signal power along the Raman amplifier is being considered, and its value depends on the initial signal power. Hence, on right hand side, the term PSR is present and it varies as exponential of other parameters. 2.2. Computation of net gain modal of HOA
2. Gain model of EDFA–Raman HOA As we mentioned earlier, the total gain of cascaded amplifiers is adding or product of individual gain. But in original the gain of second cascaded amplifier (net gain) is depend on the first amplifier gain/power as shown in Fig. 1. So in this section we have derived the net gain modal by considering the actual conditions. The mathematical model is divided into two parts. In Section 2.1, an expression of variation of pump power and signal power along the Raman amplifier is determined while, in Section 2.2, after considering the effect of EDFA output power on Raman power, an expression for a net gain is established.
In this paper, the discrete Raman amplifier is considered for optimization. The Raman-amplification process is governed by the following set of two coupled equations by considering single continuous wave pump beam to amplify an optical signal [19].
7
ð1Þ
dP PR ωP g R P PR P SR ¼ αP P PR dz ωS aP
ð2Þ
where PSR is signal power for Raman amplifier, gR is Raman gain coefficient, PPR is pump power for Raman amplifier, aP is crosssectional area of pump beam inside the fiber, αs and αP is fiber losses at signal and pump frequencies (ωs and ωp) respectively, “ þ” sign for forward pump, “–” sign for backward pump. For practical situations, pump power is so large compared with signal power that pump depletion can be neglected by setting gR ¼0 in Eq. (2) and considering forward pump only [20], then after solving we have dP PR ¼ αP dz P PR
ð3Þ
Integrating both sides, P Pout Z R
P pin R
dP PR ¼ αP P PR
Z
dz 0
where N1 is population density in ground state, N2 is Population density in meta stable state and Nt is total erbium-ion density in the core of EDFA. Then the rate of change of population (N1) at ground level (energy E1) is given as [20] ð7Þ
where PPE is pump power, PSE is signal power, σpa is absorption cross-section at pump frequency ϑp , σsa is absorption cross section at signal frequency ϑs , σse is emission cross section at signal frequency ϑs , ap is cross sectional area for fiber modes for λp, as is cross sectional area for fiber modes for λs, and τsp is spontaneous emission lifetime for transition from E2 to E1. On right hand side of Eq. (7) the first term is the rate of absorption per unit volume from E1 to E3 due to pump, second term is the rate of absorption per unit volume from E1 to E2 due to signal, third term is rate of stimulated emission per unit volume from E2 to E1 due to signal and fourth term is rate of spontaneous emission per unit volume from E2 to E1 due to signal. Similarly, the rate of change of population (N2) at upper amplifier level is [20] σ pa P PE N 1 σ sa P SE N 1 σ se P SE N 2 dN 2 N2 ¼ þ dt ap hϑp as hϑs as hϑs τsp
ð8Þ
Under steady state condition dN 2 ¼0 dt Put it into (8) and after rearrangement the expression becomes N2 σ pa P PE N 1 P SE ½σ sa N 1 σ se N 2 ¼ þ τsp ap hϑp as hϑs
dP SE ¼ ΓS ðσ se N2 σ sa N 1 ÞP SE αP SE dz PSout-R
PSout-E = PSR = PSin-R EDFA
ð6Þ
ð9Þ
By neglecting the contribution of spontaneous emission, variation of pump power Pp and signal power Ps along the length of amplifier is calculated as [21]
z
ln½P Pout R ln½P Pin R ¼ αP z PSin-E
N1 þ N2 ¼ Nt
dN 1 σ pa P PE N 1 σ sa P SE N 1 σ se P SE N2 N2 ¼ þ þ dt ap hϑp as hϑs as hϑs τsp
2.1. Analytical computation of pump power and pump signal evolution along the Raman amplifier
dP SR g P PR P SR ¼ R αS P SR dz aP
To calculate the net gain of EDFA–Raman HOA, first we have to calculate the EDFA output power (PSR) and then final gain is calculated by putting this power into Eq. (5). The EDFA is modeled as three level system but due to the high relaxation rate of pump level (E3, top level) remains almost empty, therefore
Raman
Fig. 1. Net gain/power evaluation.
7
dP PE ¼ Γp σ pa N 1 P PE α 0 P PE dz
ð10Þ ð11Þ
α and α0 are fiber losses and can be neglected for small (10–30 m) fiber length, therefore
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
dP SE ¼ ΓS ðσ se N 2 σ sa N 1 ÞP SE dz
ð12Þ
N2 ¼
7
dP PE ¼ Γp dz
σ pa N1 P PE
ð13Þ
dP SE ¼ Γs ðσ se N2 σ sa N 1 Þdz P SE
dP SE ¼ P SE
P sin E
Z
LE 0
N2 ¼
where
Integrating both sides for LE as length of EDFA, PZ sout E
Γs ðσ se N 2 σ sa N 1 Þdz
ωP ¼
σ pa P PE ¼ pumping rate ap hϑp
ωsa ¼
σ sa P SE ¼ stimulated absorption rate as hϑs
ωse ¼
σ se P SE ¼ stimulated emission rate; as hϑs
From Eq. (6), we get N 1 ¼ N t –N2
Z
Using value of N1 in above the above equation we get, PZ sout E
dP SE ¼ P SE
P sin E
LE
0
dP SE ¼ P SE
P sin E
Z
LE 0
Z ΓS σ se N 2 dz
LE 0
P sin E
P sout E P sin E
N t ½ωP þ ωsa LE ð1=τsp Þ þ ωP þ ωsa þ ωse
P sin R ¼ P sout E or P SR ¼ P sin R ¼ P sout E Put this value in Eq. (5)
Z
LE
dP SR ¼ αS P sin E exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg dz g þ R P sin E expf ΓS σ sa N t LE aP þ ΓS ðσ sa þ σ se ÞN 2avg gP Pin E expð αP zÞ
N 2 dz 0
N2 dz
dP SR ¼ αS exp ΓS σ sa N t LE þΓS ðσ sa þσ se ÞN 2avg dz P sin E g þ R expf ΓS σ sa Nt LE αP þ ΓS ðσ sa þ σ se ÞN 2avg gP Pin E expð αP zÞdz
where P sout E ¼ Γs σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg P sin E
For convenience of solving, let us denote signal power by PSR in above equation and integrating both sides
Taking exponential on both sides, P sout E ¼ exp Γs σ sa N t LE þΓS ðσ sa þσ se ÞN 2avg P sin E P sout E ¼ P sin E expf Γs σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN2avg g
PZ sout R
ð14Þ P sin R
Put this expression into Eq. (9) σ pa P PE ðNt N 2 Þ N2 P SE ¼ þ ½σ sa ðNt N 2 Þ σ se N2 ap hϑp τsp as hϑs σ pa P PE N t σ sa P SE N t σ pa P PE σ sa P SE σ se P SE τsp N2 þ þ þ ap hϑp as hϑs ap hϑp as hϑs as hϑs
αS exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg dz
LR
0
Z
LR
gR expf ΓS σ sa N t LE αP þ ΓS ðσ sa þ σ se ÞN 2avg gP Pin R expð αP zÞ
R ¼ αS exp ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg ½zL0R ½ ln P SR PPsout sin R g þ R exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg P Pin R αP expð αP zÞ LR ð αp Þ 0 ½ ln P sout R □ ½ ln P sin R ¼ αS exp ΓS σ sa N t LE þ ΓS ðσ sa þσ se ÞN 2avg LR g R PPin R expf ΓS σ sa N t LE ð aP σ P Þ þ ΓS ðσ sa þ σ se ÞN 2avg gðexp αp LR expð0ÞÞ
σ pa P PE σ sa P SE σ se P SE σ pa P PE N t σ sa P SE N t ¼ τsp N 2 þ N2 τsp þ þ þ ap hϑp as hϑs as hϑs ap hϑp as hϑs 1 σ pa P PE σ sa P SE σ se P SE σ pa P PE N t σ sa P SE Nt þ þ þ þ ¼ τsp τsp ap hϑp as hϑs as hϑs ap hϑp as hϑs
Z
0
From Eq. (6) we have N 1 ¼ N t –N2
dP SR ¼ dP SR
þ
2.3. Calculation of N2avg
þ
N 2 τsp
# ½ωP þ ωsa dz ð1=τsp Þ þ ωP þ ωsa þ ωse
Since, the input signal to Raman (Psin-R) is equal to the output signal of EDFA (Psout-E), Therefore,
0
N 2 ¼ τsp
0
LE
N 2avg ¼
ln
Nt
P sout E ¼ P sin E expf Γ S σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg g
ln ½P sout E ln ½P sin E ¼ Γs σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg Z
"
LE
From Eq. (14),
ΓS σ sa ðN t N 2 Þdz
dP SE ¼ Γs σ sa N t ½zL0E þ ΓS ðσ sa þ σ se Þ P SE
Z N 2 dz ¼
0
ΓS ðσ se N 2 σ sa ðN t N2 ÞÞdz
" Z # Z LE LE dP SE ¼ Γs σ sa N t dz þ ΓS ðσ sa þ σ se ÞN 2 dz P SE 0 0
PZ sout E
LE
N2avg ¼
N2avg ¼
PZ sout E
Z
Z
τsp N t ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ ð1=τsp Þ þ ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ þ ðσ se P SE =as hϑs Þ
Nt ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ ð1=τsp Þ þ ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ þ ðσ se P SE =as hϑs Þ ½ωP þ ωsa ¼ Nt ½ð1=τsp Þ þ ωP þ ωsa þ ωse
After rearranging Eq. (12),
τsp
91
ln
P sout R ¼ αS exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg LR P sin R
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S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
þ
g R P Pin R exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg 1 exp αp LR ð aP α P Þ
1.
Generate Initial Population
Taking exponential on both sides, P sout R ¼ exp½ αS exp ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg LR P sin R gR exp ΓS σ sa Nt LE þ ΓS ð σ sa þσ se ÞN 2avg þ ð aP σ P Þ ½1 exp αp LR P Pin R P sout R Gain ¼ ¼ P sin R P Pin R exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg g R ½1 exp αp LR exp aP α P αS expf ΓS σ sa N t LE þΓS ðσ sa þ σ se ÞN 2avg gLR
2. Start the Counter for number of generations
3.
Call sub-program to evaluate Fitness (gain value from eq. 15) by passing the combinations of parameters to be optimized
Now,
1 exp αp LR ¼ Lef f αP So,
Obtain combination of parameters for maximum fitness value
P Pin R Lef f exp ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg g R Gain ¼ exp aP αS expf ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg gLR
Selection
P Pin R Lef f g R ¼ g0 ap LR Gain ¼ exp½LR exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg g 0 αS expf ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg gLR :
Creates new Generation
4.
Also,
Cross Over ð15Þ
Mutation 3. Multi-parameter optimization using genetic algorithm (GA) This section is start with an overview of GA, followed by its implementation for optimization of EDFA–Raman HOA. The GA is a global search optimization algorithm based on biological evolution. Evolution is a method of searching among a large number of possibilities for solutions. A GA allows a population composed of many individuals to evolve to a state that maximizes the “fitness” under specified selection rules. The detailed description of GA in optical communication system is described in Ref. [11]. This simple GA for optimization of HOA can be broadly sub-divided into following steps and their sequence can be represented by a flow diagram as shown in Fig. 2. Step 1: Initialization of GA parameters and population for various system parameters i.e. Raman length, EDFA length and its pump powers. During this stage, the range for the parameters i.e. the limits of the search space is defined. The parameters for the GA and range of values for HOA are as given in Tables 1 and 2 respectively. Set the number of generations after which the algorithm will converge to optimum solution. The terminating condition is appear when our goal is achieved, which is to attain large gain 425 dB. Step 2: At this stage, the counter is started for the number of generations at the beginning. The generations proceed iteratively until the final generation is reached. Step 3: Within the above counter established for number of generations, there are sub-stages to evaluate the fitness value (i.e. gain) and then modify the set of parameters for achieving maximum gain. Evaluation of amplifier gain for various possible combinations of parameters is performed by calling HOA model as a sub-program. The set of parameters obtained from a
No
Is this last generation?
Yes Terminate/Display results End Fig. 2. Basic genetic algorithm flow diagram applied For EDFA–Raman HOA optimization.
Table 1 Parameters for the GA. Parameter
Value
Cross over probability Mutation probability Tournament selection parameter Number of generations Population Fitness function
80% 2.5% 75% 50 100 Individuals Maximum gain
randomly generated population are passed within the function call to the sub-program one by one for the whole population. This sub-program on receiving the combination of all the parameters to be optimized, evaluate the gain using Eq. (15). The average gain is returned to the program. The current fitness value is compared with the previous fitness and if it is greater
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
than the previous one, then the set of parameters is taken as the better solution. The previous combination is discarded and new combination is tracked during the current generation by comparing the previous results with the current. Step 4: During the next sub-stage, the current population of individuals is modified by appropriately employing tournament selection. The fitness value and tournament select probability are passed to call the function. Here the fitness is an array of gain values respective to the set of all parameters in current population. Tournament selection chooses a random value for chromosomes depending upon small probability as defined in Table 1. New chromosome pairs are obtained from these selected chromosomes by crossover method. These newly generated chromosomes form a temporary new population which replaces the original population after performing a mutation operation on each of the new chromosomes. Finally a new improved population is obtained.
Again step 3 followed by 4 is repeated until the final generation is reached. It can be determined that amplifier gain increases with the succession of the generations. Since, the proposed method of employing GA includes tournament selection, crossover method and mutation adopted collectively, so it converges towards maximum gain in a few generations and then further modification is not desirable. These listed steps have been implemented in widely used MATLAB Software.
93
Fig. 3 illustrated the values of the gain versus Raman length, EDFA length, pump power for Raman amplifier and for EDFA during the progress of the algorithm through last generation. In the 2D plots, the gain value is plotted versus a single parameter, but in each case the gain is obtained with the particular combination of the four optimized parameters.
Table 3 Value of parameters associated with Eq. (15). Parameter
Description
Value
σsa σPa σSe σPe λP λS τSP gR Nt αS αP aP aS
Absorption cross section at signal frequency Absorption cross section at pump frequency Emission cross section at signal frequency Emission cross section at pump frequency Pump frequency Signal frequency Spontaneous emission lifetime Raman gain coefficient Total erbium ion density Fiber losses at signal frequency Fiber losses at pump frequency Cross sectional area of pump beam Cross sectional area of signal beam
2.85 10 25 m2 1.86 10 25 m2 5.03 10 25 m2 0.42 10 25 m2 980 10 9 Hz 1601 10 25 Hz 1/100 s 9.5 10 14 8.3 1023 m 3 5.76 10 5 dB/m 5.76 10 5 dB/m 12.6 1012 m2 12.6 1012 m2
Table 4 Gain obtained from various combinations of parameters using GA. Raman length EDFA length Raman pump power EDFA pump power Gain (km) (m) (mW) (mW) (dB)
Table 2 Range of values for EDFA–Raman HOA parameters. Parameter
Value
Number of pumps Raman pump power (mW) EDFA pump power (mW) Range of Raman length (km) Range of EDFA length (km)
1 100–600 300–600 20–35 10–13
30.617 25.625 30.874 22.791 32.478 27.300 33.002 30.670
10.78 11.40 10.73 11.78 10.29s 12.51 12.84 12.8543
107.69 111.83 284.03 349.10 437.91s 353.14 433.43 427.84
498.39 543.57 404.05 504.22 523.73 501.97 531.79 435.45
Fig. 3. Convergence of the GA obtained for (a) Raman length, (b) EDFA length, (c) Raman pump power and (d) EDFA pump power.
13.76 15.07 20.58 22.90 23.46 23.75 24.81 25.13
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
The remaining parameters of Eq. (15) which is used in GA is described in Table 3. Table 4 shows the results obtained from genetic algorithm as a function of the expected gain of more than 25 dB. These parameters has been taken according to readily used in experimental systems. The maximum gain (25 dB) is obtained with the optimum solution presented in last case. For further investigation we have considered the proposed EDFA–Raman HOA with these optimized parameters called optimized HOA.
-15
10
-20
10
BER
94
-25
10
-30
10
4. System setup and results
187
188
188.5
189
189.5
Frequency [THz]
4.1. Gain and noise figure characteristics of optimized EDFA–Raman HOA To check the performance of optimized HOA at system level the numerical simulation is carried out. The system setup consists of 100 DWDM channels covering the bandwidth starting from 187 to 189.5 THz in a 25 GHz spacing using continuous wave lasers as shown in Fig. 4. We have investigated this system with per channel input laser powers of 10 dB m. The data stream from a 10 Gbps pattern generator with a NRZ binary sequence is pre-coded and drives a sine squared amplitude modulator. The optimized parameters of different fibers and pumps are taken from last case described in Table 3. Fig. 5 shows the gain and noise figure spectrum of the optimized EDFA–Raman HOA over 100 channel DWDM system. The variation of the gain with wavelength is not uniform as each amplifier induces its own nonlinearities and ASE noise. It can be observed that each frequency has a gain of more than 18 dB. In these results various nonlinear effects are considered, such as, ASE, four wave mixing, dispersion etc. unlike the mathematical
187.5
Fig. 6. BER versus DWDM frequencies.
analysis represented in Section 2. This is the reason behind the reduction of gain in the case of simulation. Using optimized parameters we have obtained 1.35 dB of gain flatness with noise figure of less than o2 dB/Channel, which shows improvement over [4,14]. Due to the gain dynamics induced by proposed EDFA–Raman HOA, the distortion of pulse shapes and crosstalk between the symbols is present. These crosstalk effects are due to induced nonlinearities such as stimulated Raman scattering, four wave mixing, self- and cross-phase modulation etc. [16]. The induced crosstalk directly affects the bit error rate performance of the system. In Fig. 6 the variation of bit error rate among the selected DWDM channels is detected due to crosstalk between the data symbols. But still, the proposed system provides good bit error rate (o1 10 ue) over the effective bandwidth. Moreover, the good quality factor (49.3) and optical signal to noise ratio (450 dB) is achieved over all the used channels.
5. Conclusion In this paper, we have proposed a new analytical gain model of EDFA–Raman HOA and the final gain equation is illustrated to optimize the multiple parameters using genetic algorithm. This algorithm has proven to be robust to refine the search of optimum Raman length, EDFA length and its pump powers required to the best configuration of proposed HOA. It is observed that, the optimized HOA with optimum parameters (i.e. Raman length: 30.67 km, EDFA length: 12.85 m, Raman pump power: 427.8 mW and EDFA pump power: 435.45 mW) provides a flat gain of 418 dB from the frequency region 187 to 189.5 THz with a gain variation of less than 1.35 dB and with acceptable BER. Fig. 4. Proposed DWDM system with optimized EDFA–Raman HOA.
Fig. 5. Gain and noise figure characterization of optimized HOA.
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[9] Carena A, Curri V, Poggiolini P. On the optimization of hybrid Raman/erbiumdoped fiber amplifiers. IEEE Technol Lett 2001;13:1170–2. [10] Kaler RS. Optimization of hybrid Raman/erbium-doped fiber amplifier for multi terabits WDM system. Opt Int J Light Electron 2013;124:575–8. [11] Zhou J, Chen J, Li X, Wu G, Wang Y, Jiang W. Robust, compact, and flexible neural model for a fiber Raman amplifier. J. Lightwave Technol 2006;24:2362–7. [12] Singh S, Saini S, Kaur G, Kaler RS. Multiparameter optimization of a Raman fiber amplifier using a genetic algorithm for an L-band dense wavelength division multiplexed system. J Opt Eng 2014;53 (016103-1–016103-7). [13] Ferreira GCM, Cani SPN, Pontes MJ, Segatto MEV. Optimization of distributed Raman amplifiers using a hybrid genetic algorithm with geometric compensation technique. IEEE Photonics J 2011;3:390–9. [14] Singh S, Kaler RS. Novel optical flat-gain hybrid amplifier for dense wavelength division multiplexed system. IEEE Photonics Technol Lett 2014;26:173–6. [15] Sakamoto T, Aozasa S, Yamada M, Shimizu M. Hybrid fiber amplifiers consisting of cascaded TDFA and EDFA for WDM signals. J Lightwave Technol 2006;24:2287–95.
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[16] Singh S, Kaler RS. Investigation of hybrid optical amplifiers for dense wavelength division multiplexed system with reduced spacings at higher bit rates. Int J Fiber Integr Opt 2012;31:208–20. [17] Singh S, Kaler RS. Influence of the word length and input power on nonlinear crosstalk induced by hybrid optical amplifiers. J Opt Fiber Technol 2013;19:428–31. [18] Singhand S, Kaler RS. Performance evaluation of hybrid optical amplifier for high-speed differential phase-shift keying-modulated optical signals. J Opt Eng 2013;52:096102. [19] Agrawal GP. Fiber-optic communication systems. New York: John Wiley and Sons; 2002; 244–5. [20] Headley, Agrawal GP. Raman amplification in fiber optical communication systems. California: Elsevier Academic Press; 2005. [21] Khare RP. Fiber optics and optoelectronics. New Delhi: Oxford University Press; 2012; 257–8.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Performance optimization of EDFA–Raman hybrid optical amplifier using genetic algorithm Simranjit Singh a,n, R.S. Kaler b a b
Department of Electronics and Communication Engineering, Punjabi University, Patiala, Punjab 147002, India Department of Electronics and Communication Engineering, Thapar University, Patiala, Punjab 147004, India
art ic l e i nf o
a b s t r a c t
Article history: Received 12 June 2014 Received in revised form 10 October 2014 Accepted 14 October 2014
For the first time, a novel net gain analytical model of EDFA–Raman hybrid optical amplifier (HOA) is designed and optimized the various parameters using genetic algorithm. Our method has shown to be robust in the simultaneous analysis of multiple parameters, such as Raman length, EDFA length and its pump powers, to obtained highest possible gain. The optimized HOA is further investigated and characterized on system level in the scenario of 100 10 Gbps dense wavelength division multiplexed (DWDM) system with 25 GHz interval. With an optimized HOA, a flat gain of 418 dB is obtained from frequency region 187 to 189.5 THz with a gain variation of less than 1.35 dB without using any gain flattened technique. The obtained noise figure is also the lowest value ( o2 dB/channel) ever reported for proposed hybrid optical amplifier at reduced channel spacing with acceptable bit error rate. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Hybrid optical amplifiers DWDM system Genetic algorithm
1. Introduction The hybrid optical amplifiers (HOAs), combination of Raman and erbium doped fiber amplifiers (EDFA), have emerged as a promising solution in extending the span and transmission capacity of DWDM system [1]. It is attractive because of their abilities to tailor the gain profile, compensate fiber dispersion/loss, and suppress the spontaneous noise [2,3]. Hasan et al. [4] proposed the various configurations of Raman and EDFA. After comparison it was observed that the EDFA–Raman HOA provides better results as compared to other with cost effective solution. Although Ramanonly amplifiers have demonstrated the capability to improve the system BER performance [5] but still the configuration of EDFA and Raman have been found to be comparatively more power-efficient and cost-effective [6]. However, a drawback with Raman amplifier is that the nonlinear effects such as stimulated Brillouin scattering, self-phase modulation, cross-phase modulation, and four-wave mixing degrade the signals when the amplifiers have large output powers [7]. On the other hand, the non-uniform gain spectrum in conjunction with the saturation effects of EDFAs cause increase in signal power levels and decrease in the optical signal-to-noise ratio to unacceptable values in systems [8]. Therefore, both the amplifiers and their applied systems must be carefully designed if we wish to install the HOA in DWDM system at reduced channel spacing.
n
Corresponding author. E-mail address: [email protected] (S. Singh).
http://dx.doi.org/10.1016/j.optlastec.2014.10.011 0030-3992/& 2014 Elsevier Ltd. All rights reserved.
So it is mandatory to optimize the important parameters (such as Raman length, EDFA length and pump power etc.) before the HOA is deployed. In literature, various optimization techniques are used to optimize the parameters of HOAs to improve the system performance. Carena et al. [9] presented the mathematical optimization to yield the optimal configuration of hybrid Raman/EDFA HOA for given target optical signal to noise ratio. It was reported that span distance is around 30 km when only EDFAs are used, while it is increased to 50–60 km in the case of HOA. Kaler [10] investigated the simulation based DWDM system to optimize the Raman–EDFA HOA. Unfortunately, this investigation is based on single/local parameter optimization (i.e. at single time only one parameter of HOA is varied). In previous research papers published [11–13], various global optimization techniques (such as genetic algorithm, hybrid genetic algorithm, neural network learning etc.) are presented to optimize the Raman and EDFA individually. Till now no global optimization technique is applied to optimize the EDFA– Raman HOA in optical communication system. As the mathematical model of HOA is concerned, according to Refs. [9,14,15] the total gain is the multiplication/addition of individual gain of cascaded amplifiers. But for the better precision, the net gain model of HOA has to be calculated, which is not done in literature. Recently, we have proposed various combinations of the optical amplifiers and investigates the impact of the reduced channel spacing at high bit rates [16]. It was observed that Raman–EDFA HOA is the best combination to achieve better results. In Refs. [14,17], to take the advantage of Raman–EDFA, we have further
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improved our previous scheme and address the various problems to achieve better performance in term of crosstalk and gain flatness without using any other costly components. But in these investigations the optimization of HOA has not been done. In this paper, we extend the previous reported results in Refs. [4,10–18] by designing the net gain mathematical model and to optimize the cost effective EDFA–Raman HOA using genetic algorithm for better performance. This paper is organized as follows. After this introductory part, the gain model of EDFA–Raman HOA is described in Section 2. In Sections 3 and 4, the proposed genetic algorithm and its analog to optical system is presented to provide the optimal parameters. The system setup and results are described in Section 4. Section 5 summarizes the conclusions.
P Pout R ¼ e αp z P Pin R i.e.
P PR ¼ P Pout R ¼ P Pin R exp αp z
ð4Þ
Substituting value of PPR (also called PPout-R) from Eq. (4) in Eq. (1), dP SR g ¼ αS P SR þ R P SR P Pin R expð αP z Þ dz αP
ð5Þ
On left hand side of Eq. (5), the distribution of signal power along the Raman amplifier is being considered, and its value depends on the initial signal power. Hence, on right hand side, the term PSR is present and it varies as exponential of other parameters. 2.2. Computation of net gain modal of HOA
2. Gain model of EDFA–Raman HOA As we mentioned earlier, the total gain of cascaded amplifiers is adding or product of individual gain. But in original the gain of second cascaded amplifier (net gain) is depend on the first amplifier gain/power as shown in Fig. 1. So in this section we have derived the net gain modal by considering the actual conditions. The mathematical model is divided into two parts. In Section 2.1, an expression of variation of pump power and signal power along the Raman amplifier is determined while, in Section 2.2, after considering the effect of EDFA output power on Raman power, an expression for a net gain is established.
In this paper, the discrete Raman amplifier is considered for optimization. The Raman-amplification process is governed by the following set of two coupled equations by considering single continuous wave pump beam to amplify an optical signal [19].
7
ð1Þ
dP PR ωP g R P PR P SR ¼ αP P PR dz ωS aP
ð2Þ
where PSR is signal power for Raman amplifier, gR is Raman gain coefficient, PPR is pump power for Raman amplifier, aP is crosssectional area of pump beam inside the fiber, αs and αP is fiber losses at signal and pump frequencies (ωs and ωp) respectively, “ þ” sign for forward pump, “–” sign for backward pump. For practical situations, pump power is so large compared with signal power that pump depletion can be neglected by setting gR ¼0 in Eq. (2) and considering forward pump only [20], then after solving we have dP PR ¼ αP dz P PR
ð3Þ
Integrating both sides, P Pout Z R
P pin R
dP PR ¼ αP P PR
Z
dz 0
where N1 is population density in ground state, N2 is Population density in meta stable state and Nt is total erbium-ion density in the core of EDFA. Then the rate of change of population (N1) at ground level (energy E1) is given as [20] ð7Þ
where PPE is pump power, PSE is signal power, σpa is absorption cross-section at pump frequency ϑp , σsa is absorption cross section at signal frequency ϑs , σse is emission cross section at signal frequency ϑs , ap is cross sectional area for fiber modes for λp, as is cross sectional area for fiber modes for λs, and τsp is spontaneous emission lifetime for transition from E2 to E1. On right hand side of Eq. (7) the first term is the rate of absorption per unit volume from E1 to E3 due to pump, second term is the rate of absorption per unit volume from E1 to E2 due to signal, third term is rate of stimulated emission per unit volume from E2 to E1 due to signal and fourth term is rate of spontaneous emission per unit volume from E2 to E1 due to signal. Similarly, the rate of change of population (N2) at upper amplifier level is [20] σ pa P PE N 1 σ sa P SE N 1 σ se P SE N 2 dN 2 N2 ¼ þ dt ap hϑp as hϑs as hϑs τsp
ð8Þ
Under steady state condition dN 2 ¼0 dt Put it into (8) and after rearrangement the expression becomes N2 σ pa P PE N 1 P SE ½σ sa N 1 σ se N 2 ¼ þ τsp ap hϑp as hϑs
dP SE ¼ ΓS ðσ se N2 σ sa N 1 ÞP SE αP SE dz PSout-R
PSout-E = PSR = PSin-R EDFA
ð6Þ
ð9Þ
By neglecting the contribution of spontaneous emission, variation of pump power Pp and signal power Ps along the length of amplifier is calculated as [21]
z
ln½P Pout R ln½P Pin R ¼ αP z PSin-E
N1 þ N2 ¼ Nt
dN 1 σ pa P PE N 1 σ sa P SE N 1 σ se P SE N2 N2 ¼ þ þ dt ap hϑp as hϑs as hϑs τsp
2.1. Analytical computation of pump power and pump signal evolution along the Raman amplifier
dP SR g P PR P SR ¼ R αS P SR dz aP
To calculate the net gain of EDFA–Raman HOA, first we have to calculate the EDFA output power (PSR) and then final gain is calculated by putting this power into Eq. (5). The EDFA is modeled as three level system but due to the high relaxation rate of pump level (E3, top level) remains almost empty, therefore
Raman
Fig. 1. Net gain/power evaluation.
7
dP PE ¼ Γp σ pa N 1 P PE α 0 P PE dz
ð10Þ ð11Þ
α and α0 are fiber losses and can be neglected for small (10–30 m) fiber length, therefore
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
dP SE ¼ ΓS ðσ se N 2 σ sa N 1 ÞP SE dz
ð12Þ
N2 ¼
7
dP PE ¼ Γp dz
σ pa N1 P PE
ð13Þ
dP SE ¼ Γs ðσ se N2 σ sa N 1 Þdz P SE
dP SE ¼ P SE
P sin E
Z
LE 0
N2 ¼
where
Integrating both sides for LE as length of EDFA, PZ sout E
Γs ðσ se N 2 σ sa N 1 Þdz
ωP ¼
σ pa P PE ¼ pumping rate ap hϑp
ωsa ¼
σ sa P SE ¼ stimulated absorption rate as hϑs
ωse ¼
σ se P SE ¼ stimulated emission rate; as hϑs
From Eq. (6), we get N 1 ¼ N t –N2
Z
Using value of N1 in above the above equation we get, PZ sout E
dP SE ¼ P SE
P sin E
LE
0
dP SE ¼ P SE
P sin E
Z
LE 0
Z ΓS σ se N 2 dz
LE 0
P sin E
P sout E P sin E
N t ½ωP þ ωsa LE ð1=τsp Þ þ ωP þ ωsa þ ωse
P sin R ¼ P sout E or P SR ¼ P sin R ¼ P sout E Put this value in Eq. (5)
Z
LE
dP SR ¼ αS P sin E exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg dz g þ R P sin E expf ΓS σ sa N t LE aP þ ΓS ðσ sa þ σ se ÞN 2avg gP Pin E expð αP zÞ
N 2 dz 0
N2 dz
dP SR ¼ αS exp ΓS σ sa N t LE þΓS ðσ sa þσ se ÞN 2avg dz P sin E g þ R expf ΓS σ sa Nt LE αP þ ΓS ðσ sa þ σ se ÞN 2avg gP Pin E expð αP zÞdz
where P sout E ¼ Γs σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg P sin E
For convenience of solving, let us denote signal power by PSR in above equation and integrating both sides
Taking exponential on both sides, P sout E ¼ exp Γs σ sa N t LE þΓS ðσ sa þσ se ÞN 2avg P sin E P sout E ¼ P sin E expf Γs σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN2avg g
PZ sout R
ð14Þ P sin R
Put this expression into Eq. (9) σ pa P PE ðNt N 2 Þ N2 P SE ¼ þ ½σ sa ðNt N 2 Þ σ se N2 ap hϑp τsp as hϑs σ pa P PE N t σ sa P SE N t σ pa P PE σ sa P SE σ se P SE τsp N2 þ þ þ ap hϑp as hϑs ap hϑp as hϑs as hϑs
αS exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg dz
LR
0
Z
LR
gR expf ΓS σ sa N t LE αP þ ΓS ðσ sa þ σ se ÞN 2avg gP Pin R expð αP zÞ
R ¼ αS exp ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg ½zL0R ½ ln P SR PPsout sin R g þ R exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg P Pin R αP expð αP zÞ LR ð αp Þ 0 ½ ln P sout R □ ½ ln P sin R ¼ αS exp ΓS σ sa N t LE þ ΓS ðσ sa þσ se ÞN 2avg LR g R PPin R expf ΓS σ sa N t LE ð aP σ P Þ þ ΓS ðσ sa þ σ se ÞN 2avg gðexp αp LR expð0ÞÞ
σ pa P PE σ sa P SE σ se P SE σ pa P PE N t σ sa P SE N t ¼ τsp N 2 þ N2 τsp þ þ þ ap hϑp as hϑs as hϑs ap hϑp as hϑs 1 σ pa P PE σ sa P SE σ se P SE σ pa P PE N t σ sa P SE Nt þ þ þ þ ¼ τsp τsp ap hϑp as hϑs as hϑs ap hϑp as hϑs
Z
0
From Eq. (6) we have N 1 ¼ N t –N2
dP SR ¼ dP SR
þ
2.3. Calculation of N2avg
þ
N 2 τsp
# ½ωP þ ωsa dz ð1=τsp Þ þ ωP þ ωsa þ ωse
Since, the input signal to Raman (Psin-R) is equal to the output signal of EDFA (Psout-E), Therefore,
0
N 2 ¼ τsp
0
LE
N 2avg ¼
ln
Nt
P sout E ¼ P sin E expf Γ S σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg g
ln ½P sout E ln ½P sin E ¼ Γs σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg Z
"
LE
From Eq. (14),
ΓS σ sa ðN t N 2 Þdz
dP SE ¼ Γs σ sa N t ½zL0E þ ΓS ðσ sa þ σ se Þ P SE
Z N 2 dz ¼
0
ΓS ðσ se N 2 σ sa ðN t N2 ÞÞdz
" Z # Z LE LE dP SE ¼ Γs σ sa N t dz þ ΓS ðσ sa þ σ se ÞN 2 dz P SE 0 0
PZ sout E
LE
N2avg ¼
N2avg ¼
PZ sout E
Z
Z
τsp N t ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ ð1=τsp Þ þ ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ þ ðσ se P SE =as hϑs Þ
Nt ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ ð1=τsp Þ þ ðσ pa P PE =ap hϑp Þ þ ðσ sa P SE =as hϑs Þ þ ðσ se P SE =as hϑs Þ ½ωP þ ωsa ¼ Nt ½ð1=τsp Þ þ ωP þ ωsa þ ωse
After rearranging Eq. (12),
τsp
91
ln
P sout R ¼ αS exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg LR P sin R
92
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
þ
g R P Pin R exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN2avg 1 exp αp LR ð aP α P Þ
1.
Generate Initial Population
Taking exponential on both sides, P sout R ¼ exp½ αS exp ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg LR P sin R gR exp ΓS σ sa Nt LE þ ΓS ð σ sa þσ se ÞN 2avg þ ð aP σ P Þ ½1 exp αp LR P Pin R P sout R Gain ¼ ¼ P sin R P Pin R exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg g R ½1 exp αp LR exp aP α P αS expf ΓS σ sa N t LE þΓS ðσ sa þ σ se ÞN 2avg gLR
2. Start the Counter for number of generations
3.
Call sub-program to evaluate Fitness (gain value from eq. 15) by passing the combinations of parameters to be optimized
Now,
1 exp αp LR ¼ Lef f αP So,
Obtain combination of parameters for maximum fitness value
P Pin R Lef f exp ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg g R Gain ¼ exp aP αS expf ΓS σ sa Nt LE þ ΓS ðσ sa þ σ se ÞN 2avg gLR
Selection
P Pin R Lef f g R ¼ g0 ap LR Gain ¼ exp½LR exp ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg g 0 αS expf ΓS σ sa N t LE þ ΓS ðσ sa þ σ se ÞN 2avg gLR :
Creates new Generation
4.
Also,
Cross Over ð15Þ
Mutation 3. Multi-parameter optimization using genetic algorithm (GA) This section is start with an overview of GA, followed by its implementation for optimization of EDFA–Raman HOA. The GA is a global search optimization algorithm based on biological evolution. Evolution is a method of searching among a large number of possibilities for solutions. A GA allows a population composed of many individuals to evolve to a state that maximizes the “fitness” under specified selection rules. The detailed description of GA in optical communication system is described in Ref. [11]. This simple GA for optimization of HOA can be broadly sub-divided into following steps and their sequence can be represented by a flow diagram as shown in Fig. 2. Step 1: Initialization of GA parameters and population for various system parameters i.e. Raman length, EDFA length and its pump powers. During this stage, the range for the parameters i.e. the limits of the search space is defined. The parameters for the GA and range of values for HOA are as given in Tables 1 and 2 respectively. Set the number of generations after which the algorithm will converge to optimum solution. The terminating condition is appear when our goal is achieved, which is to attain large gain 425 dB. Step 2: At this stage, the counter is started for the number of generations at the beginning. The generations proceed iteratively until the final generation is reached. Step 3: Within the above counter established for number of generations, there are sub-stages to evaluate the fitness value (i.e. gain) and then modify the set of parameters for achieving maximum gain. Evaluation of amplifier gain for various possible combinations of parameters is performed by calling HOA model as a sub-program. The set of parameters obtained from a
No
Is this last generation?
Yes Terminate/Display results End Fig. 2. Basic genetic algorithm flow diagram applied For EDFA–Raman HOA optimization.
Table 1 Parameters for the GA. Parameter
Value
Cross over probability Mutation probability Tournament selection parameter Number of generations Population Fitness function
80% 2.5% 75% 50 100 Individuals Maximum gain
randomly generated population are passed within the function call to the sub-program one by one for the whole population. This sub-program on receiving the combination of all the parameters to be optimized, evaluate the gain using Eq. (15). The average gain is returned to the program. The current fitness value is compared with the previous fitness and if it is greater
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
than the previous one, then the set of parameters is taken as the better solution. The previous combination is discarded and new combination is tracked during the current generation by comparing the previous results with the current. Step 4: During the next sub-stage, the current population of individuals is modified by appropriately employing tournament selection. The fitness value and tournament select probability are passed to call the function. Here the fitness is an array of gain values respective to the set of all parameters in current population. Tournament selection chooses a random value for chromosomes depending upon small probability as defined in Table 1. New chromosome pairs are obtained from these selected chromosomes by crossover method. These newly generated chromosomes form a temporary new population which replaces the original population after performing a mutation operation on each of the new chromosomes. Finally a new improved population is obtained.
Again step 3 followed by 4 is repeated until the final generation is reached. It can be determined that amplifier gain increases with the succession of the generations. Since, the proposed method of employing GA includes tournament selection, crossover method and mutation adopted collectively, so it converges towards maximum gain in a few generations and then further modification is not desirable. These listed steps have been implemented in widely used MATLAB Software.
93
Fig. 3 illustrated the values of the gain versus Raman length, EDFA length, pump power for Raman amplifier and for EDFA during the progress of the algorithm through last generation. In the 2D plots, the gain value is plotted versus a single parameter, but in each case the gain is obtained with the particular combination of the four optimized parameters.
Table 3 Value of parameters associated with Eq. (15). Parameter
Description
Value
σsa σPa σSe σPe λP λS τSP gR Nt αS αP aP aS
Absorption cross section at signal frequency Absorption cross section at pump frequency Emission cross section at signal frequency Emission cross section at pump frequency Pump frequency Signal frequency Spontaneous emission lifetime Raman gain coefficient Total erbium ion density Fiber losses at signal frequency Fiber losses at pump frequency Cross sectional area of pump beam Cross sectional area of signal beam
2.85 10 25 m2 1.86 10 25 m2 5.03 10 25 m2 0.42 10 25 m2 980 10 9 Hz 1601 10 25 Hz 1/100 s 9.5 10 14 8.3 1023 m 3 5.76 10 5 dB/m 5.76 10 5 dB/m 12.6 1012 m2 12.6 1012 m2
Table 4 Gain obtained from various combinations of parameters using GA. Raman length EDFA length Raman pump power EDFA pump power Gain (km) (m) (mW) (mW) (dB)
Table 2 Range of values for EDFA–Raman HOA parameters. Parameter
Value
Number of pumps Raman pump power (mW) EDFA pump power (mW) Range of Raman length (km) Range of EDFA length (km)
1 100–600 300–600 20–35 10–13
30.617 25.625 30.874 22.791 32.478 27.300 33.002 30.670
10.78 11.40 10.73 11.78 10.29s 12.51 12.84 12.8543
107.69 111.83 284.03 349.10 437.91s 353.14 433.43 427.84
498.39 543.57 404.05 504.22 523.73 501.97 531.79 435.45
Fig. 3. Convergence of the GA obtained for (a) Raman length, (b) EDFA length, (c) Raman pump power and (d) EDFA pump power.
13.76 15.07 20.58 22.90 23.46 23.75 24.81 25.13
S. Singh, R.S. Kaler / Optics & Laser Technology 68 (2015) 89–95
The remaining parameters of Eq. (15) which is used in GA is described in Table 3. Table 4 shows the results obtained from genetic algorithm as a function of the expected gain of more than 25 dB. These parameters has been taken according to readily used in experimental systems. The maximum gain (25 dB) is obtained with the optimum solution presented in last case. For further investigation we have considered the proposed EDFA–Raman HOA with these optimized parameters called optimized HOA.
-15
10
-20
10
BER
94
-25
10
-30
10
4. System setup and results
187
188
188.5
189
189.5
Frequency [THz]
4.1. Gain and noise figure characteristics of optimized EDFA–Raman HOA To check the performance of optimized HOA at system level the numerical simulation is carried out. The system setup consists of 100 DWDM channels covering the bandwidth starting from 187 to 189.5 THz in a 25 GHz spacing using continuous wave lasers as shown in Fig. 4. We have investigated this system with per channel input laser powers of 10 dB m. The data stream from a 10 Gbps pattern generator with a NRZ binary sequence is pre-coded and drives a sine squared amplitude modulator. The optimized parameters of different fibers and pumps are taken from last case described in Table 3. Fig. 5 shows the gain and noise figure spectrum of the optimized EDFA–Raman HOA over 100 channel DWDM system. The variation of the gain with wavelength is not uniform as each amplifier induces its own nonlinearities and ASE noise. It can be observed that each frequency has a gain of more than 18 dB. In these results various nonlinear effects are considered, such as, ASE, four wave mixing, dispersion etc. unlike the mathematical
187.5
Fig. 6. BER versus DWDM frequencies.
analysis represented in Section 2. This is the reason behind the reduction of gain in the case of simulation. Using optimized parameters we have obtained 1.35 dB of gain flatness with noise figure of less than o2 dB/Channel, which shows improvement over [4,14]. Due to the gain dynamics induced by proposed EDFA–Raman HOA, the distortion of pulse shapes and crosstalk between the symbols is present. These crosstalk effects are due to induced nonlinearities such as stimulated Raman scattering, four wave mixing, self- and cross-phase modulation etc. [16]. The induced crosstalk directly affects the bit error rate performance of the system. In Fig. 6 the variation of bit error rate among the selected DWDM channels is detected due to crosstalk between the data symbols. But still, the proposed system provides good bit error rate (o1 10 ue) over the effective bandwidth. Moreover, the good quality factor (49.3) and optical signal to noise ratio (450 dB) is achieved over all the used channels.
5. Conclusion In this paper, we have proposed a new analytical gain model of EDFA–Raman HOA and the final gain equation is illustrated to optimize the multiple parameters using genetic algorithm. This algorithm has proven to be robust to refine the search of optimum Raman length, EDFA length and its pump powers required to the best configuration of proposed HOA. It is observed that, the optimized HOA with optimum parameters (i.e. Raman length: 30.67 km, EDFA length: 12.85 m, Raman pump power: 427.8 mW and EDFA pump power: 435.45 mW) provides a flat gain of 418 dB from the frequency region 187 to 189.5 THz with a gain variation of less than 1.35 dB and with acceptable BER. Fig. 4. Proposed DWDM system with optimized EDFA–Raman HOA.
Fig. 5. Gain and noise figure characterization of optimized HOA.
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