International Journal of Optics

International Journal of Optics / 2009 / Article

Research Letter | Open Access

Volume 2009 |Article ID 276538 | 5 pages | https://doi.org/10.1155/2009/276538

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

Academic Editor: Gang-Ding Peng
Received19 Jan 2009
Accepted13 Mar 2009
Published29 Apr 2009

Abstract

We present for the first time a theoretical model of Er3+-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.

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) [35] 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 of Er3+-Tm3+co-doped and Pr3+-Er3+ co-doped fibers showed that the combination of the emission at 1530 nm window due to Er3+:4I13/24I15/2 transition with the emission at 1470 nm window due to Tm3+:3H4-3F4 transition may generate a larger seamless emission spectrum up to 200 nm in the co-doped system [712]. 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+:4I13/24I15/2 transition with the emission at 1310 nm window due to Pr3+:3F4-3H5 transition may generate an emission spectrum having two peaks centered at 1310 nm and 1530 nm windows [713]. 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

Figure 1 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)𝑁4𝑊ET63𝑁1𝑁6𝑊ET74𝑁1𝑁7,𝜕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+𝑊68𝑁26+𝑊ET63𝑁1𝑁6+𝑊ET74𝑁1𝑁7+(𝑊65+𝐴65)𝑁6+𝑊ET610𝑁6𝑁9+𝑊ET711𝑁7𝑁9𝑊ET128𝑁5𝑁12,𝜕𝑁6𝜕𝑡=𝑊ET63𝑁1𝑁6(𝑊65+𝐴65)𝑁6𝑊ET610𝑁6𝑁9+𝐴76𝑁72𝑊68𝑁26,𝜕𝑁7𝜕𝑡=𝑊57𝑁5+𝐴87𝑁8(𝑊ET74𝑁1+𝐴76)𝑁7𝑊ET711𝑁7𝑁9,𝜕𝑁8𝜕𝑡=𝑊58𝑁5𝑊ET128𝑁12𝑁5𝐴87𝑁8+𝑊68𝑁26,𝜕𝑁9𝜕𝑡=(𝑊912+𝑊ET610𝑁6+𝑊ET711𝑁7)𝑁9+𝑊ET128𝑁5𝑁12+(𝑊109+𝐴109)𝑁10𝑊910𝑁9,𝜕𝑁10𝜕𝑡=(𝑊109+𝐴109)𝑁10+𝑊910𝑁9+𝑊ET610𝑁6𝑁9+𝐴1110𝑁11+(𝑊1210+𝐴1210)𝑁12𝑊1012𝑁10𝑊1013𝑁10,𝜕𝑁11𝜕𝑡=𝑊ET711𝑁7𝑁9𝐴1110𝑁11+𝐴1211𝑁12,𝜕𝑁12𝜕𝑡=𝑊912𝑁9+𝐴1312𝑁13(𝑊ET128𝑁5+𝐴1211+𝑊1210)𝑁12+𝑊1012𝑁10,𝜕𝑁13𝜕𝑡=𝑊1013𝑁10𝐴1312𝑁13,(1) where 𝑁1-𝑁4 are the population densities of Pr3+ ion at energy levels 3H4, 3H5, 3F4, 1G4, 𝑁5-𝑁8 are the population densities of Er3+ ion at energy levels 4I15/2, 4I13/2, 4I11/2, and 4I9/2, 𝑁9-𝑁13 are the population densities of Tm3+ ions at energy levels 3H6, 3F4, 3H5, 4H4, 1G4. 𝑊13, 𝑊31, 𝐴31 are the stimulated absorption and emission rates, spontaneous emission rate between 3H4 and 3F4 levels of Pr3+, respectively. 𝑊24, 𝑊42, 𝐴42 are the stimulated absorption and emission rates, spontaneous emission rate between the 3H5 and 1G4 levels of Pr3+, respectively. 𝐴21 is the spontaneous emission rate between the 3H4 and 3H5 levels of Pr3+. 𝑊56, 𝑊65, 𝐴65 are the stimulated absorption and emission rates, spontaneous emission rate between the 4I15/2 and 4I13/2 levels of Er3+, respectively. 𝑊58, 𝐴87, 𝐴76 are the 800 nm- pump absorption rate, spontaneous emission rate from 4I9/2 to 4I11/2 levels, spontaneous emission rate from 4I11/2 to 4I13/2 levels of Er3+, respectively. 𝑊10-12, 𝑊12-10, 𝐴12-10 are the stimulated absorption and emission rates, spontaneous emission rate between the 3H4 and 3F4 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 3H6 and 3F4 levels of Tm3+, nonradiation transition rate from 3H4 to 3H5, nonradiation transition rate from 3H5 to 3F4, respectively. 𝑊1-4, 𝑊5-8, 𝑊10-13 are 980 nm pump absorption rates between the 3H4 and 1G4 levels of Pr3+, between the 4I15/2 and 4I19/2 levels of Er3+, and between the 3H6 and 3H4 levels of Tm3+, respectively. 𝑊ET6-3, 𝑊ET7-4, 𝑊ET6-10, 𝑊ET7-11, 𝑊ET12-8 stand for the transfer rates from Er3+:4I13/2, Pr3+:3H4 to Er3+:4I15/2, Pr3+:3F4, from Er3+:4I11/2, Pr3+:3F4 to Er3+:4I15/2, Pr3+:1G4, from Er3+:4I11/2, Tm3+:3H6 to Er3+:4I15/2, Tm3+:3H5, from Er3+:4I13/2, Tm3+:3H6 to Er3+:4I15/2, Tm3+:3F4, from Tm3+:3H4, Er3+:4I15/2 to Tm3+:3H6, and from Er3+:4I9/2, Tm3+:3H6 to Er3+:4I15/2, Tm3+:3F4, respectively. The transition rates: 𝑊𝑖𝑗=𝜎𝑖𝑗𝑃𝑘𝜈𝑘𝐴e(𝑖,𝑗=112,𝑘=𝑠,𝑝),(2) where 𝜎𝑖𝑗 is cross-section of the transition between 𝑖 and 𝑗 level, and 𝐴e 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:𝑑𝑃𝑆1𝑑𝑧=Γ1310(𝑁3𝜎prse𝐵𝑁2𝜎prsa𝐵)𝑃𝑆1𝛼1310𝑃𝑆1,𝑑𝑃𝑆2𝑑𝑧=Γ1470(𝑁12𝜎tmse𝐴𝑁11𝜎tmsa𝐴)𝑃𝑆2𝛼1470𝑃𝑆2,𝑑𝑃𝑆3𝑑𝑧=Γ1550(𝑁6𝜎erse𝑁5𝜎ersa𝐴𝑁8𝜎ersa𝐵)𝑃𝑆3𝛼1550𝑃𝑆3,𝑑𝑃𝑆4𝑑𝑧=Γ1600(𝑁3𝜎prse𝐴𝑁1𝜎prsa𝐴)𝑃𝑆4𝛼1600𝑃𝑆4,𝑑𝑃𝑆5𝑑𝑧=Γ1650(𝑁10𝜎tmse𝐵𝑁9𝜎tmsa𝐵)𝑃𝑆5𝛼1650𝑃𝑆5,𝑑𝑃𝑝1𝑑𝑧=Γ800[(𝑁5𝜎erpa𝑁8𝜎erpe)+(𝑁9𝜎tmpa𝑁12𝜎tmpe)]𝑃𝑝1𝛼800𝑃𝑝1,𝑑𝑃𝑝2𝑑𝑧=Γ980[(𝑁1𝜎prpa𝑁4𝜎prpe)+(𝑁5𝜎erpa𝑁7𝜎erpe)+(𝑁10𝜎tmpa𝑁13𝜎tmpe)]𝑃𝑝2𝛼980𝑃𝑝2,𝑑𝑃ASE1𝑑𝑧=Γ1310(𝑁3𝜎prse𝐵𝑁2𝜎prsa𝐵)𝑃ASE1+2𝜐Δ𝜐𝑁3𝜎prse𝐵𝛼1310𝑃ASE1,𝑑𝑃ASE2𝑑𝑧=Γ1470(𝑁12𝜎tmse𝐴𝑁11𝜎tmsa𝐴)𝑃ASE2+2𝜐Δ𝜐𝑁12𝜎tmse𝐴𝛼1470𝑃ASE2,𝑑𝑃ASE3𝑑𝑧=Γ1550(𝑁6𝜎erse𝑁5𝜎ersa𝐴𝑁8𝜎ersa𝐵)𝑃ASE3+2𝜐Δ𝜐𝑁6𝜎erse𝛼1550𝑃ASE3,𝑑𝑃ASE4𝑑𝑧=Γ1600(𝑁3𝜎prse𝐴𝑁1𝜎prsa𝐴)𝑃ASE4+2𝜐Δ𝜐𝑁3𝜎prse𝐴𝛼1600𝑃ASE4,𝑑𝑃ASE5𝑑𝑧=Γ1650(𝑁10𝜎tmse𝐵𝑁9𝜎tmsa𝐵)𝑃ASE5+2𝜐Δ𝜐𝑁10𝜎tmse𝐵𝛼1650𝑃ASE5,(3) 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 3H4-3F4 (1470 nm) and 3F4-3H6 (1650 nm) in Tm3+ ions and 4I13/2-4I15/2 (1530 nm) in Er3+ ions, respectively. 𝜎tmsa𝐴, 𝜎tmsa𝐵, 𝜎ersa are the absorption cross-sections of 3H4-3F4 (1470 nm) and 3F4-3H6 (1650 nm) in Tm3+ ions and 4I13/2-4I15/2 (1530 nm) in Er3+ ions, respectively. 𝜎prse𝐴, 𝜎prsa𝐴 and 𝜎prse𝐵, 𝜎prsa𝐵 are the emission cross-sections of 1G4-3H5 (1310 nm) and 3F4-3H4 (1600 nm) in Pr3+ ions.

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 𝑁𝑡Er, 𝑁𝑡Tm, 𝑁𝑡𝑃𝑟, respectively, [15, 16] and are expressed with equations:𝑊ET63=𝑊ET74=1.0×1022+4.0×1049(𝑁𝑃𝑟𝑁Er)1/21.0×1025,𝑊ET6-10=𝑊ET7_11=1.0×1022+4.0×1049(𝑁Tm𝑁Er)1/21.0×1025,𝑊ET12-8=1.0×1022+4.0×1049(𝑁Tm𝑁Er)1/21.0×1025.(4)

3. Result and Discussion

Figure 2 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.

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 1G4 and 3H5 level of Pr3+ ions, the 3H4 and 3F4 level of Tm3+ ions, the 4I13/2 and 4I15/2 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 3F4 to 3H6 levels of Tm3+, it shares same level (3F4) with the channel at 1470 nm arising from the transition from 3H4 and 3F4 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.


ParameterSymbolValueUnitRemarks

Core diameter2r5.0 𝜇 m
Background loss 𝛼 0.1dB/m

P r 3 + σ prseB,σ prsaB,2.0 × 10-25m2
σ prseA,σ prsaA,6.3 × 10-25m2[17]
𝐴 3 1 40001/s
𝐴 4 2 27781/s

T m 3 + σ tmseA4.5 × 10-25m2
σ tmsaA4.5 × 10-25m2
σ tmseB8.6 × 10-25m2
σ tmsaB8.6 × 10-25m2
𝐴 1 0 - 9 3111/s[18]
𝐴 1 1 - 1 0 1311/s
𝐴 1 0 - 9 4001/s
σ tmpa4.5 × 10-25m2
σ tmpe1.0 × 10-27m2

E r 3 + σ erse 8.6 × 10-25m2
σ ersa8.5 × 10-25m2
σ erpe1.0 × 10-26m2
σ erpa4.48 × 10-25m2
σ erpe1.0 × 10-27m2[18]
𝐴 6 5 172.41/s
𝐴 8 5 1804.31/s
𝐴 7 6 10001/s
𝐴 8 7 51000 1/s

Overlap factor Γ ( 𝜆 ) 0.876800 nm
0.5001310 nm
0.6411470 nm
0.4511530 nm
0.3001650 nm

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grants no. 60377023 and no. 60672017) and Program for New Century Excellent Talents in University and Shanghai Optical Science and Technology (no. 05DZ22009) and sponsored by Shanghai Pujiang Program.

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Copyright © 2009 Chun Jiang and Li Jin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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