# Optimization of Multiple Active Ion Doped Fiber Amplifiers for Three Communication Windows

Authors: Chun Jiang; Li Jin
Journal: Research Letters in Optics
 (2009)

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## Abstract

We present for the first time a theoretical model ofEr3+-Tm3+-Pr3+ codoped fiber pumped with both 800 nm and 980 nm lasers to explore possibility of this co-doped system as all-wave fiber amplifier. The rate and power propagation equations of the model are solved numerically and the dependence of the gains at 1310, 1470, 1530, 1600, 1650 nm windows on fiber length is calculated. The results show that with pump power of 200 mW/200 mW, when the concentrations of Pr3+, Tm3+, Er3+ are around 1.7×1024, 3.9×1024, 1.2×1024 (ions/m3), respectively, the signals at 1310, 1470, 1530, 1600, 1650 nm may be nearly equally amplified with gain of 13–16.0 dB in the active fiber with length of 23.5 m; the co-doping concentrations and fiber length and pump powers may be further optimized to reduce the ripple.


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## Body

## 1. Introduction

All-wave fiber in which OH group was
suppressed is attracting increasing interest in optical transmission system and network because it has low loss windows of
400 nm covering the range 1250–1650 nm. Wavelength Division Multiplexing
(WDM) has been the most important technology of large capacity optical transmission system, and optical
amplifiers are the key devices of WDM system. Although Fiber Raman
Amplifier (FRA) is a promising candidate for long haul and large capacity
transmission system, it requires high pump power due to its lower pump
efficiency; thus, the solution scheme for all-wave fiber transmission system is
not available yet. Compared to FRA, rare-earth doped fiber amplifier has high
gain and high pump efficiency, and in the past decade, the research on the rare-earth doped fiber amplifier
has been focusing on the
single-rare earth-doped fiber amplifiers, and all the amplifiers have their own bandwidths.Er3+-doped fiber
amplifier (EDFA) with new split-band configuration [1, 2] was
reported providing gain bandwidth of more than 100 nm covering the range 1500–1600 nm; Tm3+-doped fiber amplifiers (TDFAs) [3–5] and Pr3+-doped
fiber amplifiers (PDFA) [6] separately provided amplification in
range of 1450–1520 nm and 1280–1340 nm, respectively.Recent
research on emission properties ofEr3+-Tm3+co-doped and Pr3+-Er3+ co-doped fibers showed that the combination
of the emission at 1530 nm window due to Er3+:I13/24→I15/24 transition with the
emission at 1470 nm window due to Tm3+:H4–F433 transition may generate a larger seamless emission spectrum up to 200 nm in the co-doped system [7–12].
Meanwhile, the research on
emission properties of Pr3+-Er3+ co-doped fiber showed that the combination of the emission at 1530 nm window due to Er3+:I13/24→I15/24 transition with the
emission at 1310 nm window due to Pr3+:F4–H533 transition may generate an
emission spectrum having two
peaks centered at 1310 nm and 1530 nm windows [7–13]. In this article, we
present a theoretical model of
Er3+-Tm3+-Pr3+ co-doped fiber amplifier for
the first time to explore the possibility of this multiple rare-earth doped system for all-wave fiber transmission system
application. After the rate and power propagation equations of the doped system are solved numerically and analyzed, the parameters of doped fiber are optimized to achieve the equalized gains for 1310, 1470, 1530, 1600, 1650 nm
bands.


## 2. Theoretical Model

Figure1 shows
the schematic of the energy levels and electron transitions and energy transfer
process of Er3+-Tm3+-
Pr3+-co-doped system pumped by both 800 nm and 980 nm lasers. Following the diagram, the rate equations can be
written as an equation
group:∂N1∂t=−(W13+W14)N1+A21N2+(W31+A31)N3+(W41+A41)N4−WET63N1N6−WET74N1N7,∂N2∂t=−(W24+A21)N2+(W42+A42)N4,∂N3∂t=W13N1−(W31+A31)N3+WET63N1N6,∂N4∂t=W24N2−(W41+W42+A41)N4+WET74N1N7,∂N5∂t=−(W57+W58)N5+W68N62+WET63N1N6+WET74N1N7+(W65+A65)N6+WET6−10N6N9+WET7−11N7N9−WET12−8N5N12,∂N6∂t=−WET63N1N6−(W65+A65)N6−WET6−10N6N9+A76N7−2W68N62,∂N7∂t=W57N5+A87N8−(WET74N1+A76)N7−WET7−11N7N9,∂N8∂t=W58N5−WET12−8N12N5−A87N8+W68N62,∂N9∂t=−(W9−12+WET6−10N6+WET7−11N7)N9+WET12−8N5N12+(W10−9+A10−9)N10−W9−10N9,∂N10∂t=−(W10−9+A10−9)N10+W9−10N9+WET6−10N6N9+A11−10N11+(W12−10+A12−10)N12−W10−12N10−W10−13N10,(1)∂N11∂t=WET7−11N7N9−A11−10N11+A12−11N12,∂N12∂t=W9−12N9+A13−12N13−(WET12−8N5+A12−11+W12−10)N12+W10−12N10,∂N13∂t=W10−13N10−A13−12N13,  where N1–N4 are  the population densities of Pr3+ ion at energy levels
H43, H53, F43, G41, N5–N8 are the population densities of Er3+ ion at energy levels I15/24, I13/24, I11/24, and I9/24,
N9–N13 are the population densities of Tm3+ ions at energy levels H63, F43, H53, H44, G41.  W13, W31, A31 are the
stimulated absorption and emission rates, spontaneous
emission rate between  H43 and F43 levels of Pr3+,
respectively. W24, W42, A42 are the stimulated
absorption and emission rates, spontaneous emission rate between the H53 and G41 levels of Pr3+, respectively. A21 is the spontaneous
emission rate between the H43 and H53 levels of Pr3+.  W56, W65, A65 are the stimulated absorption and emission rates, spontaneous emission rate
between the I15/24 and I13/24 levels of Er3+, respectively. W58,  A87, A76 are the 800 nm- pump absorption rate, spontaneous emission rate from I9/24 to I11/24 levels, spontaneous emission rate from I11/24 to I13/24 levels of Er3+, respectively. W10–12, W12–10,  A12–10 are the
stimulated absorption and emission rates, spontaneous emission rate between the  H43 and F43 levels of  Tm3+, respectively.  W9–12, W9–10, W10–9,
A10–9, A12–11, A11–10 are the 800 nm pump
absorption rate, stimulated absorption rate, stimulated emission rate, spontaneous emission rate between H63 and F43 levels of Tm3+,
nonradiation transition rate from  H43 to H53,
nonradiation transition rate from H53 to F43,
respectively.  W1–4,  W5–8,
W10–13 are 980 nm pump
absorption rates between the H43 and G41 levels of Pr3+,
between the I15/24 and I19/24 levels of Er3+, and between the H63 and H43 levels of Tm3+, respectively. WET6–3,  WET7–4, WET6–10, WET7–11, WET12–8 stand for the transfer rates
from Er3+:I13/24,
Pr3+:H43 to  Er3+:I15/24,
Pr3+:F43,
from Er3+:I11/24, Pr3+:F43 to  Er3+:I15/24, Pr3+:G41, from Er3+:I11/24, Tm3+:H63 to  Er3+:I15/24, Tm3+:H53, from
Er3+:I13/24, Tm3+:H63 to Er3+:I15/24, Tm3+:F43, from Tm3+:H43,
Er3+:I15/24 to Tm3+:H63,
and from Er3+:I9/24, Tm3+:H63 to  Er3+:I15/24, Tm3+:F43, respectively. The transition rates: (2)Wij=σijPkhνkAeff(i,j=1~12,k=s,p),   where σij is cross-section of the transition between i and j level, and Aeff is the
effective cross-section area. Propagation of the pump and signal and ASE power
along the fiber is described by the differential equation group:(3)dPS1dz=Γ1310(N3σprseB−N2σprsaB)PS1−α1310PS1,dPS2dz=Γ1470(N12σtmseA−N11σtmsaA)PS2−α1470PS2,dPS3dz=Γ1550(N6σerse−N5σersaA−N8σersaB)PS3−α1550PS3,dPS4dz=Γ1600(N3σprseA−N1σprsaA)PS4−α1600PS4,dPS5dz=Γ1650(N10σtmseB−N9σtmsaB)PS5−α1650PS5,dPp1dz=−Γ800[(N5σerpa−N8σerpe)+(N9σtmpa−N12σtmpe)]Pp1−α800Pp1,dPp2dz=−Γ980[(N1σprpa−N4σprpe)+(N5σerpa−N7σerpe)+(N10σtmpa−N13σtmpe)]Pp2−α980Pp2,dPASE1dz=Γ1310(N3σprseB−N2σprsaB)PASE1+2hυΔυN3σprseB−α1310PASE1,dPASE2dz=Γ1470(N12σtmseA−N11σtmsaA)PASE2+2hυΔυN12σtmseA−α1470PASE2,dPASE3dz=Γ1550(N6σerse−N5σersaA−N8σersaB)PASE3+2hυΔυN6σerse−α1550PASE3,dPASE4dz=Γ1600(N3σprseA−N1σprsaA)PASE4+2hυΔυN3σprseA−α1600PASE4,dPASE5dz=Γ1650(N10σtmseB−N9σtmsaB)PASE5+2hυΔυN10σtmseB−α1650PASE5,  where Pp1, Pp2 are
the pump powers at 800 nm, 980 nm, respectively. PS1, PS2, PS3, PS4,  PS5 are the powers of the signals at 1310, 1470, 1530, 1600, and 1650 nm bands,
respectively. PASE1,  PASE2, PASE3, PASE4, PASE5 are the powers
of the ASE at 1310, 1470, 1530, 1600, and 1650 nm bands,
respectively. Γ1310,  Γ1470, Γ1530,
Γ1600, Γ1650 are overlapping factors at 1310, 1470, 1530,
1600, 1650 nm bands, respectively, and calculated from
[14], and υ is signal frequency. α(v) is the frequency dependent background loss of the active fiber. σtmseA, σtmseB, σerse are the emission cross-sections of H43-F43 (1470 nm) and F43-H63 (1650 nm) in Tm3+ ions and I13/24-I15/24 (1530 nm) in Er3+ ions, respectively. σtmsaA, σtmsaB, σersa are the absorption cross-sections of H43-F43 (1470 nm) and F43-H63 (1650 nm) in Tm3+ ions and I13/24-I15/24 (1530 nm) in Er3+ ions, respectively. σprseA, σprsaA and σprseB, σprsaB are the emission cross-sections of G41-H53 (1310 nm)  and F43-H43 (1600 nm) in Pr3+ ions.Figure 1
Schematic of energy levels and transition configurations of Er3+-Tm3+-Pr3+ co-doped
telluride fiber amplifier pumped with both
800 nm and 980 nm laser diodes.The above differential equation  group is solved by numerical
integration along the active fiber using Newton
iterative method and Runge-Kutta
method. It was assumed
that the energy transfer rates (WET63, WET74, WET6–10,WET7–11, WET12–8) were linearly increasing functions of NErt, NTmt, NPrt, respectively,
[15, 16]   and are expressed with
equations:(4)WET63=WET74=1.0×10−22+4.0×10−49[(NPrNEr)1/2−1.0×1025],WET6–10=WET7_11=1.0×10−22+4.0×10−49[(NTmNEr)1/2−1.0×1025],WET12–8=1.0×10−22+4.0×10−49[(NTmNEr)1/2−1.0×1025].


## 3. Result and Discussion

Figure2 shows the variation of the gains at the five bands (1310,
1470, 1530, 1600, 1650 nm)
with the fiber length and with optimized dopant
concentrations: Pr3+ concentration at  1.7×1024, Tm3+ concentration at  3.9×1024, Er3+ concentration at 1.2×1024 ions/m3 and fixed pump powers at 200 mW/200 mW for 800 nm/980 nm.Figure 2
Variation of the gain at 1310, 1470, 1530, 1600, 1650 nm with fiber length. Pump
power, input signal power are 200 mW/200 mW,−30 dB m, respectively. The optimal
concentration Pr3+=1.9×1024,
Tm3+=3.9×1024, Er3+=1.2×1024 ions/m3,
and energy transfer coefficient Wet6–3=63×10−20, Wet6–10=200×10−22.When fiber length increases from 0.0 to 30.0 m, the gain at 1310 nm increases monotonically from 0.0 to 17.6 dB, and the gains at 1470, 1530, and 1600 nm increase  from 0.0 to 17.7 dB, 27.0 dB, 16.0 dB at the fiber lengths
18.0, 14.0, 23.0 m,
respectively; after these lengths, they drop. The  gain at 1650 nm decreases  from 0.0 to−4.8 dB; after the length 14.0 m, it rises. We think that the variation of the gains at 1310–1600 nm with
fiber length is reasonable. With fixed pump power and fiber length
increasing from 0 to certain level, pump powers are so high that the number of population inversions between the G41 and H53 level of Pr3+ ions, the H43 and F43 level of Tm3+ ions, the I13/24 and I15/24 levels
of Er3+ ions increases; thus,
the gains increase. When fiber length is over the level, pump powers are comsumpted
so much that the inversion number drops; thereby the gain decreases. For the
channel at 1650 nm originating from the transition from the F43 to H63 levels of Tm3+, it shares same level (F43)  with the channel at 1470 nm
arising from the transition from H43 and F43  level of the ions, but the
shared level acts as the upper level for 1650 nm channel and the terminated
level for 1470 nm;  therefore, the gains at 1470 nm and 1650 nm have opposite
variation trend with increased fiber length.


## 4. Conclusions

In conclusion, we have presented a theoretical model of Er3+-Tm3+-Pr3+ co-doped fiber amplifier pumped with 800 nm and 980 nm lasers. The rate and power propagation equations of the model have been solved numerically and the dependence of
the gains at 1310, 1470, 1530, 1600, 1650 nm windows on the fiber length has been calculated. The results showed that with pump power of 200 mW/200 mW, when
concentrations of Pr3+, Tm3+, Er3+ are around 1.7 × 1024,
3.9 × 1024, 1.2 × 1024 (ions/m3), respectively, the signals at 1310, 1470, 1530,1600, 1650 nm may be nearly equally amplified with gain
of 13–16.0 dB in the active fiber with fiber length of 23.5 m. The co-doping concentrations and fiber length and pump powers of the
co-doped system may be further optimized to reduce the ripple.Table 1
Spectral
parameters of Er3+-doped and Tm3+ and
Pr3+ doped telluride fiber for numerical calculation.
ParameterSymbolValueUnitRemarksCore diameter2r5.0μmBackground lossα0.1dB/mPr3+σprseB,σprsaB,2.0 × 10-25m2σprseA,σprsaA,6.3 × 10-25m2[17]A3140001/sA4227781/sTm3+σtmseA4.5 × 10-25m2σtmsaA4.5 × 10-25m2σtmseB8.6 × 10-25m2σtmsaB8.6 × 10-25m2A10–93111/s[18]A11–101311/sA10–94001/sσtmpa4.5 × 10-25m2σtmpe1.0 × 10-27m2Er3+σerse8.6 × 10-25m2σersa8.5 × 10-25m2σerpe1.0 × 10-26m2σerpa4.48 × 10-25m2σerpe1.0 × 10-27m2[18]A65172.41/sA851804.31/sA7610001/sA87510001/sOverlap factorΓ(λ)0.876800 nm0.5001310 nm0.6411470 nm0.4511530 nm0.3001650 nm



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*Source: 276538-2009-04-29.xml*