Numerical Simulation of 980 nm-LD-Pumped Yb3+-Er3+-Tm3+-Codoped Fiber Amplifier for 1500 nm and 1600 nm Bands

Jiang, Chun

doi:https://doi.org/10.1155/2009/278105

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Research Article | Open Access

Volume 2009 | Article ID 278105 | https://doi.org/10.1155/2009/278105

Numerical Simulation of 980 nm-LD-Pumped Yb³⁺-Er³⁺-Tm³⁺-Codoped Fiber Amplifier for 1500 nm and 1600 nm Bands

Chun Jiang¹

Academic Editor: Samir K. Mondal

Received02 Mar 2009

Accepted01 May 2009

Published28 Jun 2009

Abstract

The theoretical model of ---codoped fiber amplifier pumped by 980 nm laser is proposed, and the rate and power propagation equations are numerically solved to analyze the dependences of the gains at 1500 nm and 1600 nm bands on the activator concentrations, fiber length, pump power, and signal wavelength. The numerical results show that our model is in good agreement with experimental result, and with pump power of 200 mW and fiber length varying from 0.15 to 1.5 m, the gains at the two bands may reach 10.0–20.0 dB when the codoping concentrations of , , and are in the ranges 1.0–, 1.0–, and 1.0– ions/, respectively. The fiber parameters may be optimized to flatten the gain spectra.

1. Introduction

The All-wave fiber without residual OH group is being considered for Coarse Wavelength Division Multiplexing (CWDM) transmission systems and metro area optical networks because it has low-loss bandwidth of about 400 nm (1250–650 nm). WDM technology has been the most important technology of large-capacity optical transmission system, and optical amplifiers are key devices of WDM system. Although Fiber Raman Amplifier (FRA) using split-band and multipump schemes might simultaneously amplify multichannel signal within 130nm bandwidth, it would increase the power penalty of the system and degrade the performance of the system since the introduction of the multiplexing/de-multiplexing caused additional insertion loss [1]. Another kind of FRA could provide distributed amplification within 140 nm bandwidth using pump-signal interleaving method, but its gain spectra had relatively large ripple [1]. Later, a novel multiband FRA was reported theoretically providing flat bandwidth of 200 nm with ripple of 1 dB [2]. However, the FRA requires higher pump power due to its lower pump efficiency. Rare-earth doped fiber amplifiers have higher gain and pump efficiency, and in the past decades the researches on rare-earth-doped fiber amplifiers have been focusing on the singly-doped fiber amplifiers, and all of these amplifiers have their own bandwidths, Er³⁺-doped fiber amplifier (EDFA) with new parallel configuration [3–5] was reported providing gain bandwidth of more than 100 nm, and Tm³⁺-doped- and Pr³⁺-doped fiber amplifiers [6–9] could provide the gains in the ranges 1400–1500 nm, 1280–1340 nm, respectively. Recent reports on emission properties of Er³⁺-Tm³⁺-codoped silicate and telluride fibers showed that the combination of the emission at 1500 nm windows with that at 1400 nm windows in a single fiber may generate a large seamless emission spectra with emission width up to 200 nm in the codoped system [10–14]. The upconversion and energy transfer in Yb³⁺-Er³⁺-Tm³⁺- and Er³⁺-Tm³⁺-codoped glasses were reported [15]. Energy transfer and upconversion luminescence of Bismuth, Tm³⁺/Ho³⁺, Tb³⁺/Yb³⁺, Er³⁺/Tm³⁺/Yb³⁺-codoped inorganic materials for display systems were reported [16–30]. In our previous works [31, 32], we presented the numerical model of Er³⁺-Tm³⁺ codoped telluride fiber amplifier pumped at 800 nm and calculated the dependence of the gains at 1470 nm and 1530 nm bands on the fiber parameters, and analyzed the transmission performance of the WDM system based on the codoped amplifier. Although the rate equations of Er³⁺-Tm³⁺, Er³⁺-Yb³⁺-Tm³⁺-codoped fluoride glasses was reported in [15], the equations just considered the upconversion of infrared to visible light for display system, did not consider the spontaneous and stimulated emissions of 1470 nm, 1530 nm, and 1630 nm bands. Other references on this codoped system just concentrated on the spectral properties. Owing to importance of the double and multidoped systems for broadband amplification of telecommunication wavelength, a theoretical model will be desirable for designing and optimizing the codoped broadband amplifiers. In present paper, we propose a new numerical model of Yb³⁺ and Er³⁺ and Tm³⁺ codoped fiber system pumped by 980 nm laser for amplification of the signal at 1470, 1530, and 1630 nm bands. This model considers the excited state absorption and upconversion of Er³⁺ and Tm³⁺ ions and cross-relaxation of Tm³⁺-Er³⁺. The dependence of the gain spectra covering 1500 and 1600 nm bands on codoping concentrations, fiber length, and pump power is calculated and analyzed.

2. Theoretical Model

Figure 1 shows the schematic of the energy levels and electron transitions and energy transfer process of an Er³⁺-Tm³⁺-Yb³⁺ codoped telluride glass system pumped by 980 nm. With the excitation of 980 nm pump, the electrons of Yb³⁺ ions are excited from the ground state (²F_7/2) to the excited state (²F_5/2) and the energy at the ²F_5/2 level transfers to the ⁴I_11/2 level of Er³⁺ due to matching energy gap between the two levels, meanwhile, the energy at the level also can transfer to the ³F₄ level of Tm³⁺ ion through multiphonon process. With the excitation, moreover, the electrons of Er³⁺ ions are excited from the ground state ⁴I_15/2 to the excited state ⁴I_11/2, then nonradiately relax to the ⁴I_13/2 level through multiphonon process, and transit from the level to the ground state (⁴I_15/2 level), emitting photons at 1500 nm band. In addition, the electrons at ⁴I_11/2 level of Er³⁺ ions can be excited to the ⁴F_7/2 level due to excited state absorption (ESA), and the electrons at the ⁴F_7/2 level transit to the ground state with emission of red photon. On the other hand, energy transfer also can take place between Er³⁺-Tm³⁺ and Yb³⁺-Tm³⁺ via cross-relaxation process. The energy at the ⁴I_13/2 level of Er³⁺ ions and the ²F_5/2 level of Yb³⁺ ions can transfer to the ³F₄, ³F₂ levels of Tm³⁺ ions via the electron transition from the ³F₄ level to ³F₂ level of Tm³⁺ at which the electron nonradiately relax to ³H₄ level from which is excited to the ¹G₄ level via another cross-relaxation process. Electron at the ¹G₄ level transit to the ³F₂, ³F₄, and ³H₆ levels with emission of lights at 1630, 650, and 476 nm bands, respectively. The electron at ³F₂ level nonradiately relaxes to ³H₄ level and then transites to the ³F₄ level with emission of light at 1470 nm band. The electrons at ³F₄ level transit to ground state (³H₆), emitting the light at 1680 nm band.

According to Figure 1, a rate equation group can be written as follows: where , , are the population densities of Er³⁺ at energy levels 1, 2, 3, and 4, and and are the population densities of Yb³⁺ at energy levels 1 and 2 and , , are the population densities of Tm³⁺ at energy levels 1, 2, 3, 4, and 5, , and are the pump transition rates, is the transition rate between energy levels i and j of the activating ions (Er³⁺, Yb³⁺, Tm³⁺), and is the transfer rate between energy level and . is the spontaneous transition rate between energy level and . , , are total concentrations of Er³⁺, Yb³⁺, and Tm³⁺ ions, respectively. The transition rates are as follows: where are the pump absorption cross-section, is the absorption and emission cross-sections of the transitions between levels and . is the effective cross-section area of the fiber.

The power propagations of the pump and signal and amplified spontaneous emission (ASE) along the fiber are described by differential equation group (3), where is the pump power at 980 nm, , and are the power of the signals at 1470 nm, 1530 nm, and 1630 nm, respectively. , are the ASE powers in the 1470, 1530, and 1630 bands, and _1470, _1530, _1630, and _ are overlap factors at 1470 nm, 1530 nm, and 1630 nm, and ASE wavelength, respectively, and are signal and pump frequencies, respectively. and are Plank constant, the frequency-independent back-ground loss of the active fiber, respectively,

The above power propagation equation group forms a system of coupled differential equations, which will be solved by numerical integration using Newton and Lung-Kutta methods along the active fiber. It was assumed that the energy transfer rates were increasing functions of and [33–35], and expressed in the following equation:

3. Results and Discussion

3.1. Comparison with Experimental Results

The spontaneous spectra of Yb³⁺-Er³⁺-Tm³⁺-telluride glasses excited near 980 nm were measured with two emission peaks [36]. The ratio of Yb³⁺, Er³⁺, Tm³⁺ ion concentrations in the glass samples with thickness of 1.5 mm was and , two stronger emission peaks were observed in the samples. To verify our theoretical model, same parameters as the sample are used to calculated the luminescence intensity, and calculated emission spectra and measured emission spectra from the reference are normalized and plotted in Figure 2 where solid line represent calculated spectra, and the measured spectra from [36] are denoted using circle, it is shown that calculated spectra are in good agreement with the measured, verifying feasibility of our model.

3.2. Activator Concentration Dependence

The gain spectra is calculated by solving numerically the equation groups (1)–(3). Table 1 is the spectroscopic parameters for the Er³⁺-doped and Tm³⁺-doped telluride glass fiber for this calculation, the parameters of Yb³⁺ is from [36], the core diameter of fiber is 5 m and numerical aperture is 0.21, and the input power of signal is 30 dBm.

Dependence of the gain spectra in the range 1450–1700 nm on Er³⁺ concentration is shown Figure 3(a). With Yb³⁺ concentration of ions/m³ and Tm³⁺ concentration of ions/m and fixed fiber length at 1.5 m and when the Er³⁺ concentration increases from to ions/m³, the gains at the range 1510–1630-nm increase, where the gain at the 1530 nm increases from 10.0 to 21.0 dB, the gains beyond 1630 nm keep constant. Figure 3(b) demonstrates variation of the gain spectra with Tm³⁺ concentration. With Yb³⁺ concentration of ions/m³ and Er³⁺ concentration of ions/m and fixed fiber length at 1.5 m and when the Tm³⁺ concentration increases from to ions/m³, the gains at the range 1510–1650 nm increase, where the gain at the 1530 nm increases from 10.5 to 17.8 dB, and the gain at 1630 nm increases from 7.0 to 9.8-dB . Effect of Yb³⁺ concentration on the gain spectra is shown Figure 3(c). With both Er³⁺ and Tm³⁺ concentrations of ions/m³ and fixed fiber length at 1.5 m and when the Yb³⁺ concentration increases from to ions/m³, the gains at the range 1510–1610 nm decrease, and the gain at the 1610–1650 nm increase.

(a)

(b)

(c)

3.3. Fiber Length Effect

Effect of fiber length on the gain spectra is shown Figure 4. With Yb³⁺ concentration of ions/m³, Er³⁺ concentration of ions/m and Tm³⁺ concentration of ions/m, when fiber length increases from 0.15 to 0.25 m, the gains at the range 1500–1630 nm increase, where the gain at the 1530 nm increases from 12.5 to 24.5 dB, and the gains at 1630 nm decreases from 10.0 to 5.0 dB .

3.4. Variation with Pump Power

Variation of the gain spectra with pump power is shown in Figure 5. With Yb³⁺ concentration of 20.0 × 10²⁴ ions/m³, Er³⁺ concentration of 1.0 × 10²⁴ ions/m and Tm³⁺ concentration of 3.0 × 10²⁴ ions/m and fiber length of 1.5 m, when pump power increases from 100 to 300 mW, the gains at the range 1500–1610 nm increase, where the gain at the 1530 nm increases from 14.0 to 27.0 dB, and the gain at 1630 nm decreases from 10.0 to 1.0 dB.

4. Discussion

In above results, one notes that with increasing Yb³⁺ concentration from 1.0 × 10²⁵ to 3.0 × 10²⁵ ions/m³, the gains at the range 1510–1610 nm decrease, and the gains at the 1610–1650 nm increase, showing different Yb³⁺ ion concentration dependences of gain spectra in different wave band. These different dependences, we think, may be explained using energy transfer from Yb³⁺ to Er³⁺ and from Yb³⁺ to Tm³⁺ ions. When Yb³⁺ ion concentration increases, the pump absorption induced by Yb³⁺ increases and the pump absorption by Er³⁺ decreases, this leads to (1) increased energy transfer from Yb³⁺ to Tm³⁺ ions and increased population inversion between ³H₄ and ³F₄ of Tm³⁺ ions and thus increased gain at 1630 nm band, and (2) increased energy transfer from Yb³⁺ to Er³⁺ ions, but reduced pump absorption of Er³⁺ probably dominates over the increased energy transfer, thus results in reduced population inversion between the ⁴I_13/2 and ⁴I_15/2 levels of Er³⁺ and decreased gain at 1530 nm band.

Meanwhile, one also notes that with increasing pump power, the increasing of the gain spectra in 1500–1610 nm and the decreasing of the gain spectra in 1610–1650 nm show different pump-power effect on the gain spectra in different wave band. These different effects may be explained using energy transfer from Yb³⁺ to Er³⁺ and from Yb³⁺ to Tm³⁺ ions. With the power increasing, the pump absorptions caused by Yb³⁺ and Er³⁺ and Tm³⁺ increase simultaneously, this leads to increased population inversion between the ⁴I_13/2 and ⁴I_15/2 levels of Er³⁺ and thus increased gain at 1500–1610 nm band. The efficiency of the increasing of pump absorption caused by Tm³⁺ is less than that caused by Er³⁺ because the former depends highly on the population number of the ³F₄ level of Tm³⁺ ions coming from energy transfer from Yb³⁺ and Er³⁺ to Tm³⁺. Moreover, increasing pump absorption can increase the population of the ³F₂ level of Tm³⁺ ions, hence the population inversion between ¹G₄ and ³F₂ of Tm³⁺ ions and the gain at 1610–1650 nm band is reduced if the lifetime at ¹G₄ level is shorter than that at ³F₂ level.

It is shown from Figures 3, 4, and 5 that two weak peaks in the gain spectra appear at 1470 nm and 1680 nm, resulting separately from the transitions from the ³H₄ to ³F₄ levels and from ³H₄ to ³H₆ levels of Tm³⁺ ions. If both pumps at 800 nm and 980 nm are used, the gain spectra covering 1470 nm, 1530 nm, 1630 nm, 1680 nm bands may appear, further study is needed to optimize the fiber parameter and pump configuration to reduce the ripple of the gain spectra.

5. Conclusions

In conclusion, we present the numerical model of Yb³⁺-Er³⁺-Tm³⁺-codoped fiber amplifier pumped by 980 nm laser and analyzed the dependences of the gains at 1530 nm and 1630 nm on the activator codoping concentrations, fiber length, signal wavelength. The numerical results showed that our model was in good agreement with experimental result, and with pump power of 200 mW and fiber length varying from 0.15 to 1.5-m, the gains at the two bands could reach 10.0–20.0 dB when the codoping concentrations of Yb³⁺, Er³⁺, and Tm³⁺ were in the ranges 1.0–3.0 × 10²⁵, 1.0–3.0 × 10²⁴, 1.0–3.0 × 10²⁴ ions/m³, respectively. Two weak peaks in the gain spectra appeared at 1470 nm and 1680 nm, resulting separately from the transitions from the ³H₄ to ³F₄ levels and from ³H₄ to ³H₆ levels of Tm³⁺ ions. If both pumps at 800 nm and 980 nm will be used, the gain spectra covering 1470 nm, 1530 nm, 1630 nm, 1680 nm bands may appear. The optimization of the fiber parameter and two-pump configuration will be desirable for reducing the ripple of the gain spectra.

Acknowledgments

This work is supported in part by National Natural Science Foundation of China (Grant No.60377023 and No.60672017) and Program for New Century Excellent Talents in University and Shanghai Optical Science and Technology (No.05DZ22 0-09) and sponsored by Shanghai Pujiang Program. Thank is given to Mr. Jianda Liu for his numerical analysis code when he was with SJTU.

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Copyright © 2009 Chun Jiang. 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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