Proposal of a Pr3+-doped telluride fiber amplifier for1.3, 1.49, and 1:6 μm transmission windows

Chun JiangState 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 22 July 2008; revised 9 October 2008; accepted 13 October 2008;posted 27 October 2008 (Doc. ID 99270); published 15 December 2008

A numerical model of a Pr3+-doped low-phonon-energy fiber pumped with 488, 980, and 1480 nm lasers ispresented to explore the possibility for simultaneous 1300, 1490, and 1600nm band amplification for thefirst time, to the best of my knowledge. The rate and power propagation equations of the model are solvednumerically and the dependence of the gains at the three bands on pump power and input signal powerare calculated. The results predict that, with 488, 980, and 1480 nm pump power of 100, 12, and 1.5 mW,and with Pr3+ concentrations of 1:2 × 1025 ions=m3, the signals around 1300, 1490, and 1600nm can beequally amplified with a gain of 21:0 × dB in the active fiber with a length of 6:0m. © 2008 OpticalSociety of America

OCIS codes: 060.4510, 060.2320.

1. Introduction

Recently, erbium and praseodymium codoped fiberamplifiers for 1.31 and 1:53 μm windows have at-tracted a significant amount of interest in optical fi-ber communication because doubly doped fibers havebroad emission spectra from 1250 to 1400nm andfrom 1450 to 1650nm [1–4]. Although an erbium-doped fiber amplifier having a 120nm gain band-width was reported [5], its further extension becomesvery difficult. Similarly, praseodymium-doped fiberamplifiers pumped by a laser around 1000nm wereextensively researched in the past decade, but itsamplification was limited to the 1280–1350nmrange. On the other hand, all-wave fibers with a lowloss bandwidth from 1250 to 1650nm as well as a lossless than 0:70dB=km are promising for metro areanetworks and coarse wavelength division multiplex-ing system applications. However, optical amplifiersfor all-wave fiber transmission systems and net-works are not yet been available. Currently, thebroadest fiber Raman amplifier has only a 136nmbandwidth [6,7], and fiber-optic parametric ampli-fiers are being investigated. Rare-earth-doped fiber

amplifiers with high gain and pump-signal energytransfer efficiency have been investigated in the pastdecade. The energy transfer between Er3+ and Pr3+in chalcogenide, selenide, fluoride, and heavy-metaloxide glasses was studied [2–4,8,9]. The resultsshowed that the energy could transfer from the4I11=2 and 4I13=2 levels of Er3+ to the 1G4, 3F4, and3F3 levels of Pr3+. The broad emission spectra from1.25 to 1:65 μm were observed in the Pr3+-doped tell-uride fiber excited by a 488nm laser, and the emis-sion contributed to the transition of the 1D2–

1G4 and1G4–

3H5 levels of Pr3+ [10]. With 980 or 800nm ex-citation, fluorescence emissions centered at 1350 and1550nm were observed in Ge–As–Ga–S glasses co-doped with Er3+ and Pr3+ ions [11].

I present a numerical model of Pr3+-doped low-phonon-energy fiber pumped with 488, 980, and1480 nm lasers to explore the possibility for simulta-neous 1300, 1490, and 1600nm band amplification.The rate and power propagation equations of themodel are solved numerically and the dependenceof the gains at the three bands on pump powerand input signal power are analyzed. The resultsshow that, with 488, 980, and 1480nm lasers, pumppower of 100, 12, and 1:5mW, and Pr3+ concentra-tions of 1:2 × 1025 ions=m3, the signals at 1340,

0003-6935/08/366811-05$15.00/0© 2008 Optical Society of America

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1500, and 1625nm can be equally amplified with again of 21:0dB in active fiber with a length of 6:0m.

2. Theoretical Model

The schematic of the energy levels and transitionconfiguration of a Pr3+-doped system pumped withtri-pumps of 488, 980, and 1480nm laser diodes(LDs) are shown in Fig. 1. Under excitation of488nm, the ground-state electron 3H4 of Pr3+ is ex-cited to excited state 1D2, from which the electrontransits to the 1G4 level with light emission at the1490nm band, then relaxes to ground state 3H5 withemission of the 1310nm band. Under excitation of980nm, the electron in ground state 3H4 of Pr3+ isexcited to excited state 1G4, from which the electrontransits to the 3H5 level with emission of light at the1310nm band, then relaxes into ground state 3H4.Meanwhile, with excitation of 1480nm, the electronin ground state 3H4 of Pr3+ is excited into excitedstate 3F4, from which the electron nonradiatively re-laxes to the 3F3 level, and then transits from that le-vel to the ground state with emission of light at the1600nm band. Following this diagram, the rateequations can be written as

∂N1

∂t¼ −ðW13+W14+W15ÞN1+A21N2

+ðW31+A31ÞN3+ðA41+W41ÞN4

+ðA51+W51ÞN5;

∂N2

∂t¼ −ðW24+A21ÞN2+ðW42+A42ÞN4;

∂N3

∂t¼ W13N1 − ðW31+A31ÞN3+A43N4;

∂N4

∂t¼ W14N1 − ðW41+A43ÞN4+A54N5;

∂N5

∂t¼ W15N1+W25N2

− ðW52+A51+A52+A54+W56ÞN5

+ðW65+A65ÞN6;

∂N6

∂t¼ W16N1+W56N5 − ðW65+A65ÞN6;

where the Wij terms represent the stimulatedtransition rates between the i level and the j level,and Aij represents the nonradiative transition ratesand the spontaneous emission rates. The total Pr3+ion density distributions N are assumed to beconstant within the entire fiber cross section andalong the fiber length. They satisfy the reservationequations

N ¼ N1+N2+N3+N4+N5+N6:

The propagation of the pump power along the fiber isdescribed by the following differential equation:

∂P1

∂z¼ Γ1½ðσ488eN5 − σ488aN1Þ�P1+αpP1;

∂P2

∂z¼ Γ2½ðσ980eN4 − σ980aN1Þ�P2+αpP2;

∂P3

∂z¼ Γ3½ðσ1480eN3 − σ1480aN1Þ�P3+αpP3;

where σ488pa, σ488pe, σ980pa, σ980pe, σ1480pa, and σ1480peare the pump absorption and emission cross sectionsof Pr3+ at 488, 980, and 1480nm wavelengths,respectively. The signal power and amplified sponta-neous emission (ASE) powers are amplified accord-ing to

Fig. 1. (Color online) Schematic of energy levels and transitionconfiguration of Pr3+-co-doped fiber pumped with 488, 980, and1480 nm LDs.

6812 APPLIED OPTICS / Vol. 47, No. 36 / 20 December 2008

∂P1310

∂z¼ Γ1310½σ42seN4 − σ24saN2�P1310 − αsP1310;

∂P1490

∂z¼ Γ1490½σ54seN5 − σ45saN4�P1490 − αsP1490;

∂P1600

∂z¼ Γ1600½σ31seN3 − σ13saN1�P1600 − αsP1600;

∂P�ase1

∂z¼ ðσ42seN4 − σ24saN2ÞP�

ase1

� 2hνΔνσ42se+αase1P�ase1;

∂P�ase2

∂z¼ ðσ54seN5 − σ45saN4ÞP�

ase2

� 2hνΔνσ54se+αase2P�ase2;

∂P�ase3

∂z¼ ðσ31seN3 − σ13saN1ÞP�

ase1

� 2hνΔνσ31se+αase3P�ase3;

where αasei (i ¼ 1; 2; 3) is the frequency-independentbackground loss of active fiber and σ24sa, σ42se, σ45sa,σ54se, σ13sa, σ31se are the signal absorption and emis-sion cross sections for different transitions in thefiber. The power propagation equations form a sys-tem of coupled differential equations that can besolved by numerical integration along the active fiberby use of the Runge–Kutta method.

3. Results and Discussion

A. Effect of Pump and Input Signal Powers on Gain

The gain is calculated with the spectral parameterslisted in Table 1. Figure 2 shows the gain variationsat three bands with pump and input signal powers.In Fig. 2(a), with a fixed Pr3+ concentration at 2:4 × 1025 ions=m3 , a fiber length at 6.0 m, without 488

and 1480 nm pumps, and when 980 nm pump powerincreases from 0.0 to 400:0mW, the gains at 1310nmmonotonically increase from 0.0 to 40:0dB and beginto saturate when the power is greater than 150mW.With constant Pr3+ concentration and fiber lengthand without 980 and 1480 nm pumps, when 488nmpump power increases from 0.0 to 400:0mW,the gain at 1490nm monotonically increases from0.0 to 45:0dB and begins to saturate when the poweris greater than 100mW. With constant Pr3+ concen-tration and fiber length and without 980 and 488 nmpumps, when 1480nm pump power increases from0.0 to 400:0mW, the gain at 1600nm monotonicallyincreases from 0.0 to 46:0dB and begins to saturatewhen the power is greater than 100mW.

In Fig. 2(b), with fixed Pr3+ concentration at2:4 × 1025 ions=m3, the fiber length at 6:0m, 980nmpump power at 100mW, without 488 and 1480 nmpumps, when input signal power increases from0.0 to 1:0mW, the gain at 1310nm monotonicallydecreases from 25.5 to 15:5dB. Without 980 nmand 1480nm pumps and with 488nm of 100mW,when the input signal power increases from 0.0 to1:0mW, the gain at 1490nm monotonically de-creases from 20.0 to 10:5dB. Without 488 and

Table 1. Spectroscopic Parameters of Pr3+-Doped Telluride Fiberfor Numerical Calculation

Parameter Symbol Value Unit

Core diameter 2 r 5.0 μmBackground loss α 0.1 m−1

Spectral parameters σpr16 2:10 × 10−25 m−2

σpr16 0 m−2

σpr15 2:245 × 10−25 m−2

σpr51 0 m−2

σpr65 3:913 × 10−25 m−2

σpr56 3:913 × 10−25 m−2

σpr52 3:913 × 10−25 m−2

σpr25 3:913 × 10−25 m−2

σpr13 3:913 × 10−25 m−2

σpr31 3:913 × 10−25 m−2

σpr41 0 m−2

σpr14 2:26 × 10−25 m−2

A21 10000 1=SA31 100 1=SA41 100 1=SA51 100 1=SA52 100 1=SA43 10000 1=SA54 100 1=SA65 100 1=S

Fig. 2. (Color online) Variation of the gain at 1310, 1490, and1600 nm with (a) pump and (b) input signal powers. Fiber lengthis 6:0m and Pr3+ concentration is 2:4 × 1025 ions=m3.

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980nm pumps and with 1480nm pump power of100mW, when the input signal power increases from0.0 to 1:0mW, the gain at 1600nmmonotonically de-creases from 27.0 to 17:0dB.

B. Effect of Pump Wavelength on Gain Spectra

To study the gain as a function of signal wave-length, we used absorption and emission cross sec-tions from Ref. [10] to calculate the gain spectra withdifferent pump configurations as shown in Figs. 3and 3(a)–3(c). With a fixed Pr3+ concentration at 2:4×1025 ions=m3, a fiber length of 6:0m, and just 100mW

power 980nm pump, the gains at 1270–1400 and1580–1700nm vary from 0.0 to 41:0dB, and the gainat other wavelengths is negative. With the same Pr3+concentration and fiber length as in Fig. 3(a) but just100mW power and a 1480nm pump, the gain at1580–1700nm varies from 0.0 to 47:0dB, and thegain at other wavelengths is negative. With the samePr3+ concentration and fiber length as in Fig. 3(a)but with 488nm=980nm=1480nm pump power of100mW=12mW=1:5mW, the gain at 1270–1700nmvaries from 0.0 to 22:0dB, and the signals at 1340,1500, and 1625nm can be equally amplified with again of approximately 21:0dB in the active fiber witha length of 6:0m.

4. Conclusion

In conclusion, we have presented the numerical mod-els of Pr3+-doped low-phonon-energy fiber pumpedwith 488, 980, and 1480 nm lasers to explore the pos-sibility for simultaneous 1300, 1490, and 1600nmband amplification. The rate and power propagationequations of the model are solved numerically, andthe dependence of the gains at the three bands onpump power and input signal power were calculated.The results show that, with 488, 980, and 1480 nmpumping power of 100, 12, and 1.5 mWand Pr3+ con-centrations of 1:2 × 1025 ions=m3, the signals at 1340,1500, and 1625nm can be equally amplified with again of approximately 21:0dB in the active fiber witha length of 6:0m.

This research was supported by the National Nat-ural Science Foundation of China, grants 60377023and 60672017, and the Program for NewCentury Ex-cellent Talents in University.

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