Research Letters in Optics
Volume 2009 (2009), Article ID 276538, 5 pages
doi:10.1155/2009/276538
Research Letter

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

Chun Jiang and Li Jin

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

Received 19 January 2009; Accepted 13 March 2009

Academic Editor: Gang-Ding Peng

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.

Abstract

We present for the first time a theoretical model of E r 3 + - T m 3 + - P r 3 + 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 P r 3 + , T m 3 + , E r 3 + are around 1 . 7 × 1 0 2 4 , 3 . 9 × 1 0 2 4 , 1 . 2 × 1 0 2 4 (ions/ m 3 ), 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. E r 3 + -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; T m 3 + -doped fiber amplifiers (TDFAs) [3–5] and P r 3 + -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 E r 3 + -T m 3 + co-doped and P r 3 + - E r 3 + co-doped fibers showed that the combination of the emission at 1530 nm window due to E r 3 + : 4 I 1 3 / 2 → 4 I 1 5 / 2 transition with the emission at 1470 nm window due to T m 3 + : 3 H 4 - 3 F 4 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 P r 3 + -E r 3 + co-doped fiber showed that the combination of the emission at 1530 nm window due to E r 3 + : 4 I 1 3 / 2 → 4 I 1 5 / 2 transition with the emission at 1310 nm window due to P r 3 + : 3 F 4 - 3 H 5 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 E r 3 + -T m 3 + -P r 3 + 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 E r 3 + -T m 3 + - P r 3 + -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: 𝜕 𝑁 1 𝜕 𝑡 = − ( 𝑊 1 3 + 𝑊 1 4 ) 𝑁 1 + 𝐴 2 1 𝑁 2 + ( 𝑊 3 1 + 𝐴 3 1 ) 𝑁 3 + ( 𝑊 4 1 + 𝐴 4 1 ) 𝑁 4 − 𝑊 E T 6 3 𝑁 1 𝑁 6 − 𝑊 E T 7 4 𝑁 1 𝑁 7 , 𝜕 𝑁 2 𝜕 𝑡 = − ( 𝑊 2 4 + 𝐴 2 1 ) 𝑁 2 + ( 𝑊 4 2 + 𝐴 4 2 ) 𝑁 4 , 𝜕 𝑁 3 𝜕 𝑡 = 𝑊 1 3 𝑁 1 − ( 𝑊 3 1 + 𝐴 3 1 ) 𝑁 3 + 𝑊 E T 6 3 𝑁 1 𝑁 6 , 𝜕 𝑁 4 𝜕 𝑡 = 𝑊 2 4 𝑁 2 − ( 𝑊 4 1 + 𝑊 4 2 + 𝐴 4 1 ) 𝑁 4 + 𝑊 E T 7 4 𝑁 1 𝑁 7 , 𝜕 𝑁 5 𝜕 𝑡 = − ( 𝑊 5 7 + 𝑊 5 8 ) 𝑁 5 + 𝑊 6 8 𝑁 2 6 + 𝑊 E T 6 3 𝑁 1 𝑁 6 + 𝑊 E T 7 4 𝑁 1 𝑁 7 + ( 𝑊 6 5 + 𝐴 6 5 ) 𝑁 6 + 𝑊 E T 6 − 1 0 𝑁 6 𝑁 9 + 𝑊 E T 7 − 1 1 𝑁 7 𝑁 9 − 𝑊 E T 1 2 − 8 𝑁 5 𝑁 1 2 , 𝜕 𝑁 6 𝜕 𝑡 = − 𝑊 E T 6 3 𝑁 1 𝑁 6 − ( 𝑊 6 5 + 𝐴 6 5 ) 𝑁 6 − 𝑊 E T 6 − 1 0 𝑁 6 𝑁 9 + 𝐴 7 6 𝑁 7 − 2 𝑊 6 8 𝑁 2 6 , 𝜕 𝑁 7 𝜕 𝑡 = 𝑊 5 7 𝑁 5 + 𝐴 8 7 𝑁 8 − ( 𝑊 E T 7 4 𝑁 1 + 𝐴 7 6 ) 𝑁 7 − 𝑊 E T 7 − 1 1 𝑁 7 𝑁 9 , 𝜕 𝑁 8 𝜕 𝑡 = 𝑊 5 8 𝑁 5 − 𝑊 E T 1 2 − 8 𝑁 1 2 𝑁 5 − 𝐴 8 7 𝑁 8 + 𝑊 6 8 𝑁 2 6 , 𝜕 𝑁 9 𝜕 𝑡 = − ( 𝑊 9 − 1 2 + 𝑊 E T 6 − 1 0 𝑁 6 + 𝑊 E T 7 − 1 1 𝑁 7 ) 𝑁 9 + 𝑊 E T 1 2 − 8 𝑁 5 𝑁 1 2 + ( 𝑊 1 0 − 9 + 𝐴 1 0 − 9 ) 𝑁 1 0 − 𝑊 9 − 1 0 𝑁 9 , 𝜕 𝑁 1 0 𝜕 𝑡 = − ( 𝑊 1 0 − 9 + 𝐴 1 0 − 9 ) 𝑁 1 0 + 𝑊 9 − 1 0 𝑁 9 + 𝑊 E T 6 − 1 0 𝑁 6 𝑁 9 + 𝐴 1 1 − 1 0 𝑁 1 1 + ( 𝑊 1 2 − 1 0 + 𝐴 1 2 − 1 0 ) 𝑁 1 2 − 𝑊 1 0 − 1 2 𝑁 1 0 − 𝑊 1 0 − 1 3 𝑁 1 0 , 𝜕 𝑁 1 1 𝜕 𝑡 = 𝑊 E T 7 − 1 1 𝑁 7 𝑁 9 − 𝐴 1 1 − 1 0 𝑁 1 1 + 𝐴 1 2 − 1 1 𝑁 1 2 , 𝜕 𝑁 1 2 𝜕 𝑡 = 𝑊 9 − 1 2 𝑁 9 + 𝐴 1 3 − 1 2 𝑁 1 3 − ( 𝑊 E T 1 2 − 8 𝑁 5 + 𝐴 1 2 − 1 1 + 𝑊 1 2 − 1 0 ) 𝑁 1 2 + 𝑊 1 0 − 1 2 𝑁 1 0 , 𝜕 𝑁 1 3 𝜕 𝑡 = 𝑊 1 0 − 1 3 𝑁 1 0 − 𝐴 1 3 − 1 2 𝑁 1 3 , ( 1 ) where 𝑁 1 - 𝑁 4 are the population densities of P r 3 + ion at energy levels 3 H 4 , 3 H 5 , 3 F 4 , 1 G 4 , 𝑁 5 - 𝑁 8 are the population densities of E r 3 + ion at energy levels 4 I 1 5 / 2 , 4 I 1 3 / 2 , 4 I 1 1 / 2 , and 4 I 9 / 2 , 𝑁 9 - 𝑁 1 3 are the population densities of T m 3 + ions at energy levels 3 H 6 , 3 F 4 , 3 H 5 , 4 H 4 , 1 G 4 . 𝑊 1 3 , 𝑊 3 1 , 𝐴 3 1 are the stimulated absorption and emission rates, spontaneous emission rate between 3 H 4 and 3 F 4 levels of P r 3 + , respectively. 𝑊 2 4 , 𝑊 4 2 , 𝐴 4 2 are the stimulated absorption and emission rates, spontaneous emission rate between the 3 H 5 and 1 G 4 levels of P r 3 + , respectively. 𝐴 2 1 is the spontaneous emission rate between the 3 H 4 and 3 H 5 levels of P r 3 + . 𝑊 5 6 , 𝑊 6 5 , 𝐴 6 5 are the stimulated absorption and emission rates, spontaneous emission rate between the 4 I 1 5 / 2 and 4 I 1 3 / 2 levels of E r 3 + , respectively. 𝑊 5 8 , 𝐴 8 7 , 𝐴 7 6 are the 800 nm- pump absorption rate, spontaneous emission rate from 4 I 9 / 2 to 4 I 1 1 / 2 levels, spontaneous emission rate from 4 I 1 1 / 2 to 4 I 1 3 / 2 levels of E r 3 + , respectively. 𝑊 1 0 - 1 2 , 𝑊 1 2 - 1 0 , 𝐴 1 2 - 1 0 are the stimulated absorption and emission rates, spontaneous emission rate between the 3 H 4 and 3 F 4 levels of T m 3 + , respectively. 𝑊 9 - 1 2 , 𝑊 9 - 1 0 , 𝑊 1 0 - 9 , 𝐴 1 0 - 9 , 𝐴 1 2 - 1 1 , 𝐴 1 1 - 1 0 are the 800 nm pump absorption rate, stimulated absorption rate, stimulated emission rate, spontaneous emission rate between 3 H 6 and 3 F 4 levels of T m 3 + , nonradiation transition rate from 3 H 4 to 3 H 5 , nonradiation transition rate from 3 H 5 to 3 F 4 , respectively. 𝑊 1 - 4 , 𝑊 5 - 8 , 𝑊 1 0 - 1 3 are 980 nm pump absorption rates between the 3 H 4 and 1 G 4 levels of P r 3 + , between the 4 I 1 5 / 2 and 4 I 1 9 / 2 levels of E r 3 + , and between the 3 H 6 and 3 H 4 levels of T m 3 + , respectively. 𝑊 E T 6 - 3 , 𝑊 E T 7 - 4 , 𝑊 E T 6 - 1 0 , 𝑊 E T 7 - 1 1 , 𝑊 E T 1 2 - 8 stand for the transfer rates from E r 3 + : 4 I 1 3 / 2 , P r 3 + : 3 H 4 to E r 3 + : 4 I 1 5 / 2 , P r 3 + : 3 F 4 , from E r 3 + : 4 I 1 1 / 2 , P r 3 + : 3 F 4 to E r 3 + : 4 I 1 5 / 2 , P r 3 + : 1 G 4 , from E r 3 + : 4 I 1 1 / 2 , T m 3 + : 3 H 6 to E r 3 + : 4 I 1 5 / 2 , T m 3 + : 3 H 5 , from E r 3 + : 4 I 1 3 / 2 , T m 3 + : 3 H 6 to E r 3 + : 4 I 1 5 / 2 , T m 3 + : 3 F 4 , from T m 3 + : 3 H 4 , E r 3 + : 4 I 1 5 / 2 to T m 3 + : 3 H 6 , and from E r 3 + : 4 I 9 / 2 , T m 3 + : 3 H 6 to E r 3 + : 4 I 1 5 / 2 , T m 3 + : 3 F 4 , respectively. The transition rates: 𝑊 𝑖 𝑗 = 𝜎 𝑖 𝑗 𝑃 𝑘 ℎ 𝜈 𝑘 𝐴 e ff ( 𝑖 , 𝑗 = 1 ∼ 1 2 , 𝑘 = 𝑠 , 𝑝 ) , ( 2 ) where 𝜎 𝑖 𝑗 is cross-section of the transition between 𝑖 and 𝑗 level, and 𝐴 e ff 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: 𝑑 𝑃 𝑆 1 𝑑 𝑧 = Γ 1 3 1 0 ( 𝑁 3 𝜎 p r s e 𝐵 − 𝑁 2 𝜎 p r s a 𝐵 ) 𝑃 𝑆 1 − 𝛼 1 3 1 0 𝑃 𝑆 1 , 𝑑 𝑃 𝑆 2 𝑑 𝑧 = Γ 1 4 7 0 ( 𝑁 1 2 𝜎 t m s e 𝐴 − 𝑁 1 1 𝜎 t m s a 𝐴 ) 𝑃 𝑆 2 − 𝛼 1 4 7 0 𝑃 𝑆 2 , 𝑑 𝑃 𝑆 3 𝑑 𝑧 = Γ 1 5 5 0 ( 𝑁 6 𝜎 e r s e − 𝑁 5 𝜎 e r s a 𝐴 − 𝑁 8 𝜎 e r s a 𝐵 ) 𝑃 𝑆 3 − 𝛼 1 5 5 0 𝑃 𝑆 3 , 𝑑 𝑃 𝑆 4 𝑑 𝑧 = Γ 1 6 0 0 ( 𝑁 3 𝜎 p r s e 𝐴 − 𝑁 1 𝜎 p r s a 𝐴 ) 𝑃 𝑆 4 − 𝛼 1 6 0 0 𝑃 𝑆 4 , 𝑑 𝑃 𝑆 5 𝑑 𝑧 = Γ 1 6 5 0 ( 𝑁 1 0 𝜎 t m s e 𝐵 − 𝑁 9 𝜎 t m s a 𝐵 ) 𝑃 𝑆 5 − 𝛼 1 6 5 0 𝑃 𝑆 5 , 𝑑 𝑃 𝑝 1 𝑑 𝑧 = − Γ 8 0 0 [ ( 𝑁 5 𝜎 e r p a − 𝑁 8 𝜎 e r p e ) + ( 𝑁 9 𝜎 t m p a − 𝑁 1 2 𝜎 t m p e ) ] 𝑃 𝑝 1 − 𝛼 8 0 0 𝑃 𝑝 1 , 𝑑 𝑃 𝑝 2 𝑑 𝑧 = − Γ 9 8 0 [ ( 𝑁 1 𝜎 p r p a − 𝑁 4 𝜎 p r p e ) + ( 𝑁 5 𝜎 e r p a − 𝑁 7 𝜎 e r p e ) + ( 𝑁 1 0 𝜎 t m p a − 𝑁 1 3 𝜎 t m p e ) ] 𝑃 𝑝 2 − 𝛼 9 8 0 𝑃 𝑝 2 , 𝑑 𝑃 A S E 1 𝑑 𝑧 = Γ 1 3 1 0 ( 𝑁 3 𝜎 p r s e 𝐵 − 𝑁 2 𝜎 p r s a 𝐵 ) 𝑃 A S E 1 + 2 ℎ 𝜐 Δ 𝜐 𝑁 3 𝜎 p r s e 𝐵 − 𝛼 1 3 1 0 𝑃 A S E 1 , 𝑑 𝑃 A S E 2 𝑑 𝑧 = Γ 1 4 7 0 ( 𝑁 1 2 𝜎 t m s e 𝐴 − 𝑁 1 1 𝜎 t m s a 𝐴 ) 𝑃 A S E 2 + 2 ℎ 𝜐 Δ 𝜐 𝑁 1 2 𝜎 t m s e 𝐴 − 𝛼 1 4 7 0 𝑃 A S E 2 , 𝑑 𝑃 A S E 3 𝑑 𝑧 = Γ 1 5 5 0 ( 𝑁 6 𝜎 e r s e − 𝑁 5 𝜎 e r s a 𝐴 − 𝑁 8 𝜎 e r s a 𝐵 ) 𝑃 A S E 3 + 2 ℎ 𝜐 Δ 𝜐 𝑁 6 𝜎 e r s e − 𝛼 1 5 5 0 𝑃 A S E 3 , 𝑑 𝑃 A S E 4 𝑑 𝑧 = Γ 1 6 0 0 ( 𝑁 3 𝜎 p r s e 𝐴 − 𝑁 1 𝜎 p r s a 𝐴 ) 𝑃 A S E 4 + 2 ℎ 𝜐 Δ 𝜐 𝑁 3 𝜎 p r s e 𝐴 − 𝛼 1 6 0 0 𝑃 A S E 4 , 𝑑 𝑃 A S E 5 𝑑 𝑧 = Γ 1 6 5 0 ( 𝑁 1 0 𝜎 t m s e 𝐵 − 𝑁 9 𝜎 t m s a 𝐵 ) 𝑃 A S E 5 + 2 ℎ 𝜐 Δ 𝜐 𝑁 1 0 𝜎 t m s e 𝐵 − 𝛼 1 6 5 0 𝑃 A S E 5 , ( 3 ) where 𝑃 𝑝 1 , 𝑃 𝑝 2 are the pump powers at 800 nm, 980 nm, respectively. 𝑃 𝑆 1 , 𝑃 𝑆 2 , 𝑃 𝑆 3 , 𝑃 𝑆 4 , 𝑃 𝑆 5 are the powers of the signals at 1310, 1470, 1530, 1600, and 1650 nm bands, respectively. 𝑃 A S E 1 , 𝑃 A S E 2 , 𝑃 A S E 3 , 𝑃 A S E 4 , 𝑃 A S E 5 are the powers of the ASE at 1310, 1470, 1530, 1600, and 1650 nm bands, respectively. Γ 1 3 1 0 , Γ 1 4 7 0 , Γ 1 5 3 0 , Γ 1 6 0 0 , Γ 1 6 5 0 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. 𝜎 t m s e 𝐴 , 𝜎 t m s e 𝐵 , 𝜎 e r s e are the emission cross-sections of 3 H 4 - 3 F 4 (1470 nm) and 3 F 4 - 3 H 6 (1650 nm) in T m 3 + ions and 4 I 1 3 / 2 - 4 I 1 5 / 2 (1530 nm) in E r 3 + ions, respectively. 𝜎 t m s a 𝐴 , 𝜎 t m s a 𝐵 , 𝜎 e r s a are the absorption cross-sections of 3 H 4 - 3 F 4 (1470 nm) and 3 F 4 - 3 H 6 (1650 nm) in T m 3 + ions and 4 I 1 3 / 2 - 4 I 1 5 / 2 (1530 nm) in E r 3 + ions, respectively. 𝜎 p r s e 𝐴 , 𝜎 p r s a 𝐴 and 𝜎 p r s e 𝐵 , 𝜎 p r s a 𝐵 are the emission cross-sections of 1 G 4 - 3 H 5 (1310 nm) and 3 F 4 - 3 H 4 (1600 nm) in P r 3 + ions.

276538.fig.001
Figure 1: Schematic of energy levels and transition configurations of E r 3 + -T m 3 + -P r 3 + 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 ( 𝑊 E T 6 3 , 𝑊 E T 7 4 , 𝑊 E T 6 - 1 0 , 𝑊 E T 7 - 1 1 , 𝑊 E T 1 2 - 8 ) were linearly increasing functions of 𝑁 𝑡 E r , 𝑁 𝑡 T m , 𝑁 𝑡 𝑃 𝑟 , respectively, [15, 16] and are expressed with equations: 𝑊 E T 6 3 = 𝑊 E T 7 4 = 1 . 0 × 1 0 − 2 2 + 4 . 0 × 1 0 − 4 9 ( 𝑁 𝑃 𝑟 𝑁 E r ) 1 / 2 − 1 . 0 × 1 0 2 5 , 𝑊 E T 6 - 1 0 = 𝑊 E T 7 _ 1 1 = 1 . 0 × 1 0 − 2 2 + 4 . 0 × 1 0 − 4 9 ( 𝑁 T m 𝑁 E r ) 1 / 2 − 1 . 0 × 1 0 2 5 , 𝑊 E T 1 2 - 8 = 1 . 0 × 1 0 − 2 2 + 4 . 0 × 1 0 − 4 9 ( 𝑁 T m 𝑁 E r ) 1 / 2 − 1 . 0 × 1 0 2 5 . ( 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: P r 3 + concentration at 1 . 7 × 1 0 2 4 , T m 3 + concentration at 3 . 9 × 1 0 2 4 , E r 3 + concentration at 1 . 2 × 1 0 2 4 ions/ m 3 and fixed pump powers at 200 mW/200 mW for 800 nm/980 nm.

276538.fig.002
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 P r 3 + = 1 . 9 × 1 0 2 4 , T m 3 + = 3 . 9 × 1 0 2 4 , E r 3 + = 1 . 2 × 1 0 2 4 ions/ m 3 , and energy transfer coefficient W e t 6 - 3 = 6 3 × 1 0 − 2 0 , W e t 6 - 1 0 = 2 0 0 × 1 0 − 2 2 .

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 1 G 4 and 3 H 5 level of P r 3 + ions, the 3 H 4 and 3 F 4 level of T m 3 + ions, the 4 I 1 3 / 2 and 4 I 1 5 / 2 levels of E r 3 + 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 3 F 4 to 3 H 6 levels of T m 3 + , it shares same level ( 3 F 4 ) with the channel at 1470 nm arising from the transition from 3 H 4 and 3 F 4 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 E r 3 + -T m 3 + -P r 3 + 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 P r 3 + , T m 3 + , E r 3 + 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.

tab1
Table 1: Spectral parameters of E r 3 + -doped and T m 3 + and P r 3 + doped telluride fiber for numerical calculation.

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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