1. Introduction

Mid-infrared (MIR) lasers have found wide applications in monitoring plasma etching processes, combustion flow monitoring, trace gas sensors for pollution monitoring, military, and clinical diagnosis [1–3]. Among the gain media for MIR lasers, Er³⁺-doped inorganic materials have received much attention because of the intense 2.7 μm emission from the ⁴I_11/2 → ⁴I_13/2 transition of Er³⁺ ions and its convenient 976 nm pump band. Since the ⁴I_11/2 → ⁴I_13/2 transition of Er³⁺ ions is a self-terminating transition [4], namely the upper level (⁴I_11/2) has a shorter lifetime than the lower one (⁴I_13/2), it requires some ways to deplete the lower laser level for efficient laser operation. Efficient depleting approaches include cross relaxation (CR) (i.e., ⁴I_13/2 → ⁴I_15/2 (Er³⁺): ⁴I_13/2 → ⁴I_9/2 (Er³⁺)) from the lower laser level at high Er³⁺ concentration [5], energy transfer to Pr³⁺ [6], and co-lasing of the ⁴I_13/2 → ⁴I_15/2 transition at 1.6 μm [7]. Furthermore, host materials with low phonon energy are desirable for 2.7 μm laser operation because low phonon energy can decrease the non-radiative relaxation rate. In addition, the vibration absorption of OH⁻ matches well with the ⁴I_11/2 → ⁴I_13/2 transition of Er³⁺ and quenches the 2.7 μm emission, thus the hydroxyl (OH⁻) groups in the host should be completely removed. Up to now, 2.7 μm laser has been realized in heavily (~50 mol %) Er³⁺-doped crystalline hosts such as YAG, YLF, and Lu₂O₃ [2, 8]. In case of optical glass fibers, 2.7 μm laser has only been obtained in Er³⁺-doped fluoride glass fibers owing to their low phonon energy and high transmittance in the MIR spectral region. In 2009, Tokita et al reported a liquid-cooled 24W mid-infrared Er: ZBLAN fiber laser [9]. Later, they demonstrated a tunable fiber laser covering the wavelength range from 2.71 to 2.88 μm and a 12 W Q-switched fiber laser at 2.8 μm [10, 11]. In 2011, Faucher et al reported a 20 W passively cooled single-mode all-fiber laser at 2.8 μm by using a heavily (~7 mol %) Er³⁺-doped fluoride fiber [12]. However, fluoride glasses have poor thermal and chemical durability, and therefore it is still necessary to develop new glass hosts with high stability for 2.7 μm fiber laser operation.

Recently, 2.7 μm emission properties of Er³⁺-doped heavy metal oxide glasses including germanate, tellurite, and bismuthate glasses have been widely investigated due to their relatively low phonon energy and high thermal and chemical stability [6, 13–16]. Fluorotellurite glasses have been reported to be of the relatively lower phonon energy (~760 cm⁻¹) among all the oxide glasses. Furthermore, they possess a broad transmission window of 0.4 ~6 μm, stable chemical and physical properties comparable to fluoride glasses, and easy fibering. They are the new group of MIR glasses combining the advantages of fluoride and oxide glasses. In 2012, Zhan et al reported an intense 2.7 μm emission from Er³⁺-doped water-free fluorotellurite glasses [17]. However, the maximum doping concentration of Er³⁺ in the fluorotellurite glass was just 1.25 wt % (less than 0.5 mol %) owing to the crystallization caused by introducing ZnF₂ into the tellurite glass system. Such low doping concentration of Er³⁺ ions is not sufficient for efficient 2.7 μm operation. Therefore, it is necessary to develop heavily Er³⁺-doped anhydrous fluorotellurite glasses.

In this work, we reported a series of heavily erbium-doped low-hydroxyl fluorotellurite glasses with molar compositions of (85.7−x)TeO₂ + xBaF₂ + (14.3−y)Na₂CO₃ + yEr₂O₃ (x = 38.1, 28.6, 19; y = 4.8, 6.7, 7.6, 8.6, 9.5; named as TBNE-1a, b, c, d, e, TBNE-2, TBNE-3, respectively). The glass samples in our experiments possessed maximum Er³⁺ doping concentration up to 19 mol %, which was much higher than those ever reported in fluorotellurite glass system [17]. Under 980 nm excitation, intense mid-infrared emissions around 2.7 μm from the ⁴I_11/2 → ⁴I_13/2 transition of Er³⁺ ions were observed in these heavily erbium-doped glasses. We also studied the characteristics of 2.7 μm emission for laser applications. The stimulated emission cross section and absorption cross section at 2.7 μm of TBNE-1e glass were calculated as 1.94 × 10⁻²⁰ cm² and 2.08 × 10⁻²⁰ cm², respectively. Meanwhile, the thermal analysis data showed that TBNE-1e glass could be easily fiberized without surface crystallizations.

2. Experimental

The well mixed batches (about 10 g) were preheated at 130 °C for 90 min in a vacuum drier to remove the free water. Then they were prepared by a conventional melting-quenching method in corundum crucibles at 900 °C for 35 min under ultrapure oxygen atmosphere. The pressured oxygen flow passed through the drying tower to the furnace for keeping the water content in the oxygen atmosphere at a relatively low level. The samples were annealed at 300 °C in a copper mold for 15 h and cooled naturally inside the furnace by turning off the power supply. They were polished to the same thickness as 1.55 mm for optical measurements, and the photos of all glass samples in our experiments are displayed in Fig. 1

 

Fig. 1 Photos of TBNE glasses.

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The compositions of the as-prepared glass samples were measured by a METEK JSM-7500F energy dispersive X-ray spectroscopy (EDS) and the measured results showed that the glass compositions were slightly changed compared to the initial constituents. The transmission spectra from ultraviolet (UV) to MIR were recorded with a Shimadzu UV3600 spectrophotometer in the range of 150 ~2500 nm and a Nicolet 6700 FTIR spectrophotometer in the range of 2500 ~7000 nm, respectively. The refractive indexes of the glass samples were characterized by a XLS-100 spectroscopic ellipsometer (J. A. Woollam Co., Inc.). The upconversion emission spectra were recorded by using a Hitachi F4500 spectrometer in the range of 750 ~900 nm when the pump power of a 980 nm laser diode was fixed as 90 mW. The infrared (IR) emission spectra were recorded with a Triax 320 spectrometer in the range of 2500 ~2860 nm. All the above measurements were carried out at room temperature. The thermal characteristic was determined by differential thermal analysis (DTA) with a PerkinElmer TG-DTA6200 analyser at a heating rate of 10 °C/min in the range of 30 ~1000 °C using about 10 mg glass sample powder in a platinum pan.

3. Results and Discussions

Figure 2 shows the comparison of transmission spectra from UV to MIR of low-hydroxyl TBNE glasses with various BaF₂ concentrations. Absorption bands in the spectral range of 400 ~2000 nm are due to the transitions from the ground level ⁴I_15/2 to highly excited levels (including ⁴I_13/2, ⁴I_11/2, ⁴I_9/2, ⁴F_9/2, ⁴S_3/2, and ²H_11/2) of Er³⁺ in TBNE glasses. A wideband absorption from 2700 to 4000 nm is due to the vibration absorption of OH⁻ in TBNE glasses. Three absorption bands peaked at 3423 nm, 3512 nm, and 4234 nm are due to the vibration absorption of CO₂ on the surfaces of TBNE glasses. Most interestingly, with increasing BaF₂ content from 19 mol % to 38.1 mol %, the transmission ratio at 3000 nm increases from 63% to 77%, the MIR absorption edge shifts from 6302 nm to 6498 nm, and the UV absorption edge shifts from 343 nm to 318 nm. It indicates that the OH⁻ content reduces with the addition of BaF₂ into TBNE glasses. We consider that, with the addition of BaF₂, F⁻ can break the O–H bond, generate HF gas and furthermore reduce the OH⁻ content [18]. The OH⁻ content of TBNE glasses is given by the hydroxyl absorption coefficient as

 

Fig. 2 Transmission spectra of low-hydroxyl TBNE glasses with different BaF₂ concentrations (9.5 mol % Er₂O₃).

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It indicates that the larger mass and the smaller field strength bring about the smaller IR cut-off frequency. So we deduce that the heavy metal oxide BaF₂ can provide lower framework oscillation frequency than TeO₂ under the same covalence condition. That is, the influence of Ba²⁺ and F⁻ may decrease the field strength and loosen the structure of the basic TeO₂ unit; hence, the IR cut-off frequency can be decreased, resulting in the redshift of the MIR absorption edge. In addition, since the electronegativity of fluorine atoms is higher than that of oxygen atoms, the band gap of fluorotellurite glass becomes larger than that of tellurite glass, corresponding to the blueshift of the UV absorption edge.In addition, we also measured the refractive index values of TBNE glasses at 1550 nm. The measured results (as shown in Table 1 and 2) show that the refractive index becomes smaller with the addition of BaF₂, and larger with the addition of Er₂O₃.

Table 1. Refractive indexes of TBNE glasses at 1550 nm with various BaF₂ concentrations.

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Table 2. Refractive indexes of TBNE glasses at 1550 nm with various Er₂O₃ concentrations.

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To investigate the effects of BaF₂ concentration on 2.7 μm emission, we measured the emission spectra of low-hydroxyl TBNE glasses with different BaF₂ concentrations when the pump power of a 980 nm laser diode was fixed at 90 mW, as shown in Fig. 3(a). The inset of Fig. 3(a) shows the dependence of 2.7 μm emission integral area on BaF₂ concentration, assuming that of the TBNE-3 glass as 1. The broadband emission has a full width at half maximum (FWHM) of ~150 nm, and two obvious Stark split emission peaks located at 2645 nm and 2715 nm, respectively. The emission from 2600 to 2850 nm is due to the ⁴I_11/2 → ⁴I_13/2 transition of Er³⁺ in fluorotellurite glasses and increases monotonically with the BaF₂ addition. Especially, the 2.7 μm emission integral area elevates from 1 to 1.53 and up to 3.58 eventually. That is to say, the enhancement rate is about 50% when increasing BaF₂ concentration from 19 mol % to 28.6 mol % and up to 250% when increasing BaF₂ concentration to 38.1 mol %. Such a change of the enhancement ratio coincides with the dependence of the OH⁻ content on BaF₂ concentration as shown in Fig. 2. This result indicates that the enhancement of 2.7 μm emission is caused by the diminishment of the OH⁻ content when adding BaF₂ into the TBNE glass system.

 

Fig. 3 (a) 2.7 μm emission spectra (Er³⁺: ⁴I_11/2 → ⁴I_13/2 transition) of low-hydroxyl TBNE glasses (19 mol % Er³⁺) with different BaF₂ concentrations. Inset: Dependence of 2.7 μm emission integral area on BaF₂ concentrations. (b) 2.7 μm emission spectra of TBNE-1 glasses with different Er³⁺ concentrations. Inset: Dependence of 2.7 μm emission integral area on Er³⁺ concentration.

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The mechanism of the IR emissions can be explained by the energy level diagram in Fig. 4. First, by the excitation from a 980 nm laser, the electrons at the ground state ⁴I_15/2 of Er³⁺ ions are promoted to the ⁴I_11/2 level. Then a part of them populate highly excited levels, i.e., ⁴F_9/2, ⁴S_3/2, ²H_11/2, and ²H_9/2 through the excited state absorption (ESA) and nonradiative processes, so ralated visible upconversion emissions can occur readily. At the same time, some Er³⁺ ions in the ⁴I_11/2 state transit to the ⁴I_13/2 and ⁴I_15/2 state in cascade to achieve 2.7 μm and 1.5 μm emissions, respectively. Especially in heavily erbium doped materials, the efficient CR1 process (⁴I_13/2 → ⁴I_15/2: ⁴I_13/2 → ⁴I_9/2) can promote the population of the ⁴I_9/2 level, then the ⁴I_11/2 level, and cause the depopulation of the ⁴I_13/2 level, which is promising for efficient 2.7 μm emission. The CR2 (⁴I_13/2 → ⁴I_15/2: ⁴I_9/2 → ²H_11/2, ⁴S_3/2) and CR3 (⁴I_13/2 → ⁴F_9/2: ⁴I_11/2 → ⁴I_15/2) processes can also deplete the population of the ⁴I_13/2 level to assist the 2.7 μm emission. All above CR processes break the intrinsic self-terminating transition (⁴I_11/2 → ⁴I_13/2) of Er³⁺ ions to contribute the 2.7 μm emission efficiently. We also note that the CR4 (⁴I_11/2 → ⁴I_15/2: ⁴I_11/2 → ⁴F_7/2) process is detrimental for 2.7 μm emission.

 

Fig. 4 Energy level diagram and mechanism of the IR emissions of heavily erbium doped low-hydroxyl TBNE glasses.

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High Er³⁺ concentration can give strong 2.7 μm emission owing to the existence of efficient CR process ⁴I_13/2 → ⁴I_15/2 (Er³⁺): ⁴I_13/2 → ⁴I_9/2 (Er³⁺), even though it may also cause concentration quenching. A possible reason for high erbium doping concentration was that the radius and relative atomic mass of Ba (2.78 Å, 137.33 amu) was larger than Zn (1.39 Å, 65.39 amu), which could cause larger space between Ba atom and O atom (or F atom), and make the glass framework become more firm. So it increased the free molar volume, as a result, high concentration erbium ions could be filled in the gap as network modifiers. When the concentrations of BaF₂ and Er₂O₃ were more than 38.1 mol % and 9.5 mol %, respectively, the glass sample became opaque due to the crystallization induced by Ba²⁺ and Er³⁺ ions involving the oxyfluoride glass network.

To investigate the concentration quenching effects for 2.7 μm emission, we measured the intensity dependence of 2.7 μm emission in the TBNE-1e glass on Er³⁺ concentration when the 980 nm pump power was fixed at 90 mW, as shown in Fig. 3(b). The inset of Fig. 3(b) shows the dependence of 2.7 μm emission integral area on Er³⁺ concentration, assuming that of 9.6 mol % Er³⁺ concentration as 1. 2.7 μm emission intensity increases monotonically from 1 to 2.66 with increasing Er³⁺ concentration from 9.6 mol % to 19 mol %. No obvious concentration quenching effect was observed even when increasing Er³⁺ concentration to 19 mol %, which is promising for 2.7 μm laser applications. The enhancement of 2.7 μm emission is caused by the efficiency of CR ⁴I_13/2 → ⁴I_15/2 (Er³⁺): ⁴I_13/2 → ⁴I_9/2 (Er³⁺) when increasing Er³⁺ concentration. If the above CR process became efficient, the population of the ⁴I_9/2 level would be increased and cause the enhancement of 805 nm emission (corresponding to the ⁴I_9/2 → ⁴I_15/2 transition). To verify it, we also measured the dependence of 805 nm emission intensity on Er³⁺ concentration when the pump power of a 980 nm laser diode was fixed at 90 mW, as shown in Fig. 5. The inset of Fig. 5 shows the dependence of 805 nm emission integral area on Er³⁺ concentration, assuming that of 9.6 mol % Er³⁺ concentration as 1. It is seen that 805 nm emission integral area increases monotonically from 1 to 4.54 with increasing Er³⁺ concentration from 9.6 mol % to 19 mol %. It shows that the enhancement of 2.7 μm emission was mainly caused by the efficiency of CR ⁴I_13/2 → ⁴I_15/2 (Er³⁺): ⁴I_13/2 → ⁴I_9/2 (Er³⁺) and the nonradiative relaxation (NR) from ⁴I_9/2 to ⁴I_11/2 when increasing Er³⁺ concentration. These processes make the ⁴I_11/2 level populated and the ⁴I_13/2 level depopulated efficiently, so the self-terminating of the ⁴I_11/2 → ⁴I_13/2 transition relaxes partly.

 

Fig. 5 805 nm emission spectra of low-hydroxyl TBNE-1 glasses with different Er³⁺ doping concentrations. Inset: Dependence of 805 nm emission integral area on Er³⁺ concentrations.

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In order to examine the characteristics of 2.7 μm emission for potential laser applications, we calculated its emission cross section (σ_em) in TBNE-1e glass by Fuchtbauer-Ladenhburg equation [21]

 

Fig. 6 (a) Calculated stimulated emission and absorption cross section spectra of 2.7 μm emission in TBNE-1e glass. (b) Calculated gain cross section spectra of 2.7 μm emission in TBNE-1e glass.

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Meanwhile, we characterized the thermal stability through DTA to determine the fiberized capacity of TBNE glasses. The onset crystallization temperature (T_x) and the transition temperature (T_g) are 358 °C and 492 °C in TBNE-1e glass, respectively. The working temperature range ΔT = T_x − T_g was around 134 °C, which means that TBNE-1e glass can be easily fiberized without surface crystallizations during fiber drawing. We deduce that the introduction of fluoride can raise T_x and decrease T_g because of the loose oxyfluoride matrix structure and the high electronegativity of fluorine atoms.

4. Conclusion

In summary, we reported a series of heavily erbium-doped low-hydroxyl fluorotellurite glasses for 2.7 μm laser applications. The maximum doping concentration of erbium ions was up to 19 mol % by introducing BaF₂ into the tellurite glass system. Under the excitation from a 980 nm laser diode, an intense 2.7 μm emission was obtained in 47.6TeO₂ + 38.1BaF₂ + 4.8Na₂CO₃ + 9.5Er₂O₃ glass (TBNE-1e) owing to the existence of efficient CR ⁴I_13/2 → ⁴I_15/2 (Er³⁺): ⁴I_13/2 → ⁴I_9/2 (Er³⁺) caused by high erbium doping concentration, low hydroxyl content, and low phonon energy. The stimulated emission cross section at 2.7 μm in TBNE-1e glass was calculated as 1.94 × 10⁻²⁰ cm². In addition, the thermal analysis data indicated that the TBNE-1e glass has suitable fiberized capacity as a prospective candidate for MIR laser applications.

Appendix

The details of the J-O parameter calculation are given as follows.

The intensity of an absorption band can be evaluated by the dipole strength S which is determined using the relation [24]

(7)$$S=\frac{2303m{c}^2}{N\pi e^2}{\displaystyle \int {\epsilon }_i}(\sigma )d\sigma =4.32\times {10}^{-9}\times A,$$

where m is the electron mass, c the speed of light, N the Avogadro number, and e the electron charge. A is the integrated absorption associated with the considered transition.

According to the J-O theory from the standard 4f-4f intensity model, the oscillator strength of a transition between two multiplets aJ and bJ’ is given by

(8)$$S=\frac{8{\pi }^{2}mc}{3h\overline{\lambda }(2J+1)}n{\left(\frac{n^2+2}{3n}\right)}^2{{\displaystyle \sum _{\lambda =2,4,6}{\Omega }_{\lambda }\left|〈aJ\Vert U^{(\lambda )}\Vert bJ\text{'}〉\right|}}^2,$$

where h is the Planck constant, $\overline{\lambda }$is the average wavelength, n[(n² + 2)/3n]² is the Lorentz local field correction for absorption, here n is the refractive index of the medium. ║U^(λ)║ are the doubly reduced matrix element of the unit tensor operator of rank λ, and the Ω_λ (λ = 2, 4, 6) are the J-O intensity parameters. The Ω_λ parameters can be determined using the S values obtained from Eqs. (7) and (8).

The probability of radiative emission A between the aJ and bJ’ levels is given by

(9)$$A(J\to J\text{'})=\frac{64{\pi }^4{e}^2}{3h(2J\text{'}+1){\overline{\lambda }}^3}\times n{\left(\frac{n^2+2}{3}\right)}^2{{\displaystyle \sum _{\lambda =2,4,6}{\Omega }_{\lambda }\left|〈aJ\Vert U^{(\lambda )}\Vert bJ\text{'}〉\right|}}^2,$$

where n[(n² + 2)/3]² is the effective field correction for emission at a well-localized center in a medium of isotropic refractive index n, h is the Planck’s constant and e is the electron charge.

A(J→J’) is related to the radiative lifetime τ_r of an excited state by

(10)$$\frac{1}{{\tau }_r}={\displaystyle \sum _{J}A(J\to J\text{'})},$$

The branching ratio β(J→J’), corresponding to the emission from an excited level J to J’, is given by

(11)$$\beta (J\to J\text{'})=\frac{A(J\to J\text{'})}{{\displaystyle \sum _{J}A(J\to J\text{'})}}.$$

The calculated results are shown as Table 3.

Table 3. Energy gap (ΔE), spontaneous transition probability (A), radiative lifetime (τ_r), branching ratio (β) and the J-O parameters (Ω_λ) of the present TBNE-1e glass for various selected levels of doped Er³⁺ ions.

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According to the Eqs. (4), (5), and (6) quoted in main text, the emission cross section (σ_em), the absorption cross section (σ_ab) and gain cross section G(λ) were calculated by using the radiative lifetime and branching ratio of the transition from ⁴I_11/2 to ⁴I_13/2 (as shown in Table 3).

Acknowledgments

This work was supported by the NSFC (grants 51072065, 61178073, 60908031, 60908001 and 61077033), the Program for NCET in University (No: NCET-08-0243), the Opened Fund of the State Key Laboratory on Integrated Optoelectronics, and Tsinghua National Laboratory for Information Science and Technology (TNList) Cross-discipline Foundation.

References and links

1. Y. Yao, A. J. Hoffman, and C. F. Gmachl, “Mid-infrared quantum cascade lasers,” Nat. Photonics 6(7), 432–439 (2012). [CrossRef]  

2. S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012). [CrossRef]  

3. G. R. Nash, J. L. Stokes, J. R. Pugh, S. J. B. Przeslak, P. J. Heard, J. G. Rarity, and M. J. Cryan, “Single lateral mode mid-infrared laser diode using wavelength-scale modulation of the facet reflectivity,” Appl. Phys. Lett. 100(1), 011103 (2012). [CrossRef]  

4. M. Ebrahim-Zadeh and I. T. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2008).

5. D. F. de Sousa, L. F. C. Zonetti, M. J. V. Bell, J. A. Sampaio, L. A. O. Nunes, M. L. Baesso, A. C. Bento, and L. C. M. Miranda, “On the observation of 2.8 μm emission from diode-pumped Er³⁺- and Yb³⁺-doped low silica calcium aluminate glasses,” Appl. Phys. Lett. 74(7), 908–910 (1999). [CrossRef]  

6. Y. Guo, Y. Tian, L. Zhang, L. Hu, N. K. Chen, and J. Zhang, “Pr³⁺-sensitized Er³⁺-doped bismuthate glass for generating high inversion rates at 2.7 µm wavelength,” Opt. Lett. 37(16), 3387–3389 (2012). [CrossRef]   [PubMed]  

7. M. Pollnau, Ch. Ghisler, G. Bunea, M. Bunea, W. Lüthy, and H. P. Weber, “150 mW unsaturated output power at 3 μm from a single-mode-fiber erbium cascade laser,” Appl. Phys. Lett. 66(26), 3564–3566 (1995). [CrossRef]  

8. T. Li, K. Beil, C. Kränkel, and G. Huber, “Efficient high-power continuous wave Er:Lu₂O₃ laser at 2.85 μm,” Opt. Lett. 37(13), 2568–2570 (2012). [CrossRef]   [PubMed]  

9. S. Tokita, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “Liquid-cooled 24 W mid-infrared Er: ZBLAN fiber laser,” Opt. Lett. 34(20), 3062–3064 (2009). [CrossRef]   [PubMed]  

10. S. Tokita, M. Hirokane, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “Stable 10 W Er: ZBLAN fiber laser operating at 2.71-2.88 μm,” Opt. Lett. 35(23), 3943–3945 (2010). [CrossRef]   [PubMed]  

11. S. Tokita, M. Murakami, S. Shimizu, M. Hashida, and S. Sakabe, “12 W Q-switched Er: ZBLAN fiber laser at 2.8 μm,” Opt. Lett. 36(15), 2812–2814 (2011). [CrossRef]   [PubMed]  

12. D. Faucher, M. Bernier, G. Androz, N. Caron, and R. Vallée, “20 W passively cooled single-mode all-fiber laser at 2.8 μm,” Opt. Lett. 36(7), 1104–1106 (2011). [CrossRef]   [PubMed]  

13. R. Xu, Y. Tian, L. Hu, and J. Zhang, “Enhanced emission of 2.7 μm pumped by laser diode from Er³⁺/Pr³⁺-codoped germanate glasses,” Opt. Lett. 36(7), 1173–1175 (2011). [CrossRef]   [PubMed]  

14. Y. Guo, M. Li, Y. Tian, R. Xu, L. Hu, and J. Zhang, “Enhanced 2.7 μm emission and energy transfer mechanism of Nd³⁺/Er³⁺ co-doped sodium tellurite glasses,” J. Appl. Phys. 110(1), 013512 (2011). [CrossRef]  

15. Y. Guo, M. Li, L. Hu, and J. Zhang, “Intense 2.7 µm emission and structural origin in Er³⁺-doped bismuthate (Bi₂O₃-GeO₂-Ga₂O₃-Na₂O) glass,” Opt. Lett. 37(2), 268–270 (2012). [CrossRef]   [PubMed]  

16. R. Xu, Y. Tian, L. Hu, and J. Zhang, “Origin of 2.7 μm luminescence and energy transfer process of Er³⁺: ⁴I_11/2→⁴I_13/2 transition in Er³⁺/Yb³⁺ doped germanate glasses,” J. Appl. Phys. 111(3), 033524 (2012). [CrossRef]  

17. H. Zhan, Z. Zhou, J. He, and A. Lin, “Intense 2.7 µm emission of Er³⁺-doped water-free fluorotellurite glasses,” Opt. Lett. 37(16), 3408–3410 (2012). [CrossRef]   [PubMed]  

18. A. Lin, A. Ryasnyanskiy, and J. Toulouse, “Fabrication and characterization of a water-free mid-infrared fluorotellurite glass,” Opt. Lett. 36(5), 740–742 (2011). [CrossRef]   [PubMed]  

19. J. Massera, A. Haldeman, J. Jackson, C. Rivero-Baleine, L. Petit, and K. Richardsonz, “Processing of Tellurite-Based Glass with Low OH⁻ Content,” J. Am. Ceram. Soc. 94(1), 130–136 (2011). [CrossRef]  

20. S. Hazra, S. Mandal, and A. Ghosh, “Properties of unconventional lithium bismuthate glasses,” Phys. Rev. B 56(13), 8021–8025 (1997). [CrossRef]  

21. J. F. Philipps, T. Töpfer, H. Ebendorff-Heidepriem, D. Ehrt, and R. Sauerbrey, “Spectroscopic and lasing properties of Er³⁺: Yb³⁺-doped fluoride phosphate glasses,” Appl. Phys. B 72(4), 399–405 (2001). [CrossRef]  

22. D. E. McCumber, “Theory of Phonon-Terminated Optical Masers,” Phys. Rev. 134(2A), A299–A306 (1964). [CrossRef]  

23. M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental Limitations of the McCumber Relation Applied to Er-Doped Silica and Other Amorphous-Host Lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002). [CrossRef]  

24. G. Poirier, V. A. Jerez, C. B. de Araujo, Y. Messaddeq, S. J. L. Ribeiro, and M. Poulain, “Optical spectroscopy and frequency upconversion properties of Tm³⁺ doped tungstate fluorophosphates glasses,” J. Appl. Phys. 93(3), 1493–1497 (2003). [CrossRef]