1. Introduction

In the last years, Tm³⁺-doped glasses have generated a great deal of attention due to the interesting spectroscopic properties of their 1.4 μm and 1.8 μm infrared emissions. The ³H₄→³F₄ emission at around 1.4 μm is important to achieve a band extension in the spectral range corresponding to the S-band amplifier region, on the short wavelength side of the conventional erbium-doped fiber amplifier C band at 1530-1570 nm. On the other hand, the ³F₄→³H₆ transition around 1800 nm is of interest to extend lasing capability into the 1600-1900 nm atmospheric window [1-3]. To develop more efficient optical devices based on Tm³⁺ ions the choice of both the host glass and active ion concentration is very important. The host matrix should have low phonon energy to minimize multiphonon relaxation rates because the energy difference between the ³H₄ and the next lower-lying ³H₅ is not large (≈4300 cm^-1). To avoid this problem, glasses with low phonon energies such as fluorides, chalcogenides,tellurites, and heavy metal oxide glasses are required.

Tellurite glasses have attracted a considerable interest especially because of their high refractive index and low phonon energies [4,5]. Moreover, these glasses combine good mechanical stability, chemical durability, and high linear and nonlinear refractive indices,with a wide transmission window (typically 0.4-6 μm), which make them promising materials for photonic applications such as upconversion lasers, optical fiber amplifiers, non linear optical devices, and so on [6-15]. Broadband Er-doped fiber amplifiers have been achieved by using tellurite-based fibers as the erbium host [11,12] and very recently, efficient laser emission around 2 μm has been demonstrated in a tellurite fiber [15].

Another factor to be considered in achieving amplification in the S-band through the ³H₄→³F₄ emission is that this transition is affected by cross-relaxation among Tm³⁺ ions.When the activator ion concentration in glass becomes high enough, ions interact and ion-ion energy transfer occurs. The energy transfer processes reduce the lifetime and consequently the efficiency of the ³H₄ level due to the well known cross relaxation process (³H₄,³H₆→³F₄, ³F₄)[4]. In this process part of the energy of an ion in the ³H₄ level is transferred to another ion in the ground state with both ions ending up in the ³F₄ level.

In this work, we have characterized the spectroscopic properties of the infrared ³H₄→³F₄ emission of Tm³⁺ ions in two different compositions of TeO₂-WO₃-PbO tellurite glasses for three Tm₂O₃ concentrations (0.1, 0.5, and 1 wt%) by using steady-state and time-resolved laser spectroscopy. These glasses contain oxides of the heaviest metals such as tungsten and lead, which increases the linear and nonlinear refractive indexes [16]. The high linear index increases the local field correction at the rare-earth site leading to large radiative transition probabilities. On the other hand, the presence of two glass formers, such as TeO₂ and WO₃ produces a more complex network structure with a great variety of sites for the RE ions which contributes to the inhomogeneous broadening of the emission bands. The study includes absorption and emission spectroscopy and lifetime measurements for the infrared ³H₄→³F₄ emission at different concentrations. The analysis of the fluorescence decays from the ³H₄ level indicates the presence of a dipole-dipole quenching process assisted by energy migration. The average critical distance, which indicates the extent to which the energy transfer can occur, has been obtained and compared with other glasses.

2. Experimental techniques

The glasses with mol% compositions 80TeO₂-15WO₃-5PbO (TWP5) and 50TeO₂-30WO₃-20PbO (TWP20) were prepared by melting 10 g batches of high-purity TeO₂ (Sigma-Aldrich 99.995), WO3 (Aldrich 99.995) and PbO (99.999 Aldrich) reagents in a platinum crucible placed in an electrical Thermostar ^TM furnace at variable temperatures between 710 and 740° C during 30-45 min. The melts were stirred with a platinum rod and then poured onto a preheated brass plate, annealed 15 min at 390-400° C, and further cooled at a 3° C/min rate down to room temperature. The glasses were doped with different Tm₂O₃ (Aldrich 99.99%)concentrations (0.1, 0.5, and 1 wt%). No post-melting analysis was made. The optical measurements were carried out on polished planoparallel glass slabs of about 2 mm thickness.

Conventional absorption spectra were performed with a Cary 5 spectrophotometer. The samples temperature was varied between 10 and 295 K in a continuous flow cryostat. The steady-state emission measurements were made with a Ti-sapphire ring laser (0.4 cm^-1 linewidth) in the 760-940 nm spectral range as exciting light. The fluorescence was analyzed with a 0.25 monochromator, and the signal was detected by an extended IR Hamamatsu R5509-72 photomultiplier and a PbS detector. Lifetime measurements were obtained by exciting the samples with a Ti-sapphire laser pumped by a pulsed frequency doubled Nd:YAG laser (9 ns pulse width), and detecting the emission with a Hamamatsu R5509-72 photomultiplier. Data were processed by a Tektronix oscilloscope.

3. Experimental results

3.1 Absorption measurements

The room temperature absorption spectra were obtained for all samples in the 300-2000 nm range with a Cary 5 spectrophotometer. As an example, Fig. 1 shows the absorption cross-section as a function of wavelength for the two glasses. The spectra are characterized by the bands corresponding to the transitions starting from the ³H₆ ground state to the different higher levels ¹G₄, ³F_2,3, ³H₄, ³H₅, and ³F₄. The profile and the position of the absorption bands are similar with slight differences in the absorption cross-section. However, as expected, the optical band gap is shifted to longer wavelengths in the glass with the higher content of WO₃ and PbO. In both glasses, energy levels higher than ¹G₄ are not observed because of the intrinsic absorption bandgap.

 

Fig. 1. Room temperature absorption cross-section of Tm³⁺ in TWP5 and TWP20 glasses.

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Data from these spectra have been used to calculate the radiative transition rates by using the Judd-Ofelt (JO) theory [17,18]. Five absorption bands (³F_2,3,³H₄, ³H₅, and ³F₄) were chosen for the calculation. To obtain the contribution to the integrated absorption coefficient corresponding to levels ³F₂ and ³F₃ a Gaussian fit method has been used to separate the overlapping peaks. The measured absorption bands are all dominated by electric dipole transitions except the transition ³H₆→³H₅, which contains electric-dipole and magnetic-dipole contributions. The magnetic-dipole contribution, f_md, can be obtained from equation f_md=nf́[19], where n is the refractive index of the studied glasses and f́ is a quantity calculated on the basis of energy-level parameters for lanthanide aquo ions. The electric dipole oscillator strength for this transition is then obtained by subtracting the calculated magnetic-dipole contribution from the experimental oscillator strength. The error analysis of the measured quantities used in the JO calculation gives an estimated accuracy of 5%. The JO parameters obtained for these glasses together with the density, refractive index, and Tm³⁺ concentration (calculated from the density) for samples with 1 wt% of Tm₂O₃ are displayed in Table 1. As can be seen from this Table the density increases as the WO₃ and PbO content increases due to the higher atomic weight of these oxides compared with TeO₂. The refractive index also increases in the glass with the higher content of WO₃ and PbO due to their higher polarizability compared with TeO₂[20]. The values for the JO parameters are in agreement with those previously reported in other tellurite glasses [21]. It is well known that Ω₂ is the most sensitive to local structure and glass composition and its value is indicative of the amount of covalent bonding between RE ions and ligand anions [22]. As can be seen in Table 1, Ω₂ is slightly higher for the glass with the higher content of WO₃ and PbO. This behavior can not be explained in terms of covalency because the increase of WO₃ and PbO with strong W-O and Pb-O bonds of highly covalent character should reduce the covalency of the RE ions and therefore the Ω₂ value. The increase of Ω₂ as WO₃ content increases has also been observed in TeO₂-WO₃ binary glasses and related to a larger asymmetry of the local environment of the Tm³⁺ ions in the matrix [23].

Table 1. Density, Tm³⁺ ions concentration, refractive index, JO parameters, and r.m.s. deviation for the two glasses.

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The radiative transition probabilities for the excited levels of Tm³⁺ can be calculated by using the JO parameters. The radiative transition probability is given by [24],

where $\mathrm{n}\frac{{\left({\mathrm{n}}^2+2\right)}^2}{9}$ is the local field correction for electric dipole transitions and n³ for magnetic dipole transitions.

The radiative lifetime is related to radiative transition probabilities by,

The fluorescence branching ratio can be obtained from the transition probabilities by using,

The radiative transition probabilities, the branching ratios, and the radiative lifetimes of some selected levels of Tm³⁺ for both glass compositions are shown in Table 2. Since the radiative transition probability is related to the refractive index of the glass host, the glass with the highest content of PbO, which has a slightly higher refractive index presents higher radiative transition probabilities.

3.2 Emission and fluorescence lifetimes

The infrared emission in the 1300-2200 nm spectral range was obtained for all samples at room temperature by exciting at 793 nm. As an example, Fig. 2 shows the fluorescence spectra corresponding to the ³H₄→³F₄ and ³F₄→³H₆ transitions normalized to ³H₄→³F₄ transition for the three samples doped with 0.1, 0.5, and 1 wt% of Tm₂O₃ in the two glasses.

Table 2. Predicted radiative transition rates, lifetimes, and branching ratios of some excited levels of Tm³⁺ in TWP glasses.

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In both glasses, the spectra show a strong emission band centered around 1490 nm which corresponds to the ³H₄→³F₄ transition together with a less intense emission band centered around 1820 nm and corresponding to the ³F₄→³F₆ transition. The relative intensity ratio between the 1490 nm and 1820 nm emissions decreases as the Tm³⁺ concentration increases up to 1wt%. This reduction of the ³H₄→³F₄ emission intensity with concentration had been previously observed and attributed to cross-relaxation between ³H₄→³F₄ and ³H₆→³F₄ transitions [4,25].

 

Fig. 2. Room temperature emission spectra of Tm³⁺ in TWP5 (a) and TWP20 (b) glasses for three Tm₂O₃ different concentrations.

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The room temperature stimulated emission cross section of the ³H₄→³F₄ laser transition has been obtained by using the following expression [26],

where λ_p is the peak fluorescence wavelength, β is the branching ratio for the transition, n is the index of refraction of the host matrix, c the velocity of light, τ_R the radiative lifetime of the emitting level, and Δλ_eff is the effective linewidth. The effective linewidth of the transition has been calculated by using the relation ${\mathrm{\Delta \lambda }}_{\mathrm{eff}}=\int \frac{\mathrm{I}\mathrm{\left(}\mathrm{\lambda }\right)\mathrm{d\lambda }}{{\mathrm{I}}_{max}}$. The effective linewidth values are 101 and 102 nm for TWP5 and TWP20 glasses respectively. It is broader by nearly 30 nm in these glasses if compared to fluoride ones which makes them attractive for broadband amplifiers specially in the wavelength range that overlaps the conventional band of erbium doped fiber amplifiers. The maximum emission cross-section values are 0.38×10^-20 cm² and 0.40×10^-20 cm² for TWP5 and TWP20 glasses respectively, which are similar to those found in other tellurite glasses and twice the one of ZBLAN glass [27]. The gain bandwidth of an amplifier is determined by the product of the width of the emission spectrum and the emission cross-section. The obtained values for this product in these glasses are more than twice larger than in fluoride glass which suggests that these glasses may provide extended short wavelength gain of the erbium-doped C band at 1530-1570 nm. As an example, Fig. 3 shows the spectral overlap between the normalized ³H₄→³F₄ and ⁴I_13/2→⁴I_15/2 emissions of Tm³⁺ and Er³⁺ ions respectively together with the emission spectrum of a codoped sample with 0.3 wt% Tm₂O₃ and 0.3 wt% Er₂O₃ for TWP20 glass. As can be seen, a broad emission from 1400 to 1680 nm with a full width at half-maximum of ~ 180 nm is obtained by codoping the glass which suggests that these glasses could be promising materials for broadband light sources and broadband amplifiers for wavelength-division-multiplexing (WDM) transmission systems.

 

Fig. 3. Spectral overlap between the ³H₄→³F₄ (black) and ⁴I_13/2→⁴I_15/2 (red) normalized emissions of Tm³⁺ and Er³⁺ ions respectively in TWP20 glass together with the emission spectrum of a codoped sample (blue).

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We have also obtained the room temperature stimulated emission cross section of the ³F₄→³H₆ laser transition by using expression (4). In this case, for an emission between the first excited level and the ground state the branching ratio is equal to unity. The maximum emission cross sections are 0.85×10²⁰ cm² and 0.94×10²⁰ cm² for TWP5 and TWP20 glasses respectively. As for the ³H₄→³F₄ transition, this value is twice the one of ZBLAN glass [28].

The fluorescence lifetimes of level ³H₄ were measured as a function of temperature by exciting the samples at 793 nm. The observed behavior is similar in both glasses. At low concentration and temperature, the lifetime is close to the calculated radiative lifetime; however, as concentration increases, the lifetimes decrease even at low temperature, which indicates the presence of nonradiative energy transfer processes.

The fluorescence decays for the samples doped with 0.1 and 0.5% of Tm₂O₃ can be described at all temperatures by an exponential function to a good approximation; however, for the samples doped with 1 wt% the decays become non exponential. As an example, Fig. 4 shows the logarithmic plot of the experimental decays of the ³H₄ level at 295 K for the samples doped with 0.1, 0.5, and 1 wt% for both glasses.

 

Fig. 4. Logarithmic plot of the fluorescence decay of the ³H₄ level obtained under excitation at 793 nm at room temperature for TWP5 and TWP20 glasses doped with 0.1, 0.5, and 1 wt%.

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Figure 5 shows the lifetime values of the ³H₄ level between 10 K and 295 K for the samples doped with 0.1, 0.5, and 1 wt% for both glasses. The lifetime values for the samples doped with 1 wt% correspond to the average lifetime defined by $〈\tau 〉=\frac{\int I\left(t\right)\mathit{dt}}{I_0}$.

 

Fig. 5. Temperature dependence of the ³H₄ level lifetime for different Tm₂O₃ concentrations in TWP5 (a) and TWP20 (b) glasses.

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3.3 Concentration quenching of the ³H₄ emission

As we mentioned before the relative intensity ratio between the 1490 nm and 1820 nm emissions decreases as Tm³⁺ concentration increases. This concentration quenching is also made evident by the change from exponential to non-exponential decays of level ³H₄ and the lifetime reduction and can be attributed to cross-relaxation processes such as ³H₄, ³H₆→³F₄,³F₄. In this process part of the energy of an ion in level ³H₄ is transferred to another ion in the ground state with both ions ending up in level ³F₄ [4]. This process reduces the lifetime of the ³H₄ level and consequently the efficiency of the 1490 nm emission.

The characteristic decay time of the ³H₄ level should be governed by a sum of probabilities for several competing processes: radiative decay, nonradiative decay by multiphonon relaxation and by energy transfer to other Tm³⁺ ions. In these tellurite glasses nonradiative decay by multiphonon relaxation is expected to be small because of the 4300 cm-1 energy difference between ³H₄ and ³H₅ levels and the energy of the phonons involved. According to the literature, the highest phonons energy of tungsten-tellurite glasses is about 920 cm^-1 [29].This corresponds to 4.6 phonons, and indicates that the magnitude of the multiphonon relaxation rate is small. Energy transfer processes such as cross-relaxation are generally described in terms of three limiting cases: (i) direct relaxation, (ii) fast diffusion, and (iii) diffusion limited relaxation [30]. In the case of very fast diffusion, the decay of the donor fluorescence is purely exponential; however, as we have seen in Fig. 4 the decays become non exponential for the samples doped with 1 wt% of Tm₂O₃. The analysis of these decay curves shows that energy migration among Tm³⁺ ions affects the energy transfer process. The fit of the fluorescence decays with the migration assisted energy transfer models from Yokota and Tanimoto and Burshtein [31,32] indicates that the best agreement between experimental data and theoretical fits is obtained with the expression corresponding to the Burshtein model,

where τ_R is the intrinsic lifetime of donor ions, γ characterizes the direct energy transfer, and W represents the migration parameter. In the case of dipole-dipole interaction, γ is given by the expression $\gamma =\frac{4}{3}{\pi }^{\frac{3}{2}}N{C}_{\mathit{DA}}^{\frac{1}{2}}$, where N is the concentration and C_DA is the energy transfer microparameter. Figure 6 shows the fit for the samples doped with 1 wt% at room temperature.

 

Fig. 6. Experimental emission decay curves of level ³H₄ for TWP5 and TWP20 glasses doped with 1 wt% Tm₂O₃ at room temperature and the calculated fit with Eq. (5) (solid line).

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These results indicate that the electronic mechanism of energy transfer is a dipole-dipole interaction in the framework of a diffusion-limited regime. The values obtained for the energy transfer microparameter and the migration transfer rate for both glasses are shown in Table 3 together with the critical distance R₀ calculated by R ⁶ ₀ =τ_RC_DA. The critical distance for energy transfer is defined as the distance at which the energy transfer probability becomes equal to the intrinsic decay rate of the metastable level and indicates the extent to which the energy transfer between ions can occur. The obtained values for the critical distance and the migration transfer rate are slightly higher for TWP20 glass which have a higher concentration of Tm³⁺ ions. The critical distance in these glasses is similar to the one reported in other tellurite glasses [21], larger than in chalcogenide glass (7.3 Å) [33], and much shorter than the value reported in TeO₂-CdCl₂ glass [34].

Table 3. Obtained values for the energy transfer microparameter, migration transfer rate, and critical distance for the two glasses doped with 1 wt% at room temperature.

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4. Conclusions

Absorption and luminescence measurements have been performed in Tm³⁺ doped 80TeO₂-15WO₃-5PbO and 50TeO₂-30WO₃-20PbO tellurite glasses. The Judd-Ofelt intensity parameters and radiative transition rates have been calculated. The glass with the highest content of WO₃ and PbO, which has a slightly higher refractive index presents higher radiative transition probabilities and shorter radiative lifetimes.

The infrared emission at around 1490 has been characterized for three Tm₂O₃ concentrations (0.1, 0.5, and 1 wt%). Fluorescence measurements show that in both glasses the 1490 nm emission presents two noticeable features if compared to fluoride glasses. On one hand, it is broader by nearly 30 nm, and on the other, the stimulated emission cross section is twice the value for fluoride glasses. These features make these glasses attractive for broadband amplifiers specially in the wavelength range that overlaps the conventional band of the erbium doped fiber amplifier. In fact, we have shown that with an Tm³⁺-Er³⁺ codoped sample a broad emission band with an effective linewidth of around 180 nm can be obtained in these glasses.

The relative intensity ratio between the ³H₄→³F₄ and ³F₄→³H₆ emissions and the measured lifetime of the ³H₄ level decreases as thulium concentration increases, due to the presence of cross-relaxation processes. An analysis of the fluorescence decays of the ³H₄→³F₄ emission as a function of concentration reveals that a dipole-dipole quenching process assisted by energy migration is consistent with the experimental results.