ARTICLE IN PRESS

Optics & Laser Technology 41 (2009) 99– 106

Contents lists available at ScienceDirect

Optics & Laser Technology

0030-39

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/optlastec

Feasibility of Er3+-doped, Ga5Ge20Sb10S65 chalcogenide microstructuredoptical fiber amplifiers

M. De Sario a, L. Mescia a, F. Prudenzano b,�, F. Smektala c, F. Deseveday d, V. Nazabal d,J. Troles d, L. Brilland e

a DEE-Dipartimento di Elettrotecnica ed Elettronica Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italyb DIASS-Dipartimento di Ingegneria dell’Ambiente e per lo Sviluppo Sostenibile, Viale del Turismo 8, 74100 Taranto, Italyc Institut Carnot de Bourgogne UMR 5209 CNRS-Universite de Bourgogne Dpt OMR/Equipe SLCO, 9 Av. Alain Savary, BP 47870, 21078 Dijon, Franced Sciences Chimiques de Rennes, UMR 6226 CNRS-Universite de Rennes 1, Equipe Verres et Ceramiques, Campus de Beaulieu, 35042 Rennes cedex, Francee Perfos, 11 rie Lois de Broglie, 22300 Lannion, France

a r t i c l e i n f o

Article history:

Received 15 November 2007

Received in revised form

11 March 2008

Accepted 17 March 2008Available online 27 May 2008

Keywords:

Fibers

Rare-earth-doped materials

Optical amplifiers

92/$ - see front matter & 2008 Elsevier Ltd. A

016/j.optlastec.2008.03.007

esponding author. Tel.: +39 080 5963781; fax

ail address: prudenzano@poliba.it (F. Prudenz

a b s t r a c t

The feasibility of a microstructured optical fiber (MOF) amplifier, made of a novel Er3+-doped

chalcogenide glass, has been demonstrated via accurate simulations performed by employing an

oppositely implemented computer code. The optical and geometrical parameters measured on the first

MOF sample together with other physical constants from literature have been taken into account in the

simulations. The calculated optical gain of the optimized MOF amplifier, 2.79 m long, is close to 23 dB at

the signal wavelength of 1.538 mm, by using a pump power of 200 mW and a signal power of 0.1 mW.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The development of ever more efficient rare-earth (RE) dopedfiber amplifiers and lasers has revolutionized the optical commu-nication systems and has extended the optical active deviceapplications over several industrial areas. Many different rare-earth elements, such as erbium, ytterbium, praseodymium,neodymium, samarium, and thulium, can be used to fabricatefiber amplifiers operating at different wavelengths. In particular,erbium-doped fiber amplifiers (EDFAs) are nowadays available forlong-haul communication systems, allowing to replace theelectronic regenerators. After the spreading of the EDFAs basedon silica glass, different glass types have been synthesized in orderto obtain novel and higher performance host materials.

In recent years, chalcogenide glasses have been proposed aspotential host materials for RE-doped lasers and amplifiers [1].These glasses are characterized by large absorption and emissioncross-sections of rare-earth ions, exhibiting high refractive index.Other important chalcogenide glass features are: the absence ofhigh-energy phonons in vibrational spectrum and the lowprobability of multiphonon relaxation of rare-earth ions. Theaforesaid glass properties increase the efficiency of transitions

ll rights reserved.

: +39 080 5963410.

ano).

among rare-earth energy levels in comparison with silica andfluoride glasses and, moreover, enhance other radiative transitionsthat allow different amplification effects in the IR region [2].Another chalcogenide glass property useful to fabricate efficientEDFAs is the capability, for several vitreous compositions, to hosthigh dopant concentration, without ion clustering and concentra-tion quenching effects. All these properties added to thefabrication relative easiness make chalcogenide glasses veryattractive materials to be doped with erbium.

The optimization of EDFA transversal section is crucial toimprove optical gain, because the fiber geometry strongly affectsthe overlap of the pump and the signal propagation modes withthe doped core. Sophisticated design methods and fabricationtechniques have been developed to construct single-modechalcogenide optical fiber amplifiers; to this aim a fine controlof refractive index is needed. Unfortunately, a very large effectivemode area is difficult to obtain in a single-mode conventionalfiber [3]. In order to overcome these difficulties, the use ofmicrostructured optical fibers (MOFs) is a feasible and attractivesolution. In fact, the air holes running along MOF length enablethe achievement of the well-known surprising characteristicssuch as: endlessly single-mode guidance [4], controllable chro-matic dispersion [5], high birefringence [6], large mode area [7],supercontinuum generation [8], and low bending losses [9].

In recent literature, only a few papers pertaining to chalco-genide MOFs are reported.

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M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106100

In this paper, a MOF made of a novel, Er3+-doped, Ga5-

Ge20Sb10S65 chalcogenide glass is designed in order to obtain ahigh-performance optical amplifier in the third band of fiber opticcommunication. The design is realistically performed, on the basisof the optical and spectroscopic parameters measured onpreviously fabricated solid core microstructured fiber [3]. Adedicated numerical code that solves the rate equations and thepower propagation equations has been developed. The modeltakes into account the effects of ground-state absorption (GSA) atboth pump and signal wavelengths, the stimulated emission ofthe signal (SE), and the amplified spontaneous emission noise(ASE). The effects of cross-relaxation, up-conversion and excitedstate absorption (ESA) at pump wavelength have been accuratelyconsidered.

A number of simulations have been performed in order toevaluate the actual feasibility of the erbium-doped chalcogenideMOF amplifiers and with the aim to optimize the physical andgeometrical parameters of the preliminary samples [3]. Thefeasibility of the Er3+-doped, Ga5Ge20Sb10S65 MOF amplifier hasbeen demonstrated for the first time, to the best of our knowledge.Among the advantages related to the use of Er3+-doped,Ga5Ge20Sb10S65 chalcogenide glass (with respect to the conven-tional glasses) there is the prospective to construct a MOFamplifier which could operate at wavelengths larger than theconventional 1.55 mm: the wavelengths in addition or alternativeto this could be obtained by using more or different pumpwavelengths.

The paper is organized as follows: Section 2 reports a brieftheory on erbium-doped devices and the employed model;Section 3 shows the numerical results; Section 4 gives theconclusion.

2. Theory

The Er3+ ion system in the chalcogenide glasses is quitecomplex because many processes are involved [10]. The mostimportant ion transitions among the energy levels are shown inFig. 1. By using a pump beam at the wavelength lp ¼ 0.98 mm, thetypical behavior of the three-level laser systems occurs. Inparticular, the ions at the ground-state level 4I15/2 are excited tothe level 4I11/2, the GSA cross-section having a peak at thiswavelength. The decay to the metastable level 4I13/2 induces thepopulation inversion phenomenon. The power enhancement ofthe signal, via the 4I13/2-

4I15/2 transition, occurs close to thewavelength ls ¼ 1.538 mm, where the peak of the emissionspectrum takes place [10]. The other physical phenomena takeninto account in our model are the ion–ion interactions of Er3+ ion

Fig. 1. Energy levels diagram of Er3+ ion transitions.

pairs which affect the optical amplifier performance: the cross-relaxations (4I9/2,4I15/2)-(4I13/2,4I13/2), the pump up-conversions(4I11/2,4I11/2)-(4F7/2,4I15/2), the signal up-conversions (4I13/2,4I13/

2)-(4I9/2,4I15/2), and the pump excited state absorption (ESA), 4I11/

2-4F7/2. The quantum noise due to amplified spontaneous

emission (ASE) is considered, too. The MOF amplifier is simulatedby solving the nonlinear differential system constituted by

(i)

the rate Eq. (1):

�WGSAp N1 �WGSA

s N1 þWSEs N2 þ

N2

t21þ CupN2

2 þ C3N23

� C14N1N4 �WAASEN1 þWE

ASEN2 ¼ 0

WGSAs N1 þ

N3

t32�WSE

s N2 �N2

t21� 2CupN2

2 þ 2C14N1N4

þWAASEN1 �WE

ASEN2 ¼ 0

WGSAp N1 �

N3

t32�WESA

p N3 þN4

t43� 2C3N2

3 ¼ 0 (1)

�N4

t43þ

N5

t54� C14N1N4 ¼ 0

N1 þ N2 þ N3 þ N4 þ N5 ¼ NEr

in which the ion populations Ni, i ¼ 1,2, y, 5 of the energylevels are expressed as functions of the transition ratespertaining to: the GSA of the pump Wp

GSA and the signal WsGSA,

the signal stimulated emission WsSE, and both the emission (E)

and absorption (A) transition rates WASEE/A of the ASE;

(ii)

the propagation Eq. (2) of powers along the fiber longitudinalz-axis, for signal Ps and pump Pp:

dPs

dzðz; vsÞ ¼ ½sEðvsÞn2ðz; vsÞ

� sAðvsÞn1ðz; vsÞ�Psðz; vsÞ � aðvsÞPsðz; vsÞ (2)

dPp

dzz; np

� �¼ � sA np

� �n1 z; np

� �þ sESA np

� �n3 z; np

� �� �� Pp z; np

� �� a np

� �Pp z; np

� �where sA, sE and sESA are the absorption, emission and ESAcross-section, respectively. The overlap integral among thenormalized signal mode intensity and the population con-centrations of the energy levels ni, i ¼ 1, 2, 3 is

niðz; nÞ ¼ZZ

S

Niðx; y; zÞ Eðx; y; nÞ�� ��2 dx dy (3)

where S is the surface of the doped region and E(x,y,n) is thetransversal electric field profile at frequency n;

(iii)

the propagation Eq. (4) of the power spectral density of theforward, SASE

+ , and backward, SASE� , ASE noise due to the

amplified spontaneous emission (ASE) [10]:

dSþASE

dzz; nð Þ ¼ ½sEðnÞn2ðz; nÞ � sAðnÞn1ðz; nÞ�S

þ

ASEðz; nÞ

þ 2hnsEðnÞn2ðz; nÞ � aðnÞSþASEðzÞ (4)

dS�ASE

dzðz; nÞ ¼ � sEðnÞn2ðz; nÞ � sAðnÞn1ðz; nÞ½ �

� S�ASEðz; nÞ � 2hnsEðnÞn2ðz; nÞ þ aðnÞS�ASEðzÞ

ARTICLE IN PRESS

Fig. 2. Sketch of the proposed MOF. A quarter of the MOF is used in the

simulations.

Table 1Measured optical parameters of chalcogenide glass

Parameter Value Unit

Refractive index n at 632 nm 2.361375.90325e�4 –

Refractive index n at 820 nm 2.302575.75625e�4 –

Refractive index n at 1304 nm 2.259375.64825e�4 –

Refractive index n at 1540 nm 2.2575.625e�4 –

Glass density 3.2 g/cm3

Fig. 3. Three-dimensional plot of the fundamental mode HE11 at the wavelength

l ¼ 1.55 mm.

M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106 101

The set of differential equations is nonlinear due to the ion–ioninteraction equations; it has been numerically integrated via aniterative procedure based on Runge-Kutta method, accuratelyoptimized in order to reduce the computational time [11].

The electromagnetic field profile has been calculated via anefficient full-vectorial solver based on the finite element method(FEM) [12].

The symmetry analysis [13] allows adopting useful strategiesin order to minimize the computation time required by thenumerical investigation of optical waveguides having sophisti-cated cross-sections. In particular, the following steps have beenperformed: (a) classification of the MOF propagation modes, themode classes being defined on the basis of modal electromagneticfield symmetries; (b) determination of mode class degeneracy; (c)investigation of the azimuthal symmetries of the modal EM fieldfor each mode class and (d) identification of the minimum sectorof MOF cross-section allowing the complete propagation modeinvestigation [13]. By following the aforesaid symmetry theory,our MOF belongs to the C6u symmetry family. Moreover, toinvestigate the HE11 fundamental mode, only a quarter of the MOFcan be considered in the electromagnetic investigation [13] byapplying suitable perfect electric conductor (PEC) and perfectmagnetic conductor (PMC) boundary conditions.

To calculate the confinement losses of the propagation modes,the quarter of MOF has been surrounded by anisotropic perfectlymatched layers (PMLs) having appropriate physical parametersand geometry as shown in Fig. 2.

3. Numerical results

The numerical investigation has been aimed towards the testof Ga5Ge20Sb10S65 chalcogenide glass feasibility for the construc-tion of optical amplifiers in the third window of fiber opticcommunication. In order to carry out a realistic design, thesimulations have been performed by taking into account apreliminary MOF sample previously constructed and character-ized [3] but not yet optimized for optical amplification.

The refractive index wavelength dispersion of the Ga5-

Ge20Sb10S65 chalcogenide glass has been expressed via theSellmeier equation

n2 lð Þ ¼ aþbl2

l2� c2þ dl2 (5)

where l is expressed in microns, and the interpolating constantsa ¼ 3.883, b ¼ 1.164, c ¼ 0.3552 and d ¼ �0.02094 have beenoptimized to match the measured values, reported in Table 1.

Fig. 2 shows a quarter of MOF section, including the PMLs. Thesuitable PML parameters allowing the correct simulation are thefollowing: thickness t1 ¼ t2 ¼ 12mm, conductivity sPML ¼ 105 S/mand computation domain w ¼ 48 mm. The MOF section has threerings of air holes surrounding the solid core, the geometricalparameters are the following: hole-to-hole spacing (or pitch)L ¼ 8mm, hole diameter d ¼ 3.2 mm. The MOF-doped regionradius is Rd. A detailed MOF description is reported in [3]. Theconfinement losses [5], CL, have been calculated versus thewavelength l: their value at pump lp ¼ 0.98mm and signalls ¼ 1.538 mm wavelengths are CL ¼ 2.25 and 5.15 dB/km, respec-tively.

Fig. 3 illustrates a three-dimensional plot of the normalizedoptical power versus the transversal x, y rectangular coordinates:the effect of the first ring of air holes is apparent.

In order to evaluate the amplifier performance, the numericalsolution of the rate equations and power propagation equationsystem is searched by considering K ¼ 150 wavelength samples ofthe emission and the absorption cross-sections, measured for aquite similar glass in [10], in the range from 1.450 to 1.599 mm. Inthe calculation, the decay 4F7/2-

4I9/2 has been considered asimmediate, i.e. t54 ¼ 0 and the 4F7/2 ion population negligible. Theparameter values employed in the simulation are: emission andabsorption cross-sections sE ¼ 3.84�10�25 m2 and sA ¼ 4.78�10�25 m2 at pump wavelength, overall loss of the fundamentalpropagation mode as ¼ 2 dB/m at signal wavelength ls ¼ 1.538 mmand, ap ¼ 3 dB/m at pump wavelength lp ¼ 0.980 mm, erbium

ARTICLE IN PRESS

Fig. 4. (a) Optimal gain Gopt, (b) optimal length Lopt, (c) noise figure F versus doped region radius Rd for three different input pump power levels: Pp(0) ¼ 100 mW (dot

curve), Pp(0) ¼ 200 mW (dash curve), Pp(0) ¼ 300 mW (full curve). Input signal power Ps(0) ¼ 0.1 mW and erbium concentration NEr ¼ 5.76�1024 ions/m3.

M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106102

concentration NEr ¼ 0.05% (wt%) (i.e. NEr ¼ 5.76�1024 ions/m3),lifetimes t21 ¼ 4 ms, t32 ¼ 1.29 ms, t43 ¼ 53ms. The numericalvalues of the parameters pertaining to the ion–ion interactionsCup ¼ 3�10�23 m3/s, C3 ¼ 2�10�23 m3/s, C14 ¼ 5�10�24 m3/s aretaken from the data reported in the literature [10].

Fig. 4(a) shows the variation of optimal gain Gopt, calculated forthe optimal fiber length Lopt (i.e. the length for which maximumgain occurs), versus the radius of the doped region Rd into thefiber core, for different input pump powers: Pp(0) ¼ 100 mW (dotcurve), Pp(0) ¼ 200 mW (dash curve) and Pp(0) ¼ 300 mW (fullcurve). The input signal power is Ps(0) ¼ 0.1mW and the relativehole size value is d/L ¼ 0.4. The optimal gain increases byincreasing the core radius, for all the three different curves.Nevertheless, when the value of the Rd is larger than a value close5mm (it depends on the input pump power), the optimal gaindecreases.

Fig. 4(b) depicts the variation of the optimal length Lopt withrespect to the radius of the doped region Rd for three differentinput pump powers Pp(0) ¼ 100 mW (dot curve), Pp(0) ¼ 200 mW(broken curve) and Pp(0) ¼ 300 mW (full curve). The optimallength shows a peak close to Rd ¼ 2.5 mm, in all the three cases. Inparticular, the value of optimal length peak is Lopt ¼ 4.19 m (fullcurve), Lopt ¼ 3.62 m (broken curve) and Lopt ¼ 2.66 m (dot curve);then the optimal length decreases by increasing the radius ofdoped region. By the investigation of Fig. 4(a) and (b), it isworthwhile to notice that the maximum values of optimal gainand optimal length occur for two different values of doped regionradius Rd. This permits to design a high-performance MOFamplifier having compact sizes.

In order to evaluate the influence of the quantum noise on theamplifier performance, the noise figure, calculated for the optimal

length Lopt, has been investigated by taking into account theexpression derived from the linear theory of ASE noise [14]:

F ¼1

Gopt

SþASEðns; LoptÞ

hnsþ 1

� �(6)

where SASE+ (ns, Lopt) is the power spectral density of the forward

ASE noise, Gopt the MOF optimal gain and Lopt the optimal length.Fig. 4(c) shows the variation of noise figure F versus the radius

of the doped region Rd, for different input pump powers:Pp(0) ¼ 100 mW (dot curve), Pp(0) ¼ 200 mW (broken curve),and Pp(0) ¼ 300 mW (full curve). The noise figure increases untilthe doped region radius Rd is equal to about 1.8mm because of theoptimal fiber length increasing and the low optimal gain. Then thenoise figure decreases until Rd ¼ 4.5mm. For higher values ofdoped region radius Rd the noise figure increases again becauseboth the optimal fiber length and optimal gain slightly decrease.Thus the MOF amplifier exhibiting good performance could beobtained by employing pump power close to Pp(0) ¼ 300 mW orPp(0) ¼ 200 mW and a value of the doped region radius close toRd ¼ 5 mm. In fact, these values allow obtaining a high optimalgain and a low noise figure also using a MOF with limited length(see Fig. 4(b)).

It is worthwhile to note that the erbium doping levelNEr ¼ 0.05% (wt%) could seem so low. This choice is wellaccounted by Fig. 5, where the optimal noise figure versus theerbium concentration is illustrated for different input pumppowers. The minimum of the optimal noise figure is obtainedclose to the aforesaid erbium concentration for all the threeconsidered cases. Moreover, this reduced concentration valueallows to avoid the visible upconversion, which can be high in lowphonon-energy glass.

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Fig. 5. Noise figure F versus erbium concentration NEr for three different input

pump power levels: Pp(0) ¼ 100 mW (dot curve), Pp(0) ¼ 200 mW (dash curve),

and Pp(0) ¼ 300 mW (full curve). Input signal power Ps(0) ¼ 0.1 mW.

M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106 103

The pump powers and the fiber lengths considered in theprevious simulation are feasible also with reference to thenonlinear effects which can occur in chalcogenide glass. In fact,the light intensity dependence of the refractive index can bewritten as

nðlÞ ¼ n0ðlÞ þ DnðlÞ

¼ n0ðlÞ þ n2ðlÞI ¼ n0ðlÞ þn2ðlÞP

Aeff(7)

where n0 is the linear part of the refractive index, I is the opticallight intensity, Aeff is the effective area [15], Dn is the nonlinearrefractive index perturbation, P is the power launched into thefiber. The core diameter strongly affects the strength of thenonlinear effects, which can be minimized by increasing the corediameter. In our design the nonlinear effects are negligiblebecause of the large size of the active core. In fact, by consideringthat at the pump wavelength the nonlinear refractive index isn2 ¼ 0.7�10�18 m2/W [16], the effective area is Aeffffi90.9mm2 andthe nonlinear refractive index variation for a pump power P ¼ 1 Wis Dnffi7.7�10�9. The self-phase modulation and the other Kerrnonlinearities occurring in a few meters of the designed fiber arenegligible. As an example, the nonlinear phase change over a fiber1 m long is g ¼ (2p/lp)n2/Aeffffi49.36�10�3 W�1 m�1 [15].

The above analysis is also performed for three different valuesof the input signal power Ps(0) ¼ 0.1mW, Ps(0) ¼ 10 mW, andPs(0) ¼ 1 mW and the input pump power is Pp(0) ¼ 200 mW.The behavior of MOF optimal gain is shown in Fig. 6(a). Theoptimal gain G steeply increases by increasing the doped regionradius, showing a peak close to Rd ¼ 5 mm. More precisely, theoptimal gain peak is Gopt ¼ 23.01 dB (full curve), Gopt ¼ 20.34 dB(broken curve), Gopt ¼ 8.06 dB (dot curve). Then the gaindecreases because the erbium ions are less efficiently inverted.It is worthwhile to note that the maximum value of optimal gainoccurs for the lowest input signal power Ps(0) ¼ 0.1 mW. In fact,higher signal power value implies the ion population depletion ofthe metastable level 4I13/2 and the reduction of Gopt. For the inputsignal power Ps(0) ¼ 1 mW the amplifier operates in saturationregime.

Fig. 6(b) depicts the variation of optimal length Lopt withrespect to the radius of the doped region Rd for the three different

input signal powers. The optimal MOF configuration for an inputsignal power Ps(0) ¼ 0.1mW, having a doped region radius Rd ¼ 5mm, and an optimal length Lopt ¼ 2.79 m, exhibits an optimal gainclose to Gopt ¼ 23.01 dB. Fig. 6(c) shows the noise figure versus thedoped region for different input signal power Ps(0).

By the inspection of the previous figures, the doped regionradius Rd ¼ 5 mm seems a good design choice because the gainis maximized (see Fig. 4(a)), the MOF amplifier is compact(see Fig. 4(b)), and the noise figure is reduced (see Fig. 4(c)).The radius Rd ¼ 5 mm is suitable also for all the considered inputsignal power, too. Moreover, from the point of view of theelaboration of the MOF, this value of the radius is easily achi-evable by the stack and draw process. Typically, the direct fiberingof a stack of tubes of 665 mm external diameters around a centralcore, under pressure control, leads to a core of about 10 mmdiameter. For smaller cores, it would be necessary to add astretching–jacketing step in the process, with a negative impacton losses.

The effect of the variation of the signal wavelength on theamplifier characteristics has been investigated, too. The signalwavelength has been changed in the range from ls ¼ 1.510 to1.595 mm. In particular, Fig. 7(a) shows the dependence of theoptimal gain Gopt as a function of the signal wavelength, forPp(0) ¼ 100 mW (full curve), Pp(0) ¼ 200 mW (broken curve), andPp(0) ¼ 300 mW. The input signal power is Ps(0) ¼ 0.1mW and thedoped region radius is Rd ¼ 5 mm. We note that the three curveshave a peak at the wavelength ls ¼ 1.538 mm, where the bestemission and absorption cross-sections occur. More precisely, thegain peak increases by increasing the input signal power, beingGopt ¼ 27.65 dB for Pp(0) ¼ 300 mW, Gopt ¼ 22.60 dB forPp(0) ¼ 200 mW, and Gopt ¼ 13.38 dB for Pp(0) ¼ 100 mW. TheMOF amplifier exhibits a flat-gain region close to ls ¼ 1.55mm. Thewavelength range of flat gain increases by decreasing the inputpump power Pp(0).

Fig. 7(b) shows the variation of the optimal length Lopt withrespect to the signal wavelength ls; for the three different inputpump powers, the input signal power is Ps(0) ¼ 0.1mW. Theoptimal length increases by increasing the pump power.

Fig. 7(c) shows the variation of noise figure F versus the inputwavelength ls, for different input pump powers Pp(0) ¼ 100 mW(dot curve), Pp(0) ¼ 200 mW (broken curve), and Pp(0) ¼ 300 mW(full curve). The maximum noise figure occurs for the wavelengthvalue for which the gain is minimum. Moreover, in the spectrumregion from 1.537 to 1.562mm, the noise figure F calculated for thesmallest pump power Pp(0) ¼ 100 mW (dot curve) exhibits thehighest value.

The input pump power Pp(0) ¼ 200 mW seems to be advanta-geous. In fact, for an input pump power Pp(0) ¼ 100 mW and inthe wavelength range from 1.537 to 1.562mm, we obtain a largerflat-gain wavelength region and a low optimal length, but thenoise figure is higher. For the input pump power Pp(0) ¼ 300 mW,instead, good performance in terms of gain and noise figure isachieved, even if the flat-gain region is reduced, and higheroptimal length is necessary.

The long lifetime of the 4I11/2 level limits the maximum signaloutput because the pump ESA can reduce the pumping efficiency.The deleterious action of ESA can be minimized by optimizing theglass composition; thus, a number of simulations have beenperformed to investigate the amplifier performances as a functionof ESA, i.e. glass composition.

Because ESA cross-section pertaining to our chalcogenide glasshas not yet been measured, in the simulations three differentcross-section values have been considered: ESA cross-sectionpertaining to a chalcogenide glass similar to that of the MOFunder investigation [10], an ESA value two times reduced,negligible ESA.

ARTICLE IN PRESS

Fig. 6. (a) Optimal gain Gopt, (b) optimal length Lopt, (c) noise figure F versus doped region radius Rd for three different input signal power levels: Ps(0) ¼ 1 mW (dot curve),

Ps(0) ¼ 10 mW (broken curve), and Ps(0) ¼ 0.1 mW (full curve). Input pump power Pp(0) ¼ 200 mW, erbium concentration NEr ¼ 5.76�1024 ions/m3.

Fig. 7. (a) Optimal gain Gopt, (b) optimal length Lopt, (c) noise figure F versus signal wavelength ls for three different input pump power levels: Pp(0) ¼ 100 mW (dot curve),

Pp(0) ¼ 200 mW (broken curve), and Pp(0) ¼ 300 mW (full curve). Input signal power Ps(0) ¼ 0.1 mW, erbium concentration NEr ¼ 5.76�1024 ions/m3 and doped region

radius Rd ¼ 5 mm.

M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106104

ARTICLE IN PRESS

Fig. 8. (a) Optimal gain Gopt, (b) optimal length Lopt, (c) noise figure F versus input pump power Pp(0) for three different ESA cross-sections: sESA ¼ 5�10�25 m2 (dot curve),

sESA ¼ 2.5�10�25 m2 (broken curve), and sESA ¼ 0 (full curve). Input signal power Ps(0) ¼ 0.1 mW, erbium concentration NEr ¼ 5.76�1024 ions/m3 and doped region radius

Rd ¼ 5mm.

M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106 105

Fig. 8a shows the variation of the optimal gain Gopt, i.e. the gainsimulated for the optimal fiber length Lopt (for which themaximum gain occurs), versus the input pump power Pp(0) forESA cross-section s35 ¼ 5�10�25 m2 (dot curve), s35 ¼ 2.5�10�25

m2 (broken curve) and without ESA s35 ¼ 0 (full curve); the inputsignal power is Ps(0) ¼ 0.1 mW. The ESA effect reduces the optimalgain Gopt because the transition 4I11/2-

4F7/2 partially absorbs thepump power. On the other hand, ESA effect at the pumpwavelength is very heavy because the energy level 4I11/2 isstrongly populated due to its long lifetime. In all the three cases,the threshold pump power is close to 13 mW. Thus the optimiza-tion of glass composition is strategic, also because the ESA cross-section could be larger than that reported in [10].

The optimal length and noise figure are affected by ESA at thepump wavelength, too. Figs. 8(b) and (c) show the variation of theoptimal fiber length Lopt and noise figure F, respectively, versus theinput pump power Pp(0) for ESA cross-section s35 ¼ 5�10�25 m2

(point curve), 2.5�10�25 m2 (broken curve), and without ESAeffect (full curve). The results shown in both Fig. 8(b) and (c) canbe explained by considering that a higher ESA cross-sectionreduces both the pump power and the population inversion alongthe fiber length.

These results further encourage the efforts toward theimprovement of the Ga5Ge20Sb10S65 chalcogenide MOF. The MOFconstruction technology will be enhanced with the aim to reducethe high propagation losses measured on the first samples [3].Several parameters depending on the fabrication process of theMOF and leading to propagation losses have been identified. Wework actually on their control. If the propagation losses arereduced to the values considered in the simulation, then the MOFamplifier will be fabricated.

4. Conclusion

The feasibility of an Er3+-doped, Ga5Ge20Sb10S65 MOF amplifier,having remarkable performances, has been demonstrated for thefirst time, to the best of our knowledge. To simulate the amplifierperformance, a homemade computer code has been refined takinginto account all the ion transitions and ion–ion interactions.

In the small signal operation and by using a pump power of200 mW, the chalcogenide MOF amplifier, having an optimallength of 2.79 m, shows a gain close to 23 dB. The excited stateabsorption (ESA) at the pump wavelength strongly influences theamplifier efficiency and gain as well as the optimal fiber length.The simulation, performed by using both MOF measured para-meters and other ones taken from literature, indicates that, after apreliminary and feasible glass optimization, the proposed fiberamplifier can become a good candidate in optical communicationnetworks and systems. Among the advantages of the use of Er3+-doped, Ga5Ge20Sb10S65 chalcogenide glass, with respect to theconventional glasses, there is the capability to operate at largerwavelengths in addition to 1.55 mm.

These results encourage further efforts toward the improve-ment of the chalcogenide MOF.

Acknowledgments

This work has been partially supported within the MIUR planD.M 593 8/8/00 prot. 5910 10/07/2003 (FIBLAS) and UIF-Galileo2007.

ARTICLE IN PRESS

M. De Sario et al. / Optics & Laser Technology 41 (2009) 99–106106

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