S-band Tm3+/Yb3+ codoped tellurite fiber amplifier pumped by a 980nm laser diode is proposed and modeled taking into consideration of the energy transfer process from Yb3+ to Tm3+ and the laser cavity inside a codoped fiber amplifier. S-band spectral gains for the codoped fiber amplifiers are investigated. The results show that considerable gain improvement can be achieved by constructing 1050nm laser cavity inside the amplifier.
©2006 Optical Society of America
Since Yb3+ have large absorption cross-section at 980nm, Tm3+/Yb3+ codoped silica fiber , fluoride fiber , and tellurite fiber have been studied to take advantage of the low cost 980nm laser diode (LD). The sensitization of Tm3+ by Yb3+ is mainly through 2 ways: nonradiative energy transfer process [1, 4, 5] and radiative energy transfer process[2,3]. These processes have been reported in cases of lasers at 1.5µm and 2.3µm using 975nm pump in Tm3+/Yb3+ codoped YLiF4 crystal . Theoretical model were established for Tm3+ doped amplifiers (TDFA) in silica fiber  and fluoride fiber [7,8], and also for Tm3+/Yb3+ codoped amplifiers (TYDFA) in silica fiber  and fluoride fiber .
Tellurite glass fibers exhibit significant advantages over the fluoride and silicate glass fibers for amplification outside the C-band. The tellurite glass has comparatively lower phonon energy (780 cm-1) than silicate glass, and it exhibits better environmental resistance than fluoride fibers, in addition, tellurite glass provides a much broader fluorescence spectra and larger rare earth oxide solubility than silicate and fluoride glasses [3,9]. Recently, Tm3+-doped tellurite fiber for S-band amplification were reported under dual-wavelength pumping (795/1064 nm and 1047/1550 nm) schemes [10, 11], demonstrating a 35-dB internal gain and broader band amplification than in fluoride glass fiber, however, these pump scheme is complicated and the pump wavelength is difficult to get by laser diode (LD). Tm3+/Yb3+ codoped tellurite fiber was studied to take advantage of low cost 980nm LD and 6 dB gain at 1490nm was achieved in Tm3+/Yb3+ codoped tellurite fiber by single120mW 980nm pump . Here, we proposed a scheme of Tm3+/Yb3+ codoped fiber amplifier in tellurite host with an internal laser cavity operating at 1050nm. This scheme has the advantage of producing an internally generated pump wavelength for improved pump efficiency in Tm3+ fiber amplifier. The results show that S-band gain can be improved by constructing 1050nm laser cavity inside the amplifier.
2. Theoretical model
The diagram of Tm3+ and Yb3+ energy levels, the relevant absorption and emission transitions, spontaneous emission, energy transfer process between Tm3+ and Yb3+ are shown in Fig. 1, the detailed construction of the internal laser cavity can be found in Ref. . The rate equations and propagation equations for Tm3+ and Yb3+ can be established as follows:
and are radiative and nonradiative decays respectively, K YT1 and K YT2 are the energy transfer parameter between 3 H 6 (Tm 3+)+2 F 5/2(Yb 3+)→3 H 5 (Tm 3+)+2 F 7/2(Yb 3+) and 3 F 4 (Tm 3+)+2 F 5/2 (Yb 3+)→3 F 2,3 F 3 (Tm 3+)+2 F 7/2 (Yb 3+), N T0 , N T1 , N T2 , N T3 , N T4 , N T5 , N Y0 , N Y1 are population densities of relevant energy levels of Tm3+ and Yb3+, W ij denotes the interaction of the electromagnetic field and the ions and it can be written as :
Here are the spectral power densities of the radiation propagating in the forward (+) and backward (-) directions along the fiber, σ ij is the transition cross-section between the energy levels i and j, and Γ is the so-called overlap factor defined by :
It is worth noting that N(r) denotes N Tm (r) or N Yb (r), the concentration distribution of Tm3+ or Yb3+, depending on whether Tm3+ or Yb3+ ions is involved in the process of W ij . Similarly N denotes N T or N Y , the concentration of Tm3+ or Yb3+ that N T =∫0∞N Tm (r)rdr and N y = N yb (r)rdr. Powers along the fiber can be expressed by propagation equations:
The spectroscopic parameters used in our analysis are carefully chosen from the literature and are summarized in Table 1, the spectral emission cross-sections at S-band of Tm3+-doped tellurite glasses are derived from Ref. , the spectral absorption cross-section at S-band can be calculated by McCumber relation :
Because there is no available cross-section data of Tm3+ at 1050nm in tellurite glasses, so we calculated it from the data of fluoride host by σ∝(n 2+2)2/9n . The 1050nm cross-section data of Tm3+ in fluoride are obtained from Ref.7. The nonradiative transition rates ( and ) were calculated using the empirical energy-gap law .
The cross-section data of Yb3+ at 980nm and 1050nm in tellurite glasses are obtained from Ref. 16. Since there is no data available for the energy transfer parameters K YT1 and K YT2 in ytterbium-thulium codoped tellurite materials, we have made use of the experimental data of the energy transfer parameters from ytterbium and thulium codoped single crystal materials in Ref. . In Ref. , K YT1 and K YT2 were collected from Ref.  and delineated in terms of the product of the total Tm3+ and Yb3+ concentrations, NTm and NYb, here we estimate the values of K YT1 and K YT2 based on the extrapolation curves in Fig. 2 of Ref. .
3. Results and discussion
The model is numerically resolved using a point by point and iterative method. Here we first investigate the gain characteristics of the codoped tellurite fiber which has the concentration of Tm3+ 5000ppm and Yb3+ 10000ppm. The fiber has the core diameter of 3 µm and is pumped by a 980nm LD. In Fig. 2, 4 lines represent the spectral gain from 1450nm to 1520nm of 4 different cases.
The 2 lines, with square and triangle respectively, represent the spectral gain of the amplifiers under the same pump conditions and with the same fiber length. Both the amplifiers have a fiber length of 24cm and are pumped by a 980nm laser at 120mW; the only difference between them is that the line with triangle has an internal 1050nm laser cavity, while the other line with square hasn’t. It is clear that about 2dB gain improvement is obtained by the internal 1050nm laser cavity. The gain of the amplifier without the internal 1050nm laser cavity is shifted to longer wavelength. The reason is that, without the internal laser cavity, the 1050nm emission generated by the Amplified Spontaneous Emission (ASE) in the codoped fiber is not strong enough to achieve high population inversion. The low inversion leads to the gain shift to longer wavelengths [17,18].
The line with diamond represents the spectral gain of the amplifier with a fiber length of 50cm and under the 300mW pump of a 980nm laser. The line with circle represents the spectral gain of the amplifier with the same length and pumping parameters, except it has an internal 1050nm laser cavity. It is shown that a maximum of about 5dB gain improvement can be obtained with the internal 1050nm laser cavity.
In summary, a scheme that the S-band Tm3+/Yb3+ codoped tellurite fiber amplifier pumped by single 980nm laser is proposed. By introducing an internal laser cavity at 1050nm into the Tm3+/Yb3+ codoped fiber amplifier, improved gain can be obtained when pumped by a single wavelength at 980nm. Clearly the built-in laser generated in the internal cavity provides effective optical pumping at 1050nm and leads to the improvement in the amplification gain. As an example, we have shown that the gain improvement as high as 5dB can be achieved by the 1050nm internal laser cavity under 300mW 980nm laser pump.
The authors acknowledge the financial support from China Scholarship Council, Natural Science Foundation of China, Natural Science Foundation of Shandong Province of China (grant no.Y2003G01 and Y2002G06), and Research Fund for the Doctoral Program of Higher Education of China.
References and links
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