Investigation of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses for efficient 2 µm mid-infrared laser materials

Abstract

The Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses with good thermal properties were prepared. Based on the absorption spectra and the Judd–Ofelt theory, the J–O intensity parameters (Ω _t ), radiative transition probability (276.78 s^− 1), fluorescence lifetime (3.89 ms), absorption and emission cross sections (${\sigma _{\text{e}}}$ = 1.35 × 10^− 20 cm²) were calculated. The ~ 2 µm mid-infrared emission resulting from the ³F₄→³H₆ transition of Tm³⁺ sensitized by Yb³⁺ was observed pumped by 980 nm LD. Besides, the energy transfer mechanism between Yb³⁺ and Tm³⁺ was thoroughly discussed. The measured ~ 2 µm emission lifetime of Tm³⁺/Yb³⁺ co-doped glass can reach as high as 2.38 ms. The above results showed that Tm³⁺/Yb³⁺ co-doping glass could be expected to be a promising material to achieve high efficient ~ 2 µm lasing with a 980 nm LD pumping.

1 Introduction

Over the past several years, increasing efforts have been made to develop ~ 2.0 µm fiber lasers driven by their wide applications such as remote sensing, laser surgery, environmental monitoring, and eye-safe light detection and ranging (LIDAR) [1,2,3,4].

Among the rare earth ions, Tm³⁺ and Ho³⁺ are well known for the generation of ~ 2.0 µm emission, due to Tm³⁺:³F₄ → ³H₆ and Ho³⁺:⁵I₇→⁵I₈ transitions, respectively. In comparison with Ho³⁺, Tm³⁺ is of special interests for its unsurpassed advantages, such as broad emission about 800 nm suitable for tunable lasers [5] and high quantum efficiency beneficial from the cross relaxation energy transfer (³H₄ + ³H₆ → ³F₄ + ³F₄) [6]. What is more, the ³F₄ level of Tm³⁺ can be populated using sensitizer ions such as Yb³⁺ and Er³⁺ [7, 8]. Yb³⁺ ion can be used as a sensitizer and can be pumped by a more powerful and relatively inexpensive laser diode (LD) at 980 nm. Fast diffusion among the Yb³⁺ ions can enhance the efficiency of the nonresonant energy transfer from Yb³⁺ to Tm³⁺ (²F_5/2 + ³H₆ → ²F_7/2 + ³H₅). Yb³⁺ has a high absorption cross section and can effectively absorb excitation of commercial 980 nm LD emission, and then transfer energy to Tm³⁺ (³H₅ level) via non-resonant energy transfer process.

To research the luminescence properties of rare earth ions, it is very significant to select glass hosts for researchers. The first successfully Tm³⁺-doped silica fiber laser was demonstrated in 1988 by Southampton [9]. In 1999, Jackson et al. proposed a theoretical model that describes the ion-pair dynamics relevant to the Tm-doped silica system, which can deduce equations for the steady-state intracavity photon density and for the steady-state population densities of the isolated and paired ions [10]. In 2009, Moulton et al. used a piece of 25-µm-diameter and 0.08 numerical aperture (NA) core thulium-doped silica fiber to derive single mode laser output of the output powers of 300 W and the slope efficiency as high as 64.5% for launched pump power [11]. Various host materials including fluoride [12], tellurite [13], germanate [6] and silicate glasses [14] have been successfully applied to achieve ~ 2.0 µm fiber lasers with different efficiencies. Especially, actively Q-switched and mode-locked Tm³⁺-doped silicate 2 µm fiber laser have been already achieved in 2012 [14, 15]. The obvious defects of silicate glasses are the low rare earth solubility and high phonon energy. The fluoride glasses have the drawbacks of inferior mechanical and chemical properties. Germanate glasses have been intensively studied as promising candidates in mid-infrared optical applications and high-energy laser system [6, 16, 17]. Particularly, one system, germanate–tellurite (GT) glass, has been practically applied in large infrared (IR) windows, because of the excellent combinations of superior IR transparency, comparatively low phonon energy, high rare earth solubility, and good mechanical characteristics [18]. Tellurite glass has attracted a great deal of interest not only for its relatively lower maximum phonon energy (~ 760 cm⁻¹) among all the oxide glasses, but also for the improvement in chemical and mechanical stability as well as the high refractive index and excellent infrared transmission [19]. Compared with germanate glass (~ 900 cm⁻¹) [19], tellurite glass (~ 760 cm⁻¹) [20] has much lower phonon energy, which is favorable for 2 µm emission and that is helpful to reduce the multi-phonon relaxation rate for Tm³⁺:³F₄ → ³H₆ transition. However, tellurite glass has lower glass transition temperature (~ 350 °C) than germanate glass (~ 600 °C). Thus, tellurite glass has poor thermal stability to resist thermal damage at high pumping power. In contrast, the thermal stability, chemical durability and resistance to thermal damage of germanate glass are superior. Therefore, germanate–tellurite glass combines the advantages of both germanate and tellurite glasses, i.e., good thermal stability, chemical durability, lower phonon energy, high rare earth solubility and high transparency in a wide wavelength range [21, 22]. These features render germanate–tellurite glass an ideal host for mid-infrared laser material and have potential applications for cw, modelocked and Q-switched, micro-cavity lasers [23, 24]. To the best of our knowledge, the fluorescence corresponding to the ³F₄ → ³H₆ transition of the Tm³⁺ sensitized by Yb³⁺ has been under-reported in germanate–tellurite glasses [25,26,27].

In this work, we report the Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses for generating emission in the ~ 2.0 µm wavelength band. The spectroscopic properties of Tm³⁺ and energy transfer mechanism between Tm³⁺ and Yb³⁺ ions are discussed in detail. Energy transfer microscopic parameters were calculated based on the absorption spectra. Furthermore, the thermal properties are investigated and Judd–Ofelt intensity parameters were determined to evaluate the radiative properties. In this paper, the lifetime and gain spectra have also been discussed. The results verify that the Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses could be potential materials for mid-infrared lasers.

2 Experiment

2.1 Material synthesis

The sample glasses were prepared by traditional melt-quenching method using high-purity chemicals (99– 99.99+%). The investigated glasses of molar compositions: 80(GeO₂ + TeO₂) − (19.5 − y)(K₂CO₃ + Nb₂O₅ + La₂O₃) − xYb₂O₃ − yTm₂O₃(x = 0.5; y = 0.1, 0.25, 0.4, 0.5 and x = 0; y = 0.1) were placed in a Al₂O₃ crucible and heated with an SiC-resistance electric furnace at 1200 °C for 25 min. The melts were then poured onto a preheated stainless steel mold, followed by annealing at 530 °C for 5 h to remove the inner stresses. Then, it was allowed to cool slowly to room temperature. The cooled samples had been cut and polished to the size of 20 × 20 × 1.5 mm³ carefully, prepared for optical property measurements.

2.2 Performance measurements

In this paper, the refractive index (1.73) and density (4.27 g/cm³) of 0.25Tm³⁺/0.5Yb³⁺ co-doped sample were tested by prism minimum deviation method and Archimedes principle using distilled water as an immersion liquid. The maximum phonon energy of the present germanate–tellurite glass is ~ 785 cm⁻¹. The maximum phonon energy (~ 785 cm⁻¹) is less than that of tellurite glasses (~ 900 cm⁻¹) [6]. The characteristic temperatures of glass transition (T_g), onset crystallization peak (T_x) and top crystallization (T_p) were obtained at 10K/min using the NETZSCH DTA 404 PC differential scanning calorimeter. The fluorescence spectra of the samples in the range of 1500–2400 nm were measured by a liquid nitrogen-cooled PbS detector using a 980 nm laser diode (LD) as an excitation source. The absorption spectra measurements were performed by Perkin Elmer Lambda 900 UV/VIS/NIR double beam spectrophotometer (Waltham, MA) in the range from 300 to 2100 nm. The lifetime decay curves were measured and shown by TDS 3012C type Digital Phosphor Oscilloscope (100 MHz, 1.25GS/S). For different samples, they were tested under the same experimental conditions. In addition, all the test results were carried out at room temperature.

3 Results and discussions

3.1 Thermal stability analysis

To correctly evaluate the thermal properties of the glasses, as shown in Fig. 1, the DSC measurement of sample glasses were performed. The values of T_g, T_x and T_p are 538 °C, 726 °C and 750 °C, respectively. T_g is a significant factor for laser glasses. The transition temperature (T_g) of the samples (538 °C) is higher than that of bismuth (269 °C) [28], tellurite (354 °C) [29], tellurite(300 °C) [13], germanate (526 °C) [30] and fluoride glasses (332 °C) [31]. The higher T_g is generally considered to possess better thermal properties to resist thermal damage at high pumping intensities. The ∆T (T_x − T_g) can usually be used to evaluate the thermal properties of glasses. A bigger ∆T reveals that the glass possesses an excellent thermal ability against nucleation and crystallization as well. From Table 1, it is obvious that ∆T is 188 °C, which is significantly larger than that of bismuthate (67 °C) [28], tellurite (141 °C) [29], germanate (129 °C) [30] and fluoride glasses (76 °C) [31], revealing that germanate–tellurite glasses could be potential materials for mid-infrared lasers. The above results indicate that germanate–tellurite glasses have better thermal performance. Hence, the prepared germanate–tellurite glasses have good anti-crystallization properties and could be selected as potential laser material.

Fig. 1

DSC curve of germanate–tellurite glass

Table 1 The glass transition temperature (T_g), onset crystallization temperature (T_x), temperature of crystallization peak (T_p) and thermal stability parameters ΔT in various glass hosts

3.2 Absorption spectra and J–O analysis

As shown in Fig. 2, the absorption spectra of 0.25Tm³⁺, 0.5Yb³⁺ single-doped and 0.25Tm³⁺/0.5Yb³⁺ co-doped glass samples of thickness of 1.5 mm are depicted in the wavelength range of 300–1750 nm. For Tm³⁺ singly doped sample, in the range of 300 to 1750 nm absorption bands could be discerned, centered at around 468, 684, 791, 1208 and 1713 nm, corresponding to the transitions from the ³H₆ ground state to excited levels ¹G₄, ³F_2,3, ³H₄, ³H₅ and ³F₄, respectively, according to the absorption spectrum of Tm³⁺ single-doped germanate glass. The shapes and the peak positions of each transition in Tm³⁺ single-doped germanate–tellurite glasses nearly do not change when compared with the Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses and are very similar to those in other Tm³⁺-doped glasses [31]. The phenomenon could be explained by the fact that the Tm³⁺ ions are homogeneously incorporated into the glass network without clustering and any changes in the local ligand field [33]. In this paper, the 980 nm LD is used as the pumping source. As well known, the center of the absorption peak of Yb³⁺ ions at 976 nm is indeed more intense than all the absorption peaks of Tm³⁺. The radiation wavelength of high-power commercial 980 nm LD can be matched with 976 nm absorption peak of Yb³⁺ ions, showing that codoping with Yb³⁺ and Tm³⁺ is an efficient approach to enhance ~ 1.8 µm emission from Tm³⁺ [34, 35].

Fig. 2

Absorption spectra of Tm³⁺,Yb³⁺ single-doped and Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses

The Judde–Ofelt (J–O) theory [36, 37] plays a significant role in analyzing the spectroscopic properties (radiative lifetimes, intensity parameters Ω _t (t = 2, 4, 6), spontaneous emission probabilities and so on) for rare earth ions-doped glasses.

Table 2 compares the Judd–Ofelt parameters of Tm³⁺ ions in germanate, tellurite and bismuthate glasses. The Ω₂ parameter is intensively dependent on the local environment of the rare earth ions. The value of Ω₂ (4.45 × 10⁻²⁰ cm²) of Tm³⁺ is relatively large and higher than that of silicate (3.70 × 10^− 20 cm²) [38] and tellurite (3.30 × 10^− 20 cm²) [39] glasses. On the one hand, it is straightly related to the symmetry of rare earth ions with ligand formation. On the other hand, the polarization of the local structure and the covalent nature of the chemical bonds result in the formation of rare earth ions with ligands. A large field strength is mainly attributed to a high polarizability of oxygen at the rare earth site. For the crystal field parameter, the value of Ω₂ might also be affected by the asymmetry of the rare earth sites. Ω₂ is an important factor to obtain good spectral properties of the host materials. From Table 2, the value of Ω₆ is larger than those of silicate glasses (0.60 × 10⁻²⁰ cm²) [39], but smaller than tellurite (1.28 × 10⁻²⁰ cm²) [40] and germanate (1.92 × 10⁻²⁰ cm²) [41] glasses. At the same time, comparison with Ω₂, Ω₆ does not depend on the environment, but is more dependent on the overlap integrals of the 4f and 5d orbits [42].

Table 2 Comparison of J–O intensity parameters of Tm³⁺ ions in various glass hosts

From Table 3, a full understanding of the radiation characteristics of the prepared glasses, the radiative lifetimes (τ_rad), spontaneous transition probabilities (A_rad) and fluorescence branching ratios (β) were obtained. The radiative transition probability (A_rad) of Tm³⁺:³F₄ → ³H₆ transition is calculated to be 276.78 s⁻¹. The higher spontaneous radiative transition probability provides larger opportunity to achieve better laser action, so the prepared glasses could be a promising candidate for mid-infrared laser [43]. It is known from other papers that the radiative transition probability (A_rad) of Tm³⁺ in the sample is higher than that of tellurite and germanate glasses [44, 45]. We can see that the radiative lifetime of ³F₄ → ³H₆ transition is as long as 3.89 ms, which is longer than that of tellurite (1.64 ms) and germanate (0.859 ms) glasses [44, 45]. The highly efficient ~ 2 µm radiations can be achieved in the prepared glass.

Table 3 The spontaneous emission probabilities, branching ratios and radiative lifetimes of Tm³⁺ in the samples

3.3 Emission spectra and cross section

In the past studies [46], the energy transfer process between Yb³⁺ and Tm³⁺ is recognized by researchers and the efficiency of the process is very high. As shown in Fig. 3a, with the increase of Tm³⁺ concentration, the Tm³⁺:~ 1.8 µm emission is also enhanced. The fluorescence spectra of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass pumped by 980 nm LD is displayed. From Fig. 3b, it can be found that there is no fluorescence when Tm³⁺ is singly doped in germanate–tellurite glasses. With the assistance of Yb³⁺ ions, the ~ 1.8 µm emission peak of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses is excited by 980 nm LD. This confirms the lack of Tm³⁺ absorption band near 976 nm and the existence of energy transfer from Yb³⁺ to Tm³⁺. In addition, with the increase of Tm³⁺ ion concentration, the fluorescence intensities of Tm³⁺/Yb³⁺ co-doped glass samples increase initially and then rapidly decrease. When the concentration of Tm³⁺ is 0.25 mol%, the intensity of fluorescence emission reaches the maximum in these four sets of glass samples. So, the optimum concentration of Tm³⁺ is 0.25 mol%. The reason is that the energy transfer probability between Yb³⁺:²F_5/2 and Tm³⁺:³H₅ ions is enhanced. Subsequently, this emission intensity decreases gradually with the increase in Tm³⁺ concentration because of concentration quenching [47]. Therefore, the optimum concentration ratio between Tm³⁺ ions and Yb³⁺ ions is 1:2, and the results show that the Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses can be potential materials for mid-infrared lasers.

Fig. 3

a Emission spectra of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses; b emission spectra of Tm³⁺-doped and Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses

Furthermore, emission cross section is an important parameter to estimate the possibility for achieving laser action. According to the above measured absorption spectra, the absorption cross section can be expressed by the Beer–Lambert equation:

$${\sigma _{{\text{abs}}}}=\frac{{2.303}}{{N \times l}}{\text{OD}}\left( \lambda \right),$$

(1)

where N is the density of rare earth ion (ions/cm³), l is the thickness of the polished sample glass, OD(λ) is the optical density and the value of the optical density is equal to the spectra intensity.

$${\sigma _{{\text{em}}}}=\frac{{{\lambda ^4} \cdot {A_{{\text{rad}}}}}}{{8\pi c{n^2}}} \times \frac{{\lambda I\left( \lambda \right)}}{{\int {\lambda I\left( \lambda \right){\text{d}}\lambda } }},$$

(2)

where λ is the wavelength, A_rad is the spontaneous transition probability, I(λ) is the emission intensity and c and n are the light speed in vacuum and refractive index, respectively.

As shown in figure Fig. 4a, the values of emission and absorption cross sections of Yb³⁺ are 0.87 × 10⁻²⁰ and 0.59 × 10⁻²⁰ cm² in the sample glasses, respectively. From Fig. 4b, the values of emission and absorption cross sections of Tm³⁺ are 1.35 × 10⁻²⁰ and 0.56 × 10⁻²⁰ cm² at 1.8 µm, respectively. We can see that the emission cross section (1.35 × 10⁻²⁰ cm²) of Tm³⁺ is larger than those of silicate (0.2 × 10⁻²⁰ cm²) [48], tellurite (0.86 × 10⁻²⁰ cm²) [44], tellurite (0.96 × 10⁻²⁰ cm²) [13] and bismuthate glasses (0.71 × 10⁻²⁰ cm²) [49]. For a laser material, in general, the high stimulated emission cross section is helpful to increase the gain. A larger gain results in better amplification behavior.

Fig. 4

a Absorption and emission cross sections corresponding to Yb³⁺:²F_5/2→²F_7/2. b Absorption and emission cross sections corresponding to Tm³⁺:³F₄→³H₆

The process of energy transfer between Tm³⁺ and Yb³⁺ ions is presented in Fig. 5. As shown in Fig. 5, the efficient energy transfer between Tm³⁺and Yb³⁺ can be obtained through the transfer of phonons, and a main energy transfer process in the Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass has been shown. The Yb³⁺ is pumped by 980 nm LD and excited from the ground state (²F_7/2) to the upper level (²F_5/2), following an energy transfer process from Yb³⁺:²F_5/2 to Tm³⁺:³H₅ (ET: Yb³⁺:²F_5/2 + TmH₆ → Yb³⁺:²F_7/2+Tm³⁺:³H₅). The process is assisted by phonons. The Tm³⁺ ion in the ³H₅ level relaxes very quickly to the ³F₄ level, and then particle is transferred from the ³F₄ level to the ³H₆ level. Yb³⁺ ion as a sensitizer can greatly improve upconversion efficiency through energy transfer (ET), which is due to strong absorption of the Yb³⁺ ion around 980 nm when Tm³⁺/Yb³⁺ co-doped glasses are excited by a 980 nm laser. The simplified energy level diagram exhibits distinct upconversion centered at 476, 650 and 689 nm, which are assigned to the ¹G₄ → ³H₆, ¹G₄→³F₄ and ³F_2,3 → ³H₆ transitions of Tm³⁺ ions, respectively.

Fig. 5

Simplified energy level diagram of the Tm³⁺/Yb³⁺ co-doped system

The microscopic parameter based on the evaluation of the overlap integral between the absorption and emission cross sections can be obtained using the following equation:

$${C_{{\text{DA}}}}=\frac{{6cg_{{{\text{low}}}}^{D}}}{{{{\left( {2\pi } \right)}^4}{n^2}g_{{{\text{up}}}}^{D}}}\sum\limits_{{m=0}}^{\infty } {{{\text{e}}^{ - \left( {2\bar {n}+1} \right){S_0}\frac{{S_{0}^{m}}}{{m!}}{{\left( {\bar {n}+1} \right)}^m}\int {\sigma _{{{\text{ems}}}}^{D}\left( {\lambda _{m}^{+}} \right)\sigma _{{{\text{abs}}}}^{A}\left( \lambda \right){\text{d}}\lambda } }}} .$$

(3)

${\text{g}}_{{{\text{low}}}}^{{\text{D}}}$ and ${\text{g}}_{{{\text{up}}}}^{{\text{D}}}$ are the degeneracies of the respective lower and upper levels of the donor, respectively. $\bar {n}={1 \mathord{\left/ {\vphantom {1 {\left( {{e^{{{\hbar {w_0}} \mathord{\left/ {\vphantom {{\hbar {w_0}} {KT}}} \right. \kern-0pt} {KT}}}} - 1} \right)}}} \right. \kern-0pt} {\left( {{e^{{{\hbar {w_0}} \mathord{\left/ {\vphantom {{\hbar {w_0}} {KT}}} \right. \kern-0pt} {KT}}}} - 1} \right)}}$ is the average occupancy of the phonon mode at T. S₀ is Huang–Rhys factor.

Table 4 lists the energy transfer microscopic parameters of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass. It is clearly shown that effective energy transfer takes place between the Tm³⁺ and Yb³⁺ ions. As shown in Table 4, the energy transfer coefficient between Yb³⁺:²F_5/2 level and Tm³⁺:³H₅ level can be as high as 1.3826 × 10⁻⁴⁰ cm⁶/s. It is worth mentioning that the above energy transfer process is non-resonant and mainly assisted by one phonon (39.076%), two phonons (27.785%) and three phonons (1.696%). This circumstance mainly results from low phonon energy of germanate–tellurite glass. Besides, with increasing Tm³⁺ concentration, the energy transfer process can hardly happen from Yb³⁺:²F_5/2 to Tm³⁺:³H₅. As shown in Fig. 6, the decay curves can confirm this process. Hence, it is very important for mid-infrared materials to select suitable Tm³⁺ concentration.

Table 4 Energy transfer parameters between Tm³⁺ and Yb³⁺ in the glass sample

Fig. 6

Decay curve of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses

3.4 Fluorescence lifetimes and gain coefficient

As shown in Fig. 6, the 1.8 µm lifetime (2.38 ms) of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass sample is obtained, and is significantly larger than those of silicate (1.42 ms) [50] and germanate (0.36 ms) glasses [51]. The lifetime in Tm³⁺/Yb³⁺ co-doped is longer than that in Tm³⁺ single-doped germanate–tellurite glass. It indicates that there is an effective energy transfer between Tm³⁺ and Yb³⁺. We can see that the lifetime of ³F₄ level decreases gradually with increase in Tm³⁺ concentration. The reduced lifetime is not beneficial for the upconversion process. The decreased upconversion process contributes to population aggregation of Tm³⁺:³F₄ and might enhance Tm³⁺:³H₅ → ³F₄. Here, the stronger upconversion process is due in part to the excited state absorption (ESA), while the excited state absorption process reduces the ³F₄ level number of particles, which is detrimental to the 1.8 µm lifetime. Therefore, the decrease in the conversion process is beneficial to the 1.8 µm lifetime of Tm³⁺. In addition, the relatively long lifetime generally enhances the luminous efficiency of glasses and it generally reduces the laser oscillation threshold. Hence, the emission lifetime (2.38 ms) indicates that Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass is a promising material for ~ 2.0 µm fiber laser.

Besides, to further evaluate the performance of the samples, the fluorescence quantum efficiency was estimated from the lifetime values by the following equation.

$$\eta =\frac{\tau }{{{\tau _{{\text{rad}}}}}} \times 100\% ,$$

(4)

where τ is the measured fluorescence lifetime of the sample (0.5Tm³⁺/0.1Yb³⁺) and τ_rad is the theoretical lifetime of the sample (0.5Tm³⁺/0.1Yb³⁺). The measured ³F₄ lifetime (2.38 ms) for Tm³⁺ is shorter than the calculated lifetime (3.89 ms), which is due to non-radiative quenching. It can be found that the fluorescence quantum efficiency is as high as 61.18%, which is higher than that of silicate glass (13.0%) [52]. Therefore, Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass is a more promising material for improving the Tm³⁺ 2.0 µm fiber laser performance.

Another important parameter to evaluate the gain performances of the prepared sample quantitatively is gain coefficient. To calculate the gain ability of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses, the gain coefficient G(λ,P) of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses is calculated. The room temperature gain coefficient (G(λ,P)) can be simply denoted as

$$G\left( {\lambda ,\left. P \right)} \right.=N\left[ {P{\sigma _{{\text{em}}}}\left( \lambda \right) - \left( {1 - P} \right){\sigma _{{\text{abs}}}}\left( \lambda \right)} \right],$$

(5)

where N is the doping concentration of the rare earth ion and P is the population inversion.

Figure 7 shows the calculated gain coefficients of Tm³⁺ and Yb³⁺ transitions as the function of wavelength. The gain coefficient results are calculated by setting P ranging from 0 to 1 at an interval of 0.1. We can see that the gain coefficient increases as the value of P continues to increase. As shown in Fig. 7, the maximum gain coefficients of Tm³⁺ reach 3.02 cm⁻¹; furthermore, the concentrations of Tm³⁺ and Yb³⁺ are 0.1 and 0.5 mol%, respectively. Besides when P is more than 0.4, the value G(λ,P) of the Tm³⁺:³F₄ → ³H₆ transition becomes a positive number. In addition when P is less than 0.4, it becomes a negative number. The above results show that Tm³⁺/Yb³⁺ co-doped GeO₂–TeO₂–K₂CO₃–Nb₂O₅–La₂O₃ glass has high gain and low pumping threshold for the laser and is an outstanding gain host material for ~ 2 µm mid-infrared laser.

Fig. 7

Gain coefficient of Tm³⁺:³F₄ → ³H₆ transitions in germanate–tellurite glasses

4 Conclusions

In a word, efficient ~ 1.8 µm emissions have been achieved in Tm³⁺/Yb³⁺ co-doped germanate–tellurite glasses. The energy transfer process between Yb³⁺ and Tm³⁺ has been investigated in detail. The thermal stability, absorption and emission cross sections, and lifetimes have been analyzed. The results indicated that Tm³⁺ in the prepared glasses had not only superior thermo-mechanical stability (T_g = 538 °C, ΔT = 188 °C), but also large emission cross section (1.35 × 10^− 20cm²). The measured lifetime of Tm³⁺/Yb³⁺ co-doped germanate–tellurite glass is as high as 2.38 ms. It also possesses superior gain performance for Tm³⁺:³F₄ → ³H₆ and Yb³⁺:²F_5/2 → ²F_7/2 transitions. All of the results indicate that the prepared germanate–tellurite glass is a promising candidate for ~ 2.0 µm mid-infrared laser materials applications.