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Chun Jiang Vol. 26, No. 5 /May 2009/J. Opt. Soc. Am. B 1049

Modeling and gain propertiesof Er3+ and Pr3+ codoped fiber amplifier

for 1.3 and 1.5 �m windows

Chun Jiang

State Key Laboratory of Advanced Optical Communication Systems and Networks,Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China

(cjiang@sjtu.edu.cn)

Received July 21, 2008; revised December 23, 2008; accepted March 9, 2009;posted March 18, 2009 (Doc. ID 99175); published April 17, 2009

A detailed analysis is presented of the possibility of an Er3+ and Pr3+ codoped fiber as an amplifier for 1.3 and1.5 �m transmission windows. The numerical models with 1010/1480 nm and 986/1480 nm pump lasers areproposed, the rate and power propagation equations are solved numerically, and the dependence of the gains at1310, 1530, and 1600 nm windows on pump wavelength and power, active ion concentrations, and signal wave-length are calculated. The results show that with 1010/1480 nm pumps of 200/100 mW and with fixed Pr3+

and Er3+ concentrations at 8.0�1024 and 2.0�1024 ions/m3, the signals at 1310 and 1530 nm windows may beequally amplified with a gain of 26.0 dB in the active fiber with a length of 7.0 m, and with a 1480/986 nmpump power of 100/300 mW and Pr3+ and Er3+ ion concentrations of 2.0�1024 and 2.0�1024 ions/m3, the sig-nals at 1310 and 1530 nm may be nearly equally amplified with a gain of 8.0 dB in a 10.0 m long active fiber.© 2009 Optical Society of America

OCIS codes: 060.4510, 060.2320.

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. INTRODUCTIONecently, erbium/praseodymium codoped fiber amplifiers

or 1.31 and 1.53 �m windows have attracted more andore interest in the optical fiber communications area be-

ause the doubly doped fibers have broad emission spec-ra covering from 1250 to1400 nm and from450 to 1650 nm [1–5]. Though an erbium-doped fibermplifier was reported as having a 120 nm gain band-idth [6], its further extension becomes very difficult.imilarly, praseodymium codoped fiber amplifiers haveeen extensively researched in the past decade, but theirmplification is limited to the range of 1280–1350 nm.n the other hand, all-wave fibers in which OH

hydroxyl) groups are suppressed have low-loss band-idth from 1250 to 1650 nm with a loss of less than.70 dB/km and are very promising for metro-area net-orks and coarse wavelength division multiplexing

CWDM) system applications. However, optical amplifiersor all-wave fiber transmission systems are not available.urrently, the broadest fiber Raman amplifier just has36 nm of bandwidth [7,8], and promising fiber-opticalarametric amplifiers are being investigated. Rare-earth-oped fiber amplifiers, which have high gain and pump–ignal energy transfer efficiency, have been investigatedn the past decade. The energy transfers between Er3+

nd Pr3+ in chalcogenide, selenide, and fluoride glassesere studied through experiment [3] and theoreticalnalysis of simple rate and power propagation equationsith a single pump [2]. The results showed that the en-

rgy could transfer from the 4I11/2 and 4I13/2 levels of Er3+

ons to the 1G4 and 3F4 levels of Pr3+ ions, respectively.ut the numerical models including nonlinear terms in

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ate equations such as the up-conversion of Er3+ ions athe 4I13/2 level have not been reported.

In this work, we present numerical models consideringonlinear terms such as energy transfer and the up-onversion effect for an erbium/praseodymium codoped fi-er amplifier for 1310 and 1530 nm windows, and the ratend power evolution equations are solved. Based on theumerical analysis, the optimal erbium and praseody-ium codoping concentrations and the fiber length pump

ower are supposed in order to obtain equalized amplifi-ation of signals at both 1.3 and 1.5 �m windows.

. THEORETICAL MODELS. 1010/1480 nm LD Pumpsschematic of the energy levels and the transition con-

guration of an Er3+/Pr3+ doped system pumped withoth 1010 and 1480 nm laser diodes (LDs) are shown inig. 1. Under excitation of 1010 nm, the electron in theround state �3H4� of a Pr3+ ion is excited into the excitedtate �1G4�, from which the electron transits to the �3H5�evel with an emission of light at 1310 nm windows, thenelaxes into the ground state �3H4�. Meanwhile, with ex-itation of 1480 nm, the electron in the ground state4I15/2� of an Er3+ ion is excited into the metastable stateI13/2� and then transits from that state to the groundtate �4I15/2�, emitting light at 1530 nm windows. Therelso are some Er3+ ions where electrons in the excited andetastable states transfer into �1G4� and �3F4� states ofr3+ by a cross-relaxation process, respectively, and then

rom these states they transit into the 3H5 level and theround state, emitting light of 1310 and 1600 nm bands,

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1050 J. Opt. Soc. Am. B/Vol. 26, No. 5 /May 2009 Chun Jiang

espectively. Moreover, the electron at the metastabletate �4I13/2� of the Er3+ ion is excited to the 4I9/2 levelith the absorption of the photon at 1500 nm emitted by

he transition of the electron in another Er3+ ion from theI13/2 to 4I15/2 level. It then transits from the 4I9/2 to theI15/2 level with the emission of the photon at the 800 nmand. Additionally, there also are some Er3+ ions in whichhe electron in the 4I9/2 level is relaxed nonradiatively tohe 4I11/2 level and then to the 4I13/2 level (dashed lines).ollowing this diagram, the rate equations can be writtens follows:

�Npr1

�t= − �Wpr13 + Wpr14 + C23Ner2 + C34Ner3�Npr1

+ Apr21Npr2 + �Wpr31 + Apr31�Npr3 + �Apr41

+ Wpr41�Npr4,

�Npr2

�t= − �Wpr24 + Apr21�Npr2 + �Wpr42 + Apr42�Npr4,

�Npr3

�t= Wpr13Npr1 − �Wpr31 + Apr31�Npr3 + C23Npr1Ner2,

�Npr4

�t= Wpr14Npr1 + Wpr24Npr2 − �Wpr41 + Wpr42 + Apr41

+ Apr42�Npr4 + C34Npr1Ner3,

�Ner1

�t= − �Werp12 + Wers12�Ner1 + �Werp21 + Wers21�Ner2

+ Aer21Ner2 + Aer31Ner3 + Aer41Ner4 + �C23Ner2

+ C34Ner3�Npr1 + Cer24Ner22 ,

�Ner2

�t= �Werp12 + Wers12�Ner1 − �Werp21 + Wers21

+ Apr21�Ner2 + Aer32Ner3 − 2Cer24Ner22

− C N N ,

ig. 1. Schematic of energy levels and transition configurationf Er3+/Pr3+ codoped fiber amplifier pumped with 1010 and480 nm LDs.

23 pr1 er2

�Ner3

�t= Aer43Ner4 − �Aer32 + Aer31�Ner3 − C34Npr1Ner3,

�Ner4

�t= − �Aer43 + Aer41�Ner4 + Cer24Ner2

2 ,

here the Wij=�ijPs,p /h�s,pAeff terms represent the stimu-ated transition rates between the i and j levels. Aij is theonradiative transition rate and Cer24, C23, and C34 arehe up-conversion and cross-relaxation coefficients, re-pectively. The total Er3+ and Pr3+ ion density distribu-ions NEr

t and NPrt are assumed to be constant within the

hole fiber cross section and along the fiber length. Theyatisfy the following reservation equations:

NErt = Ner1 + Ner2 + Ner3 + Ner4,

NPrt = Npr1 + Npr2 + Npr3 + Npr4.

he propagation of pump power along the fiber is de-cribed by the following differential equation:

�P1480

�z= �1480���er21Ner2 − �er12Ner1��P1480 + �pP1480,

�P1010

�z= �1010���pr41Npr4 − �pr14Npr1��P1010 + �pP1010,

here �er12,�er21,�pr14, and �pr41 are the pump absorp-ion and emission cross sections of Er3+ and Pr3+ in fiber,espectively. The signal power and the amplified sporta-eous emission (ASE) powers are amplified according to

�P1310

�z= �1310��pr42Npr4 − �pr24Npr2�P1310 − �sP1310,

�P1530

�z= �1530��er21Ner2 − �er12Ner1�P1530 − �sP1530,

�P1600

�z= �1600��pr31Npr3 − �pr13Npr1�P1600 − �sP1600,

�Pase1±

�z= �ase��pr42Npr4 − �pr24Npr2�Pase1

± ± 2h����pr42

+ �ase1Pase1± ,

�Pase2±

�z= �ase��er21Ner2 − �er12Ner1�Pase2

± ± 2h����er21

+ �ase2Pase2± ,

�Pase3±

�z= �ase��pr31Npr3 − �pr13Npr1�Pase1

± ± 2h����pr31

+ �ase3Pase3± ,

here �asei �i=1,2,3� is the frequency-dependentackground loss of the active fiber.

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Chun Jiang Vol. 26, No. 5 /May 2009/J. Opt. Soc. Am. B 1051

er12,�er21,�pr13,�pr31,�pr24, and �pr42 are the signal ab-orption and emission cross sections of Er3+ and Pr3+ inber, respectively. The overlapping factors �� were calcu-

ated [9].The power propagation equations form a system of

oupled differential equations, which are solved by nu-erical integration along the active fiber using the New-

on method and the Rung–Kutta method. It was assumedhat the up-conversion coefficient Cup and the cross-elaxation coefficient Ccr are linearly increasing functionsf NEr

t and NPrt : respectively: [10–13]

Cup = 3.5 � 10−24 + 2.41 � 10−49�NErt − 4.4 � 1025�

Ccr = 1.0 � 10−22 + 4.0 � 10−49��NPrNEr�1/2 − 1.0

� 1025�.

. 986/1480 nm LD Pumpshe schematic of the energy levels and the transition con-guration of the Er3+/Pr3+ doped system pumped withoth 986 and 1480 nm LDs are shown in Fig. 2. Under ex-itation of 986 nm, the electron in the ground state �3H4�f the Pr3+ ion is excited into the excited state �1G4� andransits from that state to the 3H5 state, emitting light at310 nm windows, and then the electron relaxes into theround state �3H4�. Meanwhile, the electrons in theround state �4I15/2� of Er3+ ions are excited into the ex-ited state �4I11/2� from which some of the electrons non-adiatively decay to the 4I13/2 state and then transit fromhat state to the ground state �4I15/2�, emitting light at530 nm windows. Meanwhile, the electrons of some ofr3+ ions in the excited and metastable states transfer

nto 3F4 and 1G4 states of the Pr3+ ions via the cross-elaxation process, then transit into 3H5 and 3H4 (groundtate), emitting light of 1310 and 1600 nm windows, re-pectively. Moreover, under excitation of 1480 nm, thelectrons in the ground state �4I15/2� of the Er3+ ions arexcited into the metastable state �4I13/2� and the electronsf some of the Er3+ ions transit from that state to theround state �4I15/2�, emitting light of 1530 nm windows.oreover, the electron at the metastable state �4I13/2� of

he Er3+ ion is excited to the 4I9/2 level with the absorp-ion of the photon at 1500 nm emitted by the transition of

ig. 2. Schematic of energy level and transition configuration ofr3+/Pr3+ codoped fiber amplifier pumped with 986 and 1480 nmDs.

he electron in another Er3+ ion from the 4I13/2 level to the4I15/2 level, and then transits from the 4I9/2 level to the4I15/2 level with the emission of the photon at the 800 nmand. Additionally, there also are some Er3+ ions in whichhe electron in the 4I9/2 level is relaxed nonradiatively tohe 4I11/2 level and then to the 4I13/2 level (dashed lines).ollowing this diagram, the rate equations can be writtens

�Npr1

�t= − �Wpr13 + Wpr14 + C23Ner2 + C34Ner3�Npr1

+ Apr21Npr2 + �Wpr31 + Apr31�Npr3 + �Apr41

+ Wpr41�Npr4,

�Npr2

�t= − �Wpr24 + Apr21�Npr2 + �Wpr42 + Apr42�Npr4,

�Npr3

�t= Wpr13Npr1 − �Wpr31 + Apr31�Npr3 + C23Npr1Ner2,

�Npr4

�t= Wpr14Npr1 + Wpr24Npr2 − �Wpr41 + Wpr42 + Apr41

+ Apr42�Npr4 + C34Npr1Ner3,

�Ner1

�t= − �Werp12 + Werp13 + Wers12�Ner1 + �Wers21

+ Werp21 + Aer21�Ner2 + �Werp31 + Aer31�Ner3

+ Aer41Ner4 + �C23Ner2 + C34Ner3�Npr1

+ Cer24Ner22 ,

�Ner2

�t= �Werp12 + Wers12�Ner1 − �Werp21 + Wers21

+ Apr21�Ner2 + Aer32Ner3 − 2Cer24Ner22

− C23Npr1Ner2,

�Ner3

�t= Aer43Ner4 + �Werp13 − Aer32 − Aer31�Ner3

− C34Npr1Ner3,

�Ner4

�t= − �Aer43 + Aer43�Ner4 + Cer24Ner2

2 ,

here Wij, Aij, Cup, C14, Ccr NErt , and NPr

t are the same asn the case of 1010/1480 nm pumps, and the propagationsf pump power, signal, and ASE along the fiber are theame as in the case of the 1010/1480 nm pumps.

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1052 J. Opt. Soc. Am. B/Vol. 26, No. 5 /May 2009 Chun Jiang

. RESULTS. 1010/1480 nm LD Pumps

. Dependence of Gain on Active Ion Concentrationshe gains are calculated with spectral parameters listed

n Table 1 [14,15]. Figure 2 shows the variation of theains at the three bands with active ion concentrationnd fiber length. In Fig. 2(a), with both fixed Pr3+ andr3+ concentrations at 2.0�1024 ions/m3 and010/1480 nm pump power of 100/100 mW, when the fi-er length increases from 0.0 to 10.0 m, the gains at310 nm and 1530 nm increase linearly from.0 to 7.5 dB and 31.0 dB, respectively, and the gain at600 nm decreases from 0.0 to −6.0 dB. In Fig. 2(b), withame Er3+ concentration and pump power as Fig. 2(a) butith the Pr3+ concentration at 4.0�1024 ions/m3, when

he fiber length increases from 0.0 to 10.0 m, the gains at310 and 1530 nm increase linearly from 0.0 to 17.5 dBnd 36.0 dB, respectively, and the gain at 1600 nm de-reases from 0.0 to −8.0 dB. In Fig. 2(c), with the samer3+ concentration and pump power as Fig. 2(a) but ther3+ concentration is 6.0�1024 ions/m3, when the fiber

ength increases from 0.0 to 10.0 m, the gain at 1310 nmncreases from 0.0 to 21.8 dB and then decreases from the

aximum to 20.0 dB. The gain at 1530 nm increases mo-otonously from 0.0 to 40.0 dB, and the gain at 1600 nmecreases from 0.0 to −18.0 dB, indicating that the signals strongly absorbed.

. Dependence of Gain on Pump Powerigure 3 shows the variation of the gains at the threeands with pump power and fiber length. In Fig. 3(a),ith fixed Pr3+ and Er3+ concentrations at 6.0�1024 and.0�1024 ions/m3, respectively, and with 1010/1480 nmump power of 120/100 mW, when the fiber length in-reases from 0.0 to 10.0 m, the gains at 1310 and530 nm nearly linearly increase from 0.0 to 24.5 dB and9.0 dB, respectively, and the gain at 1600 nm decreasesrom 0.0 to −10.5 dB. In Fig. 3(b), with the same concen-

Table 1. Spectroscopic Parametersof Er3+ Doped and Pr3+ Doped Telluride Fiber

for Numerical Calculation

Parameter Symbol Value Unit Rema

ore diameter 2r 5.0 �mackground loss � 0.1 m−1

Pr3+ Spr42/Spr24 8.6�10−25/8.5�10−25 m2 [15Spr31/Spr13 8.6�10−25/8.5�10−25 m2

A31 4000 1/sA42 2778 1/s

Er3+ [14Ser21 8.6�10−25 m2

Ser12 8.5�10−25 m2

Ser31 1.0�10−26 m2

Ser13 4.48�10−25 m2

A21 172.4 1/sA41 1804.3 1/sA32 1000 1/sA43 51000 1/s

ig. 3. Variation of the gain at 1310, 1530, and 1600 nm withctive ion concentration and fiber length. Pump wavelength,ump power, and input signal power are 1010/1480 nm,00/100 mW, and −30 dBm, respectively. (a) Pr3+=2.0�1024 andr3+=2.0�1024 ions/m3; (b) Pr3+=4.0�1024 and Er3+=2.01024 ions/m3; (c) Pr3+=6.0�1024 and Er3+=2.0�1024 ions/m3.

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Chun Jiang Vol. 26, No. 5 /May 2009/J. Opt. Soc. Am. B 1053

rations and 1480 nm pump power as Fig. 3(a) but the010 nm pump power is 160 mW, when the fiber lengthncreases from 0.0 to 10.0 m, the gains at 1310 and530 nm nearly linearly increase from 0.0 to 26.0 dB and6.0 dB, and the gain at 1600 nm decreases from 0.0 to7.5 dB. In Fig. 3(c), with the same Er3+ concentrationnd 1480 nm pump power as Fig. 3(a) but the Pr3+ con-entration is 8.0�1024 ions/m3 and the 1010 nm pumpower is 200 mW, when the fiber length increases from.0 to 10.0 m, the gains at 1310 and 1530 nm monoto-ously increase from 0.0 to 30.0 dB and 37.0 dB, and theain at 1600 nm decreases from 0.0 to −8.0 dB.

It is illustrated from the above results that with00/1480 nm and 200/1010 nm pumps, when the concen-ration of Pr3+ and Er3+ are around 8.0�1024 and 2.01024 ions/m3, respectively, the signals at 1310 and

530 nm may be nearly equally amplified with a gain of6.0 dB in the active fiber with a length of 7.0 m.

. 986/1480 nm LD Pumps

. Dependence of Gain on Active Ion Concentrationigure 4 shows the variation of the gains at the threeands with active ion concentration and fiber length. Inig. 4(a), with fixed Pr3+ and Er3+ concentrations at 2.01024 ions/m3 and with a 1010/1480 nm pump power of

00/100 mW, when the fiber length increases from.0 to 10.0 m, the gain at 1310 and 1530 nm nearly lin-arly increases from 0.0 to 7.2 dB and 11.3 dB, and theain at 1600 nm decreases from 0.0 to −5.0 dB. In Fig.(b), with same pump power and Er3+ ion concentrations Fig. 4(a) but the Pr3+ concentration is 3.01024 ions/m3, when the fiber length increases from

.0 to 10.0 m, the gains at both 1310 and 1530 nm nearlyinearly increase from 0.0 to 12.5 dB, and the gain at600 nm decreases from 0.0 to −7.0 dB. In Fig. 4(c), withame pump power and Er3+ ion concentration as Fig. 4(a)ut the Pr3+ concentration is 4.0�1024 ions/m3, when theber length increases from 0.0 to 10.0 m, the gains at310 and 1530 nm monotonously increase from.0 to 17.5 dB and 15.0 dB, respectively, and the gain at600 nm decreases from 0.0 to −8.5 dB.It is illustrated from the above results that with a

480/986 nm pump power of 100/100 mW, when Pr3+ andr3+ concentrations are around 3.0�1024 and 2.01024 ions/m3, respectively, the signals at 1310 and

530 nm may be nearly equally amplified with a gain of2.5 dB in the active fiber with a length of 10.0 m.

. Dependence of Gain on Pump Powerigure 5 shows the variation of the gains at the threeands with pump power and fiber length. In Fig. 5(a),ith fixed Pr3+ and Er3+ concentrations at 2.01024 ions/m3 and the 986/1480 nm pump power at

20/100 mW, when the fiber length increases from.0 to 10.0 m, the gain at 1310 and 1530 nm linearly in-reases from 0.0 to 7.8 dB and 10.5 dB, and the gain at600 nm decreases from 0.0 to −5.8 dB. In Fig. 5(b), withame concentrations and 1480 nm pump power as Fig.(a) but the 1010 nm pump power is 200 mW, when theber length increases from 0.0 to 10.0 m, the gains at twohannels linearly increases from 0.0 to 8.0 dB and 9.0 dB,

ig. 4. Variation of the gain at 1310, 1530, and 1600 nm withump power and fiber length. Pump wavelength and input signalower are 1010/1480 nm and −30 dBm, respectively. Pumpower is (a) 120/100 mW, (b) 160/100 mW, and (c) 200/100 mW.

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nd the gain at 1600 nm decreases from 0.0 to −5.2 dB.n Fig. 5(c), with same concentrations and 1480 nm pumpower as Fig. 5(a) but the 1010 nm pump power is00 mW, when the fiber length increases from.0 to 10.0 m, the gains at two channels linearly increaseith similar slope from 0.0 to 8.0 dB and 8.5 dB, and theain at 1600 nm decreases from 0.0 to −5.0 dB.

It is illustrated from the above results that with a480/986 nm pump power of 100/300 mW and with Pr3+

nd Er3+ ion concentrations around 2.0�1024 and 2.01024 ions/m3, respectively, the signals at 1310 and

530 nm may be nearly equally amplified with a gain of.0 dB in a 10.0 m long active fiber.

. DISCUSSIONt was shown in Fig. 3 that with a 1010/1480 nm pumpower of 100/100 mW and with the Er3+ concentration of.0�1024 ions/m3 and fiber length of 7.0 m and increas-ng Pr3+ concentration from 2.0�1024 to 6.0

1024 ions/m3, the gains at 1310 and 1530 nm increaseinearly from 5.0 to 20.0 dB and from 22.0 to 30.0 dB, re-pectively, and the gain at 1600 nm decreases from4.0 to −6.0 dB. The increase of the gains at the twohannels, we think, arises from the increase of the popu-ation inversion between 1G4 and 3H5 of Pr3+; meanwhile,ome of the 1310 nm band emission is reabsorbed by Er3+

t the ground state due to the small overlap between themission spectra of Pr3+ and the absorption spectra ofr3+ [4]. Thus the population inversion between 4I13/2 and

4I15/2 of Er3+ increases, resulting in the increase of theains at two channels.

To confirm our reasonable above explanation, let us seehe case of 986/1480 nm pumps. It was shown in Fig. 5hat with the 986/1480 nm pump power of 100/100 mWnd Er3+ concentration of 2.0�1024 ions/m3, fiber lengthf 10.0 m, and increase of Pr3+ concentration from 2.01024 to 4.0�1024 ions/m3, the gains at the two chan-

els increase nearly linearly from 7.5 to 17.5 dB and from1.5 to 15.0 dB, respectively, and the gain at 1600 nm lin-arly decreases from −6.0 to −8.0 dB. Thus this case isonsistent with the previous one and this supports ournalysis.It was shown in Fig. 6 that with 1480 nm pump power

f 100 mW and Er3+ and Pr3+ concentrations of 2.01024 ions/m3, fiber length of 10.0 m, and increase of

86 nm pump power from 120 to 300 mW, the gain at310 nm increases slightly from 7.7 to 8.0 dB, the gain at530 nm decreases monotonously from 10.0 to 8.4 dB, re-pectively, and the gain at 1600 nm increases fromround −5.9 to −5.0 dB. The variation of the gains withhe pumping power may be explained as follows: theopulation inversion between the 1G4 and 3H5 of Pr3+ andhe population number at the excited state �5I11/2� of Er3+

ncrease with increasing pumping power, leading to morenergy transfer from the 4I11/2 of Er3+ to the 1G4 of Pr3+;hus, the population number at the metastable state4I13/2� of Er3+ is reduced, resulting in a smaller popula-ion inversion between the 4I13/2 and the 4I15/2 of Er3+ andhus a reduced gain at the 1530 nm band.

We note that the gain at 1600 nm is negative for thewo cases; we think that the population number at the 3F

ig. 5. Variation of the gain at 1310, 1530, and 1600 nm withctive ion concentration and fiber length. Pump wavelength,ump power, and input signal power are 986/1480 nm,00/100 mW, and −30 dBm, respectively. (a) Pr3+=2.0�1024 andr3+=2.0�1024 ions/m3; (b) Pr3+=3.0�1024 and Er3+=2.01024 ions/m3; (c) Pr3+=4.0�1024 and Er3+=2.0�1024 ions/m3.

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Chun Jiang Vol. 26, No. 5 /May 2009/J. Opt. Soc. Am. B 1055

evel of Pr3+ is so small that the population inversion be-ween the 3F4 and the 3H4 is negative or too low to am-lify the signal.To study the gain as a function of wavelength, we cal-

ulate gain spectra using the absorption and emissionross sections from [4]. The spectra with two fiber lengthss shown in Fig. 7 with a 986/1480 nm pump power of00/200 mW, Er3+ concentration of 2.0�1024 ions/m3,nd Pr3+ concentration 1.0�1024 ions/m3. It indicateshat with increasing fiber length, the gain at 1310 nm in-reases and the gains at 1530 nm and 1600 nm bands de-rease. We think that this arises from an increased en-rgy transfer from the 4I11/2 of Er3+ to the 1G4 of Pr3+ andhe reduced population at the metastable state �4I11/2� ofr3+, resulting in a reduced population inversion between

he 4I13/2 and the 4I15/2 of Er3+ and a decreased energyransfer from the 4I13/2 of Er3+ to the 3F3,4 of Pr3+. Thus,he gains at 1530 nm and 1600 nm are reduced.

. CONCLUSIONSn conclusion, we presented the numerical models ofr3+/Pr3+ codoped fiber systems pumped with010/1480 nm and 986/1480 nm lasers. The rate andower propagation equations of the models were solvedumerically, and the dependence of the gains at 1310,530, and 1600 windows on the pump power and activeon concentrations were calculated and analyzed. The re-ults showed that with 1010/1480 nm pumps of00/100 mW, and Pr3+ of 8.0�1024 ions/m3, and Er3+

oncentrations of 2.0�1024 ions/m3, or with 1480/986 nmump power of 100/300 mW and both Pr3+ and Er3+ iononcentrations of 2.0�1024 ions/m3, the signals at 1310nd 1530 nm windows may be equally amplified with aain of 26.0 dB in the active fiber with length of 7.0 m oray be nearly equally amplified with a gain of 8.0 dB in a

0.0 m long active fiber.

CKNOWLEDGMENTShis work was supported in part by the National Naturalcience Foundation of China (NNSFC) grant 60377023nd 60672017 and the Program for New Century Excel-ent Talents in University.

ig. 7. Variation of the gain spectra with fiber length. Pumpavelength and input signal power are 986/1480 nm,00/200 mW, and −30 dBm, respectively.

ig. 6. Variation of the gain at 1310, 1530, and 1600 nm withump power and fiber length. Pump wavelength and input signalower are 1010/1480 nm and −30 dBm, respectively. Pumpower is (a) 120/100 mW, (b) 200/100 mW, and (c) 300/100 mW.

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1056 J. Opt. Soc. Am. B/Vol. 26, No. 5 /May 2009 Chun Jiang

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