1. Introduction

Since Yb³⁺ have large absorption cross-section at 980nm, Tm³⁺/Yb³⁺ codoped silica fiber [1], fluoride fiber [2], and tellurite fiber[3] 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 [4]. Theoretical model were established for Tm³⁺ doped amplifiers (TDFA) in silica fiber [6] and fluoride fiber [7,8], and also for Tm³⁺/Yb³⁺ codoped amplifiers (TYDFA) in silica fiber [1] and fluoride fiber [2].

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 [3]. 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. [2]. The rate equations and propagation equations for Tm³⁺ and Yb³⁺ can be established as follows:

 

Fig. 1. Energy level of Tm ³⁺, Yb ³⁺ and pump scheme

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$A_{\mathit{\text{ij}}}^r$ and $A_i^{\mathit{\text{nr}}}$ 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 [6]:

Here $P_{\mathrm{\lambda }}^{\pm }$ 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 [6]:

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 =${\int }_0^{\infty }$ 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. [12], the spectral absorption cross-section at S-band can be calculated by McCumber relation [13]:

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 [14]. The 1050nm cross-section data of Tm³⁺ in fluoride are obtained from Ref.7. The nonradiative transition rates (${\mathrm{A}}_{\mathrm{T}43}^{\text{nr}}$ and ${\mathrm{A}}_{\mathrm{T}21}^{\text{nr}}$) were calculated using the empirical energy-gap law [15].

Table 1. Parameters used in the numerical simulations

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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. [4]. In Ref. [1], K _YT1 and K _YT2 were collected from Ref. [4] and delineated in terms of the product of the total Tm³⁺ and Yb³⁺ concentrations, N_Tm and N_Yb, here we estimate the values of K _YT1 and K _YT2 based on the extrapolation curves in Fig. 2 of Ref. [1].

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].

 

Fig.2 . pectral gain of the codoped fiber

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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.

4. Conclusion

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.