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OptimizationoftheDesignofHighPowerEr3+/Yb3(+)-CodopedFiberAmplifiersforSpaceMissionsbyMeansofParticleSwarmApproach
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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014 3100108
Optimization of the Design of High PowerEr3+/Yb3+-Codoped Fiber Amplifiers for SpaceMissions by Means of Particle Swarm Approach
Luciano Mescia, Sylvain Girard, Senior Member, IEEE, Pietro Bia, Thierry Robin, Arnaud Laurent,Francesco Prudenzano, Aziz Boukenter, and Y. Ouerdane
Abstract—In this paper, the optimization of the design of rareearth–doped cladding-pumped fiber amplifiers is investigated toimprove their performance with respect to the constraints associ-ated with space missions. This work is carried out by means of acomputer code based on particle swarm optimization (PSO) andrate equation model. We consider a fiber that is radiation toler-ant at the space dose levels, and we characterize the radiationresponse of the amplifier based on it. By simulations, we study howthe design of the radiation–tolerant double–cladding Er3+ /Yb3+ -codoped fiber amplifiers (EYDFAs) can improve the global systemresponse in space. The rate equations model includes the first andsecondary energy transfer between Yb3+ and Er3+ , the ampli-fied spontaneous emission and the most relevant upconversion andcross relaxation mechanism among the Er3+ ions. The obtainedresults highlight that the developed PSO algorithm is an efficientand reliable tool to perform the recovering of the most relevantspectroscopic parameters and the optimum design of this kind ofdevices. These results demonstrated that the performance of highpower optical amplifiers can be optimized through such a coupledapproach, opening the way for the design of radiation-hardeneddevices for the most challenging future space missions.
Index Terms—Fiber amplifiers, inversion methods, particleswarm optimization.
I. INTRODUCTION
THE rapid increasing demand for Internet traffic, due toemerging multimedia applications, and the future poten-
tials of advanced information society have stimulated the de-velopment of broadband dense wavelength division multiplex-ing optical networks as well as research for optical deviceshaving excellent flexibility and larger information capacitiesat much faster rates. Rare earth-doped optical fiber amplifiersrepresent the most widely used devices to achieve optical am-plification and to reduce the number of repeaters. In particu-lar, Er3+ -doped fiber amplifiers (EDFAs) have been employed
Manuscript received November 29, 2013; revised January 7, 2014; acceptedJanuary 7, 2014.
L. Mescia, P. Bia, and F. Prudenzano are with the Department of Electricaland Information Engineering, Politecnico di Bari, 70125 Bari, Italy (e-mail:[email protected]; [email protected]; [email protected]).
S. Girard, A. Boukenter, and Y. Ouerdane are with Laboratoire Hubert Curien,University of Saint-Etienne UMR CNRS 5516, F42000 Saint-Etienne, France(e-mail: [email protected]; [email protected];[email protected]).
T. Robin and A. Laurent are with iXFiber SAS, F-22300 Lannion, France(e-mail: [email protected]; [email protected]).
Digital Object Identifier 10.1109/JSTQE.2014.2299635
in terrestrial long–haul communication systems as in-line de-vices. Moreover, owing to the progress of booster amplifiersfor long-haul repeaterless optical links, great efforts have beendevoted to the development of high-power EDFAs [1]–[3]. Fur-thermore, these amplifiers represent also key photonic devicefor space systems as part of highly-distributed data networks,fiber optic gyroscopes, high–speed intersatellite links and deep-space optical communications. Nevertheless, such devices sufferof gain-saturation problems especially when the output powergrows up [3], [4]. The co–doping with ytterbium Yb3+ sensitizerions is an efficient way to overcome this drawback. In fact, thepresence of Yb3+ ions provides an efficient indirect pumpingmechanism for erbium, reduces the formation of Er3+ clusterand the cooperative up-conversion among Er3+ ions, extendsthe range of the possible pump wavelength band, increases thepump absorption providing a peak absorption around 975 nmabout two order of magnitude larger than a non–sensitized one.Considering the problem of the radiation environment associ-ated with space missions, it has been shown that the additionof Yb3+ ions into Er-doped glasses did not change the fiberor amplifier radiation induced degradation explaining that suchcodoped fibers are most promising candidates for high powerlasers under radiations [5], [6].
Although this kind of technology is mature and widely em-ployed, further research activities are needed to obtain amplifierswith higher efficiency in regards of the less studied constraintsrelated to operation in space harsh environment. For such appli-cations, the development of fiber amplifiers having high–powerconversion efficiency is of prime importance since the energyresources in space are extremely limited. Moreover, the require-ments of high reliability and robustness make the evaluation oftheir vulnerability to radiations a crucial point to be consideredin order to ensure the system functionality over the satellitelifetime.
Accurate theoretical models for design and analysis purposesrequire the knowledge of several spectroscopic and fiber pa-rameters. In particular, in the design and optimization of highpower fiber amplifiers the effects of numerical aperture (NA),core size, fiber length, cladding geometry, and dopant concen-tration have to be taken into account in order to obtain efficientcoupling of the pump light, high conversion of the pump power,reduction of nonlinear effects and high handling of the thermalload. Because all parameters affecting the Er3+/Yb3+ -codopedfiber amplifiers (EYDFAs) performance must be optimized, thedesign requires considerable time spent in computing and, as
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3100108 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014
a consequence, tremendous efforts have to be made to iden-tify the most efficient configuration. In this field, the use ofa particular global optimization method is welcome to find theglobal best solution. Recently, well performing and effective ap-proaches using a genetic algorithm (GA) and a neural networkfor the optimization and characterization of rare earth dopedphotonic crystal fiber amplifiers have been proposed by the au-thors [7]–[9]. Particle swarm optimizer is a new, reliable androbust evolutionary algorithm inspired to the social behavior ofdifferent animals, e.g. a flock of birds. This algorithm exhibitssome interesting advantages as low number of synthesis pa-rameters, not complicated evolutionary operators and a simpleimplementation [10].
On the basis of these considerations, in this paper a compre-hensive numerical model based on PSO and rate equations anal-ysis is presented. Such model allows the investigation of pos-sible radiation-hardened double–cladding EYDFAs structuresthat present optimized characteristics for operation in space.In detail, a novel and efficient characterization procedure en-abling the recovering of most relevant spectroscopic parametersis proposed and illustrated by taking into account experimen-tal results obtained on real amplifiers made by the manufactureriXFiber, France. The developed numerical code allows to obtainreliable qualitative and quantitative predictions for the optimumdesign of the amplifier performance in a large variety of EYD-FAs configurations and this in the presence of radiations. Infact, the model takes into account the most relevant active phe-nomena in Er3+/Yb3+ -codoped system such as the radiativeand nonradiative rates, at both pump and signal wavelengths,the stimulated emission of the signal, the ASE, the lifetimes ofthe considered energy levels, the ion–ion energy transfers, thefirst and secondary energy transfer between Yb3+ and Er3+ .This code also contains the possibility to consider the radiationeffects through the changes induced at the pump and emissionwavelengths, through the radiation induced attenuation (RIA)phenomenon [11], [12]. By using as input parameters the mea-sured RIA on the fiber on which the EYDFA is based, the modelpredictions are in good agreement with the experiments and ac-curately reproduce the amplifier behavior before, and after theirradiation.
II. THEORETICAL ANALYSIS
A. Nonlinear Rate and Power Propagation Equations
The energy manifold (numbered with |i〉, i = 1, 2 . . . , 6) tran-sitions and energy transfers of the Er3+/Yb3+ -codoped sys-tem considered in the simulations are illustrated in Fig. 1. Inparticular, the following transitions are considered: 1) pumpabsorption and stimulated emission between the 2F7/2 and2F5/2 ytterbium manifolds, 2) spontaneous decay from the2F5/2 ytterbium manifold, 3) forward energy transfer pro-cess between Er3+ and Yb3+ : 2F5/2 +4 I15/2 →2 F7/2 +4
I11/2 , backward energy transfer process between Er3+ andYb3+ : 2F7/2 +4 I11/2 →2 F5/2 +4 I15/2 , 4) spontaneous de-cays from the 4I9/2 ,
4 I11/2 ,4 I13/2 erbium manifolds, 5) pump
absorption and stimulated emission between the 4I15/2 and
Fig. 1. Energy level diagram of the Er3+ /Yb3+ -codoped system consideredin our simulations.
4I11/2 erbium manifolds, 6) signal absorption and stimulatedemission between the 4I15/2 and 4I13/2 erbium manifolds,7) uniform cooperative upconversion between a pair of ex-cited erbium ions: 4I13/2 +4 I13/2 →4 I15/2 +4 I9/2 ,
4 I11/2 +4
I11/2 →4 I15/2 +4 S3/2 , 8) cross–relaxation process takingplace between the two neighboring erbium ions: 4I15/2 +4
I9/2 →4 I13/2 . With respect to the conventional Er3+/Yb3+
models, the secondary Yb3+ to Er3+ energy transfer process(2F5/2 +4 I13/2 →2 F7/2 +4 F9/2) has been considered sinceit can reduce the pump conversion efficiency. In this process,the Yb3+ ions in the excited manifold 2F5/2 transfer a part oftheir energy to the Er3+ ions in the metastable manifold 4I13/2
exciting them to the 2F9/2 manifold. The excited Er3+ ions non-radiatively relax to the 4I13/2 manifold and, as a consequence,some pump photons are wasted.
The software written to simulate the performance of the fiberamplifier is based on the solution of the nonlinear differen-tial equation system constituted by Er3+/Yb3+ multilevel rateequations and the change rate of the propagation of opticalpower, taking into account both forward and backward ASEin the signal band. The 4F7/2 ,
2 H11/2 ,4 S3/2 , and 4F9/2 erbium
manifolds are assumed to be empty since their lifetime is negli-gible. Moreover, by considering a pump wavelength in the bandaround 915 nm, the absorption of the pump photons by the Er3+
ions in the 4I15/2 (ground state absorption) and 4I11/2 (excitedstate absorption) manifolds can be neglected in the calculations.Finally, the ASE due to the ytterbium system is also neglecteddue to the relatively small population of the 2F5/2 energy level.
By considering the steady state solutions, the populationsNi, i = 1, 2, . . . , 6 are calculated according to the equations
− N4
τ43+ CupN 2
2 + C3N23 − C14N1N4 + Ktr1N2N6 = 0
(1)
W13N1 − W31N3 −N3
τ32+
N4
τ43− 2C3N
23 +
+ KtrN1N6 − K−trN3N5 = 0 (2)
W12N1 − W21N2 +N3
τ32− N2
τ21− 2CupN 2
2 +
+ 2C14N1N4 − Ktr1N2N6 = 0 (3)
MESCIA et al.: OPTIMIZATION OF THE DESIGN OF HIGH POWER Er3 + /Yb3 + -CODOPED FIBER AMPLIFIERS 3100108
W65N6 − W56N5 +N6
τ56− K−trN3N5 + KtrN1N6 +
+ Ktr1N2N6 = 0 (4)
N1 + N2 + N3 + N4 = NEr (5)
N5 + N6 = NYb (6)
where NEr and NYb are the erbium and ytterbium concentra-tion, respectively, τ21 and τ56 are the radiative lifetimes of the4I13/2 and 2F5/2 energy levels, respectively, τ32 and τ43 are thenon–radiative relaxation lifetimes of the 4I11/2 and 4I9/2 en-ergy levels, respectively, C3 and Cup are the homogeneous up-conversion coefficients, C14 is the cross–relaxation coefficient,Ktr , K−tr , Ktr1 are the forward, backward and secondary en-ergy transfer coefficients from Yb3+ -system to Er3+ -system,respectively. The W13 , W56 absorption, W31 and W65 stimu-lated transition rates at the pump wavelength are given by
Wij (z) =Γpσij (λp)
[P+
p (z) + P−p (z)
]λp
hcAcore(7)
where P+p and P−
p are the z–depending forward and backwardpump powers, σij (λp) is the emission cross section, when i >j, and the absorption cross section, when i < j at the pumpwavelength, c is the speed of light in vacuum, and h is Planck’sconstant. Moreover, the chaotic ray dynamics in noncircularinner cladding allow an effective mode mixing which makesthe intensity distribution of all pump modes homogeneous. Asresult, the incoherent input pump field fills the inner claddinguniformly. The corresponding overlap factor between the pumpfield and the doped core is expressed by the equation Γp =Acore/Ainner−clad , where Acore and Ainner−clad are the dopedcore and inner cladding areas, respectively.
Since both the forward and backward ASE noise spreads in acontinuum wavelength range, the amplifier performance cannotbe calculated by means of analytical equations and numericalmethods must be applied in the general case. In particular, bydividing the wavelength range into M wavelength slots the ASEnoise can be modeled as M optical beams having bandwidthΔλk , k = 1, 2, . . . , M, and centered around λk . As result, theabsorption, W12 , and stimulated, W21 , transition rates at thesignal wavelength are given by
Wlm (z) =1
hcAcoreΓs (λs) σlm (λs)
[P+
s (z) + P−s (z)
]λs
+1
hcAcore
M∑
k=1
Γsσlm (λk )[P+
ASE(z)+P−ASE(z)
]λk
(8)
where P+s and P−
s are the z–depending forward and back-ward signal powers, P+
ASE and P−ASE are the z–depending for-
ward and backward ASE powers. The functions σlm (λk ) arethe wavelength–depending emission (l > m) and absorption(l < m) cross sections, and Γs(λk ) is the wavelength-dependingoverlap factor around the signal wavelength given by
Γs (λk ) =∫ 2π
0
∫ R
0|E (r, φ, λk )|2rdrdφ (9)
where R is the radius of the rare earth doped core and E is thetransverse electric field envelope normalized so that the surfaceintegral of |E(r, φ)|2 is equal to one.
The propagation equations of powers along the fiber lon-gitudinal z–axis for pump, signal, and ASE are calculated byintegrating the following first-order differential equation sys-tem
dP±p (z)dz
= ±Γp [σ31(λp)N3−σ13(λp)N1 +σ65(λp)N6 +
− σ56(λp)N5 − α(λp)]P±p (z) (10)
dP±s (z)dz
= ±Γs(λs)[σ21(λs)N2 − σ12(λs)N1 +
− α(λs)]P±s (z) (11)
dP±ASE(z, λk )
dz= ±Γ(λk )[σ21(λk )N2 − σ12(λk )N1 +
− α(λk )]P±ASE(z, λk ) ± P0k (12)
where
P0k =2hc2
λ3k
ΔλkΓ(λk )σ21(λk )N2 (13)
is the contribution of the spontaneous emission to the prop-agating mode in the wavelength slot Δλk , and α(λk ) is thepropagation loss.
B. PSO Algorithm
In order to understand how the PSO algorithm works, let usconsider that a population, called swarm, of bees, called par-ticles, is flying in a field (i.e. search or solution space). Thegoal of the group is to find the location with the highest flowerdensities. By considering an N-dimensional search space, theposition of each particle is represented by an N-dimensionalvector xi , which constitutes a potential solution. The flowerdensity corresponds to the fitness function which is engineeredby considering the design constrains. The important feature inthe swarm behavior is that each particle adjusts its trajectory inthe solution space keeping track of its location that has the bestfitness value, called personal best xbi , and considering the bestlocation found by the entire swarm, called global best xg . Theresearch of the solution, e.g., the change of current particle po-sition, is obtained by applying a proper operator called velocity,vi , which depends in part by the personal experience and in partby the collective experience of the swarm. The velocity of theparticle is changed according to the following equation [10]:
vi (t + 1) = χ {vi (t) + φ1r1 [xbi (t) − xi (t)]}+ χφ2r2 [xg (t) − xi (t)] (14)
xi (t + 1) = xi (t) + vi (t + 1) (15)
where, t is the iteration counter, r1 and r2 are two randomnumbers uniformly distributed in the range [0, 1], and
χ =2
|2 − φ −√
φ2 − 4φ|(16)
3100108 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014
is the constriction factor, where φ1 and φ2 are two real constantswith the conditions φ = φ1 + φ2 and φ > 4. The consideredPSO formulation assures the convergence of the algorithm anda simple identification of the optimal value of the algorithmparameters [10].
III. NUMERICAL RESULTS
The amplifier properties have been evaluated by means of adedicated ad hoc numerical code that solves the rate equations(1)–(6) and the propagation equations (10)–(12). Moreover, be-cause i) the complex transversal geometry of the considered op-tical fiber (octagonal double cladding) and ii) the high numericalaperture between the inner and outer cladding, the overlap factorbetween the dopant region and the pump, signal, and amplifiedspontaneous emission field intensities have been calculated byusing a full-vector modal solver based on finite element method(FEM). In fact, the key advantage of FEM over other numericalmethods is the ability to handle geometrical adaptability andmaterial generality for modeling arbitrary geometries and ma-terials. Moreover, this modal solver shows expanded capabilityand flexibility to accurately describe the transverse section ofoctagonal double cladding fiber with arbitrary size and place-ment. As a consequence, the FEM solver makes possible a veryaccurate calculation of both the propagation constants and theelectromagnetic field distribution of the guided modes.
The numerical investigation has been performed by consider-ing a fiber prototype developed by ixfiber SAS [1], [13]. Radia-tions induce a degradation of Er3+/Yb3+ -codoped optical fiberthat is related to the generation of microscopic point defects inthe silica-based matrix leading to an increase of the fiber linearattenuation. In previous work, it has been shown that this effectis mainly caused by defects linked to the dopants used to fa-cilitate the rare–earth incorporation like aluminum or phospho-rus [11]. The investigated prototype fiber presents an interestingresponse under irradiation as shown in [1], that may be furtherenhanced by optimization through the PSO approach in termsof optical efficiency and/or radiation hardness. In particular, theprototype fiber has a phosphosilicate Er3+/Yb3+ -codoped coresurrounded by an octagonal double-cladding (DC) designed foreasier coupling of the high power multimode pump radiationinto the RE–doped core. The Er3+ and Yb3+ concentration areNEr = 5.2 × 1024 ions/m3 and NYb = 1.1 × 1026 ions/m3 , re-spectively, whereas the pump and signal wavelength as well asthe fiber length are λp = 915 nm, λs = 1545 nm and L = 12 m,respectively. Fig. 2 illustrates a sketch of the fiber transverse sec-tion, and Table I reports the refractive index ncore , nclad , ncoatof core, cladding and coating, respectively.
The Er3+ and Yb3+ absorption cross sections have been de-rived directly from the spectral attenuation measurements per-formed on a fiber sample before irradiation, taking into accountthe core pumping scheme for Er3+ , and the DC pumping schemefor Yb3+ [13]. The Er3+ emission cross sections have been cal-culated by using the McCumber theory. The McCumber theoryhas been tested experimentally on several rare earth doped glasssamples by comparing measured and calculated cross-sectionspectra [14], [15]. In particular, the good agreement between
Fig. 2. Transversal section of the considered octagonal double-cladding fiber.
TABLE IREFRACTIVE INDEX OF THE CONSIDERED FIBER
TABLE IIEMISSION AND ABSORPTION CROSS SECTIONS
numerical and experimental results suggests that this theoryis not restricted to crystalline hosts but remains valid for therare earth-doped glass [14], [15]. Table II reports the computedemission and absorption cross sections at both pump and signalwavelengths.
The spectroscopic parameters used in the modeling, such ascooperative upconversion, energy transfer and cross-relaxationcoefficients cannot be measured easily. However, their estima-tion is essential to optimize the device performance. To over-come this drawback, the PSO algorithm has been applied tosolve the inversion problem [16], in which the lifetime ofthe Yb3+and Er3+ metastable levels, the first and secondaryYb3+ to Er3+ energy transfer coefficients, the upconversioncoefficients of the erbium metastable level have been recov-ered to yield the experimentally measured signal output powerfor different input pump current and doses. In this applica-tion, only five parameters have been considered since, on thebasis of a preliminary investigation, it was observed that inthe considered amplifier configuration a quite wide variationfrom literature values of both the 4I9/2 and the 4I15/2 life-times, the C14 cross relaxation coefficient and the C3 upconver-sion coefficient affect the amplifier performance weakly. There-fore, the values τ43 = 0.1 μs, τ32 = 10 μs, C14 = 10−24 m3/s,C3 = 5 × 10−23 m3/s have been taken into account, deriving
MESCIA et al.: OPTIMIZATION OF THE DESIGN OF HIGH POWER Er3 + /Yb3 + -CODOPED FIBER AMPLIFIERS 3100108
Fig. 3. Schematic experimental setup used for the characterization ofEr3+ /Yb3+ -codoped fiber amplifier.
them from the literature [17]–[19]. Finally, the following fitnessfunction has been considered:
f (xi) =18∑
k=1
(Pk − Pk
i
)2(17)
where xi = [τ21 , τ65 , Cup ,Ktr ,Ktr1 ]T , with i = 1, 2, . . . N ,
Pki is the output power corresponding to ith particle evaluated
by using the rate equation model and Pk is the measured outputpower. The parameters used in PSO algorithm are the popu-lation size N = 40, the iteration limit equal to 100, φ1 = 2.8and φ2 = 1.3. These parameters, have been chosen in order toobtain a sufficient exploration of the solution space and a lowercomputational time. In this case, the PSO algorithm has beenset to find the minimum value of the fitness function (17). Thesummation extends from 1 to 18 because the measured data setis composed by 18 measures of the output power. Moreover, themeasured output power data have been obtained by changingthe input pump power only and using an input signal power of10 mW. The experimental setup used to characterize the perfor-mance of the amplifier based on the tested fiber is illustrated inFig. 3. It allows to monitor the gain value and spectral depen-dence of the amplifier as well as the main characteristics of thepump and signal wavelengths and this both before, during andafter irradiation of the sole fiber with γ-rays. As input data, itwas necessary to evaluate the RIA at the pump and signal wave-length. This was achieved with another setup basing the spectralattenuation measurements in the domains of interest on the clas-sical cut–back technique, allowing to distinguish between thecore and cladding contributions by changing the injection con-ditions. The losses α(λp) = α(λs) = 0.04 dB/m, for pristinesample, and α(λp) = 1.6 dB/m and α(λs) = 0.45 dB/m, for 40krad irradiated one, have been evaluated with this technique.Previous radiation effects investigations [1], [2] pointed out thatthe amplifier degradation can be roughly explained by the in-crease of the attenuation with irradiation dose at the pump andsignal wavelengths. The spectroscopic properties of the rare-earth are less affected by radiations at least for this kind ofoptical fibers. A possible way to harden the fiber by varying itscomposition is to incorporate another chemical element like Ce
TABLE IIIMEAN VALUES AND STANDARD DEVIATIONS OF THE RECOVERED
PARAMETERS VIA THE PSO ALGORITHM
Fig. 4. Output signal power versus input current for pristine and 40 kradirradiated sample: experimental results (dash curve), numerical results (fullcurve).
that decreases the number of point defects and then the inducedloss levels [1].
The PSO numerical code has been evaluated by 20 inde-pendent runs and Table III reports the average values and thestandard deviation of the recovered parameters. In order to eval-uate the accuracy of these values, the output signal power fordifferent values of input current has been calculated and com-pared with the experimental ones. From the result summarizedin Fig. 4, it can be drawn that the developed PSO algorithmmakes possible a well reproduction of the fiber amplifier per-formance before and after the 40krad irradiation, this dose levelcorresponding to the one associated with today space missions.It is worthwhile to note that more accurate results have beenobtained for the irradiated sample. This occurrence is due to themore nonlinear behavior of the fitness function of the irradiatedsample with respect to the pristine one. In fact, if the fitnessfunction shows a quite constant slope, a number of very similargain curves can be associated to different solutions because thevalues of the fitness function result in a reduced range. On thecontrary, if the fitness function presents more nonlinear trendthe probability to obtain multiple solutions decreases.
On the basis of the previous calculations, further simulationshave been conducted in order to evaluate the behavior of thepristine and irradiated fiber amplifier. In particular, the PSOalgorithm has been employed in the optimization of the designto obtain values of parameters maximizing special amplifiercharacteristics [20]. A figure of merit for power amplifiers isthe power conversion efficiency (PCE), especially consideringthe space mission constraints. It quantifies the capability of
3100108 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014
Fig. 5. (a) Maximum PCE and corresponding (b) fiber length, (c) input signalpower, (d) total input pump power versus the fiber core radius for the pristinefiber: forward (full curve), backward (dash curve) and bidirectional (dot curve)pumping.
the amplifier to convert pump photons into amplified signalphotons. To this aim, the function describing the PCE has beenused as the fitness function, whereas fiber length (L), input pump(Pp(0)) and signal (Ps(0)) powers constitute the parameters tobe optimized. In this case, the considered fitness function is
f (xi) =λs
λp
P is (0)
(Gi − 1
)
P ip (0)
(18)
where xi = [L,Ps(0), Pp(0)]T , with i = 1, 2, . . . N , Gi is theoptical gain corresponding to i-th particle evaluated by usingthe rate equation model. The behavior of the fiber amplifier isrepresented in Fig. 5, where the results refer to 20 indepen-dent runnings of the PSO numerical code. Fig. 5(a) reports thecalculated maximum PCE versus the fiber radius for the for-ward (full curve), backward (dash curve) and bidirectional (dotcurve) pumping configurations. Figs. 5(b)–5(d) show the fiberlength, input signal power and total input pump power maxi-mizing the PCE. It can be observed that for all the pumpingconfigurations an improvement of about 40% in the maximumPCE is obtained by changing the fiber core radius from 1.5to 3.5 μm. The backward and bidirectional pumping schemesare more efficient than the forward one. Nevertheless, a longerfiber is required, the backward pumping scheme is the best onesince it allows a very high PCE with lower input pump andsignal powers. The same simulations have been performed forthe fiber amplifier after the 40 krad irradiation and the obtainedresults are represented in Fig. 6. It can be observed that for allthe pumping configurations the maximum PCE correspondingto the fiber core radius of 3.5 μm is almost five times higherthan the one calculated with core radius of 1.5 μm. Also in thiscase, the backward and bidirectional pumping schemes are moreefficient than the forward one. When the core radius of 3.5 μmis considered a multi–mode propagation at signal wavelength
Fig. 6. (a) Maximum PCE and corresponding, (b) fiber length, (c) input signalpower, and (d) total input pump power versus the fiber core radius for the 40 kradirradiation: forward (full curve), backward (dash curve) and bidirectional (dotcurve) pumping.
occurs. So, by the numerical estimation of the transverse modedistribution the core overlap factor has been evaluated. In par-ticular, values of 0.872 and 0.493 have been calculated for thefundamental core mode and high–order mode overlap factor, re-spectively. The obtained results highlight that the fundamentalmode is well guided and the majority of the high-order mode isdistributed outside the core. Thus, also for core radius of 3.5 μmthe fiber can be considered effectively single–mode [21]–[23].
However, with respect to the pristine case, the irradiation i)strongly reduces the maximum PCE, the fiber length, the inputpump and signal powers, ii) better equalizes the variation of thefiber length, input pump and signal powers as the fiber radiuschanges from 1.5 μm to 3.5 μm. As a consequence, the obtainedresults highlight that the amplifier should not be optimized be-fore irradiation, as usually done, and the impact of the radiationlosses has to be taken into account.
IV. CONCLUSION
In this paper, a novel numerical code based on PSO and rateequations model has been developed for the design and charac-terization of Er3+/Yb3+ -codoped radiation-hardened fiber am-plifiers. The proposed PSO approach finds solutions which arein accordance with the experiments before and after 40 kradirradiation thus allowing the estimation of direct and inverseenergy transfer coefficients, upconversion coefficients and en-ergy level lifetimes by making use of simple measurements ofoutput signal powers at different input pump powers and dose.Moreover, the proposed PSO algorithm has been employed use-fully to optimize the amplifier performance evaluating the fiberlength, input pump and signal power, which maximize the PCE.In particular, the numerical results highlights that the maximumPCE can be improved of about 40% by enlarging the fiber coresize from 1.5 μm to 3.5 μm. The impact of the radiation on
MESCIA et al.: OPTIMIZATION OF THE DESIGN OF HIGH POWER Er3 + /Yb3 + -CODOPED FIBER AMPLIFIERS 3100108
the amplifier performance has been investigated, too. In par-ticular, a reduction of the maximum PCE, fiber length, inputpump, and signal powers has been calculated with respect to thepristine amplifier. The obtained performance points out that theproposed method can be considered an useful and interestingalternative to provide an understanding of the optical amplifierbehavior and to predict the optimal parameter values in a largevariety high power Er3+/Yb3+ -codoped fiber amplifiers config-urations, especially to consider the constraints related to spacemissions like radiations and limited resources for pumping.
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Luciano Mescia received the Master’s degree in electronic engineering in 2000and the Ph.D. degree in electromagnetic fields in 2003. In January 2005, hejoined Politecnico of Bari as an Assistant Professor. His research interestsinclude theoretical aspects for the development of artificial neural networks, ge-netic algorithm, and swarm intelligence applied to rare earth doped fiber lasersand amplifiers. He is performing studies regarding the design of innovativeantenna array for energy harvesting applications, the analysis and synthesis ofnovel dielectric lens antennas operating in the microwave and millimeter fre-quency range, and the development of novel FDTD schemes based on fractionalcalculus. He has cooperated with many national and international research in-stitutions and he joined several research projects with academic and industrialpartners. His research work has resulted in more than 100 publications in scien-tific and engineering peer-reviewed journal, leading international conferences,lectures and invited papers. Dr.Mescia is a member of Italian Society of Opticsand Photonics (SIOF-EOS) and Italian Society of Electromagnetism (SIEm).
Sylvain Girard (M’05–SM’11) received the Master’s degree, the Ph.D. degreeand his Accreditation for Research Direction from Saint-Etienne University,France, in 2000, 2003, and 2010 respectively. He joined the Commissariatl’Energie Atomique (CEA) in Arpajon, France, as a Postdoctoral Fellow, wasrecruited in 2004 and became a senior member of the technical staff. He wasdirectly in charge of studies regarding the vulnerability and radiation harden-ing of optical components, more specifically fiber optics and image sensors forthe French Laser Mgajoule project devoted to fusion studies by inertial con-finement. In 2012, he joined the Saint-Etienne University as a Full Professorat Laboratoire Hubert Curien, UMR CNRS, France. His main research inter-est include the development of a coupled simulation/experiments approach tobuild predictive models for the behavior of optical materials and components inharsh environments associated with space, nuclear industry, fusion facilities, ornuclear waste storages. Dr. Girard has served the radiation effects communitywithin IEEE NPSS through different roles at RADECS and NSREC confer-ences, e.g., being elected as a Junior Member of the IEEE Radiation EffectsSteering Group since 2013. Since 2008, he served as one of the Associate Editorsfor IEEE TRANSACTIONS ON NUCLEAR SCIENCE. He has authored or coauthoredtwo patents, more than 95 journal papers, and one book chapter. He received the2013 IEEE Early Achievement Award. “For contributions to the understandingof radiation effects on fiber optics and fiber sensors and their integration in harshenvironments.”
3100108 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014
Pietro Bia received the Bachelor’s and Master’s degrees, in 2008 and 2010, re-spectively. In 2008, he received the best Italian geoscience and remote sensingthesis prize form IEEE GRSS Italian Chapter. During 2011, he received a Schol-arship for post graduate research activities for the topic Design of innovativecladding-pumped fiber lasers, nonlinear effects induced by high optical powerdensity, and microsphere laser. In 2011, he attended a Master II level coursefrom Universit degli studi di Bari on Technologies for space remote sensing.He is currently working toward the Ph.D. degree from Politecnico di Bari andhis research activity is focused on the analysis of dielectric lens antennas formicrowave application and FDTD modeling for PEF propagation in complexdispersive media. He is a member of Italian Society of Optics and Photonicsand Italian Society of Electromagnetism.
Thierry Robin received the B.Sc. degree in chemistry and physics from theUniversity of Rennes 2 and studied management within the Alcatel group in-ternal training programs. He started his carrier as a Research Assistant at theSpace Vacuum Epitaxy Center, a NASA funded Center for the CommercialDevelopment of Space based at the University of Houston, Texas, where he wasinvolved in the development of a Laser ablation technique for thin film depo-sition of YBCO high temperature superconductors. He held that position from1988 through 1991 under the supervision of Dr. R. Sega, later to become anAstronaut and former Under Secretary of the US Air Force. He joined Alcatel’ssubmarine optical fiber R&D group in 1992 where he held his first position inthe Optical fiber business as an MCVD Process Specialist. Within the Alca-tel group, he held several positions in R&D, industrialization, and productionfor both singlemode and multimode optical fibers. One of the most challengingtask consisted in the development of a large capacity multimode preform processbased on the furnace CVD technology with plasma overcladding. In 2000, hejoined a then start–up, Highwave Optical Technologies, where he was in-chargeof production and development of specialty optical fibers, such as rare-earthdoped, double clad, polarization maintaining fiber. He co-founded iXFiber infebruary 2006, where he serves as the Chief Technology Officer.
Arnaud Laurent received the Graduation degree from National School of Ap-plied Science in Technology option Optronics. He started his carrier as a ProductManager at Pirelli Optical Systems and Cisco Systems on EDFAs for Telecomapplications. Three years later, he joined Highwave Optical Technologies as anEDFA Prototyping Manager and bench top product development activities. In2004, he joined Keopsys where he was in-charge of new product developmentand especially high power laser. Since 2008, he has been working as ProductLine Manager and Department Manager of subassemblies activity at iXFiber.He was involved in radiation hardening fiber development buy means of activetests of fibers in harsh environment.
Francesco Prudenzano received the Graduation degree in electronic engineer-ing from the University of Study of Bari in April 1990. Since 2003, he hasbeen an Associate Professor in electromagnetic fields at Politecnico di Bari. Hisresearch activity regards the integrated optics on lithium niobate, the fabricationof waveguides via ion-exchange technique, the modeling of nonlinear opticaldevices, photonic crystal fibers, photonic bandgap devices, lasers, and opticalamplifiers. He is a member of the Italian Society of Optics and Photonics–European Optical Society. He has coauthored more than 260 publications ininternational journals and conference proceedings, lectures, and invited papers.He is included in several research projects and is responsible for cooperationwith numerous international research institutions.
Aziz Boukenter received the Master’s degree in physics from Rabat University,Morocco, and the Ph.D. degree on the structure of amorphous and heterogeneousmaterials from Lyon University, France, in 1988. After a Postdoctoral position atthe University of Trento, Italy, on the spectral properties of transition metal ionsin the silica-based glasses, he joined the University of St-Etienne. His researchinterests include the relationship between the structural and optical propertiesof materials through the study of the formation and transformation mechanismsof point defects in harsh environments. He authored or coauthored more than140 journal papers.
Y. Ouerdane received the Ph.D. degree in atomic and molecular physics in1983, and the Doctorat dEtat Es-Sciences Physique in 1986 from Lyon Univer-sity. Until 1992, his research was focused on the interaction of highly chargedion beams with different solid or gas targets; multi-collision processes, multi-capture phenomenon, the generation of high Rydberg ions, optical propertiesof multicharged particles were his main research domains. In 1994, he was aFull Professor at Saint-Etienne University. Since then he has managed and leadresearch in optical fibers at Hubert Curien Lab (a mixed research lab at theUniversity Jean Monnet and the French National Research Center CNRS). Hehas directed many Ph.D. students and published more than 130 papers in inter-national reviews. Over the last few years, his research activities have focusedon the optical material properties and responses in harsh environments.
