Optical characterization of Tm³⁺ doped Bi₂O₃-GeO₂-Ga₂O₃ glasses in absence and presence of BaF₂

Abstract

In this paper, Two new Bi₂O₃-GeO₂-Ga₂O₃ glasses (one presence of BaF₂) doped with 1mol% Tm₂O₃ were prepared by melt-quenching technique. Differential thermal analysis (DTA), the absorption, Raman, IR spectra and fluorescence spectra were measured. The Judd–Ofelt intensity parameters, emission cross section, absorption cross section, and gain coefficient of Tm³⁺ ions were comparatively investigated. After the BaF₂ introduced, the glass showed a better thermal stability, lower phonon energy and weaker OH⁻ absorption coefficient, meanwhile, a larger ~1.8 μm emission cross section σ_em (7.56 × 10⁻²¹ cm²) and a longer fluorescence lifetime τ_mea (2.25 ms) corresponding to the Tm³⁺: ⁴F₃ → ³H₆ transition were obtained, which is due to the addition of fluoride in glass could reduce the quenching rate of hydroxyls and raise the cross-relaxation (³H₆ + ³H₄ → ³F₄ + ³F₄) rate. Our results suggest that the Tm³⁺ doped Bi₂O₃-GeO₂-Ga₂O₃ glass with BaF₂ might be potential to the application in efficient ~1.8 μm lasers system.

Over the past decade, Tm³⁺-doped fiber lasers have attracted growing attention in numerous areas owing to their very broad transition linewidth over ~1.7 to 2.1 μm wavelength¹,²,³,⁴. As we know, near-infrared lasers at the eye-safe 2 μm region have many potential applications in medicine, remote sensing, and atmospheric pollutant monitoring⁴,⁵. Recently, the long-wavelength window around 1700 nm has attracted attention for OCT imaging⁶. Wavelengths near ~1720 nm are of interest for targeting fat/lipid-rich tissues due to the high absorption coefficient of human fat and low water scattering and absorption⁷. Nicholas G. Horton. et al. were put forward expectations that a wavelength-tunable source that covers the entire “low attenuation” spectral window from 1650 to 1850 nm can be obtained, which will further increase the number of accessible fluorophores and fluorescent proteins for Three-photon fluorescence microscopy (3PM) in the 1700 nm spectral window⁸. In addition, they can operate as pump sources for achieving 3.0~5.0 μm mid-infrared fiber lasers output at room-temperature, for national defense and commercial applications⁹,¹⁰. A typical work on Tm³⁺-Tb³⁺ co-doped tunable fiber ring laser for 1716 nm lasing was pumped by a 1.21 μm laser diode¹¹. Another type of Tm-doped silica fiber laser with narrow-linewidth and output wavelength near 1750 nm has been reported, by using a 1550 nm Er-doped fiber laser pump source and a volume Bragg grating (VBG)¹².

Tm³⁺ is a better solution to ~2 μm emissions because of its absorption band near 808 nm matching well with commercially available and high power laser diode¹³. Due to the cross-relaxation (³H₆ + ³H₄ → ³F₄ + ³F₄) process between Tm³⁺ ions, the ideal quantum efficiency of Tm³⁺: ³F₄ can reach 200%¹⁴,¹⁵. To date, in order to get powerful infrared emissions from Tm³⁺ ions, various kinds of glass hosts have been investigated including silicate¹⁶, tellurite¹⁷, germanate¹⁸, and fluorophosphates¹⁹ glasses. Yin-Wen Lee, etc. reported an 18-dB 2013-nm amplifier which was demonstrated in a 50-cm 7 wt% Tm³⁺-doped double-clad silicate fiber²⁰. Xin Wen, etc. reported a multilongitudinal-mode fiber laser at 1.95 μm has also been achieved in a 10 cm long as-drawn active fiber, yielding a maximum laser output power of 165 mW and a slope efficiency of 17%²¹. Zhi-Xu Jia reported a supercontinuum generation in Tm³⁺ doped tellurite microstructured fibers pumped by a 1.56  μm femtosecond fiber laser²². However, few researches have been paid on the bismuth germanate glass and fiber.

Among the oxide glasses, the bismuthate glass has a lower phonon energy (~440 cm⁻¹)²³,²⁴ compared with silicate (~1000 cm⁻¹)¹⁶, germanate (~900 cm⁻¹)¹³ and tellurite (~750 cm⁻¹)¹⁷ glasses, which is very useful to enhance the luminescence quantum efficiency²³ of Tm³⁺ ions and reduce the multiphonon relaxation²⁴. In addition, compared with silicate and other heavy metal oxide glasses, the bismuthate glass possesses many other material advantages such as easy preparation process, low melting temperature, large rare-earth solubility²¹, high refractive index (~2.1)²⁵ and wide transparency window²⁶, make bismuthate glass particularly promising for fiber amplifiers and infrared fiber lasers.

The OH⁻ groups may quench ³F₄ → ³H₆ emissions of Tm³⁺ ions and reduce emission efficiency⁵. But hydroxyl and the fluorine ions are isoelectronic and their ionic size was similar; hydroxyl ions could easily be removed by fluoride during melting²⁷. Therefore, 1 mol% Tm³⁺-doped bismuth-germanium-gallate glasses in absence and presence of BaF₂ were studied for ~1.8 μm emission.

Experimental

Molar composition of 36Bi₂O₃− 29GeO₂− 25Ga₂O₃− 10Na₂O− 1Tm₂O₃ (BGN) and 36Bi₂O₃− 29GeO₂− 25Ga₂O₃− 10BaF₂− 1Tm₂O₃ (BGF) glasses were fabricated by conventional melting-quenching method in an alumina crucible at 1200 °C under oxygen atmosphere respectively. The glass samples were formed by casting molding and finally annealed at 480 °C for 3 h to remove thermal strains. Samples were cut and polished to 10 × 10 × 2 mm³ for property measurements.

Differential thermal analysis (DTA) was performed using a SETARAM TAG24 analyser, for characteristic temperatures (the temperature of glass transition T_g, temperature of onset crystallization T_x and temperature of peak crystallization T_p). Density and refractive index of samples was obtained by Archimedes method and spectroscopic ellipsometer method, respectively. The absorption spectrum was recorded using a spectrophotometer (Perkin Elmer Lambda9). The near-infrared emission spectra and luminescence lifetime were measured by FLSP920 (Edinburgh instruments Ltd., UK) under 808 nm laser diode pumped. Raman spectra were monitored with a FT Raman spectrophotometer (Nicolet Module). All measurements were carried out at room temperature.

Results and Discussions

Thermal property

Figure 1 shows the DTA curve of the studied glass, and the values of T_g, T_x and T_p in Tm³⁺-doped BGN and BGF samples are indicated. The difference between the glass transition temperature T_g and the onset crystallization temperature T_x, ΔT = T_x − T_g, has been frequently used as a rough estimate of glass formation ability or glass thermal stability. It can be seen that the values of T_g is decreased from 520 °C to 495 °C as the Na₂O is replaced by BaF₂ in BGF glass. However, it is still higher than of fluoride²⁸, tellurite²⁹ glasses, this results show that the glasses have good thermal shock resistance performance under the condition of high power pump. Generally, the ΔT of the glass sample should be higher than 100 °C to obtain a better thermal stability and to avoid crystallization during the optical fiber drawing process³⁰,³¹. After the addition of BaF₂, the thermal stability (ΔT) of Bi₂O₃-GeO₂-Ga₂O₃ glass is increased quite significantly. The value of ΔT for BGF sample is 110 °C,which is higher than of BGN (59 °C), indicating that the BGF sample has better thermal stability against crystallization for ~1.8 μm emission.

Figure 1. DTA curves of BGN and BGF glasses doped with 1 mol% Tm₂O₃ at the heating rate of 10 K/min.

Absorption and IR transmittance spectra

Figure 2 shows the absorption spectra of the Tm³⁺ doped BGN and BGF samples under room temperature. All absorption bands belong to transition of Tm³⁺ ions from ground state to higher levels are labeled in Fig. 2. As expected, BGN and BGF samples have similar absorption peaks, and the ³H₆-¹G₄ transition has not appeared, due to the UV cut-off wavelength of bismuthate glasses is redshift. Strong absorption around 790 nm indicates that these glasses can be excited efficiently by 808 nm LD. As shown in Fig. 3, BGF sample shows better IR transmittance than BGN sample. The absorption band ranging from 2700 to 3700 cm⁻¹ is due to stretching vibrations of free OH⁻ groups. Hydroxyl and the fluorine ions are isoelectronic and their ionic size is similar²⁸, hydroxyl ions can easily be removed by fluoride during melting through the reaction OH⁻ + F⁻ → HF + O²⁻. The OH⁻ absorption coefficient in the glass can be calculated by the IR transmission spectra, which is given by³¹

Figure 2. Room temperature absorption spectra in the range from 400 to 2000 nm of the BGN and BGF glass samples doped with 1 mol% of Tm₂O₃.

Figure 3. Infrared transmission spectrum of the BGN and BGF glasses doped with 1 mol% of Tm₂O₃ in the range of the absorption bands of water.

where l is the thickness of a sample, T₀ and T are the transmission value of maximum and at 3000 cm⁻¹, respectively. The OH⁻ absorption coefficient of BGN and BGF samples are calculated according to Eq. (1)cm⁻¹ and 0.05 cm⁻¹, respectively. It is obvious that typical OH⁻ groups’ absorption of BGN sample is much stronger than that of BGF sample at 3 μm regions, which is one of the main reasons for the difference between BGN and BGF samples in ~1.8 μm emission.

Judd-Ofelt analysis

According to absorption spectra (Fig. 1), Judd-Ofelt (J-O) theory has been applied to determine the important spectroscopic and laser parameters of Tm³⁺ ion. In this paper, J-O intensity parameters Ω_t (t = 2, 4, and 6) are calculated and radiative transitions within 4f ⁿ configuration of Tm³⁺ is analyzed, the value of them list in Table 1. The value Ω₂ of BGF are lower than those of BGN, however, they are still much larger than that of silicate³¹, tellurite³², fluoride³³ and germanate³⁴ glasses. As known Ω₂ is related with the covalency between rare earth ions and ligands anions and reflects the asymmetry of local environment at Tm³⁺ site in the glass hosts. Large Ω₂ means stronger covalency between the rare-earth ions and ligand anions, while the Ω₆ has a relation with the overlap integrals of 4f and 5d orbits²⁶. Large value of Ω₆ exhibits the large value of emission bandwidth and spontaneous radiative probability of rare earth³¹. Values of Ω₄ and Ω₆ also provide some information on the rigidity and viscosity of hosts.

Table 1. Judd-Ofelt intensity parameters in BGN and BGF samples.

Glass	Ω2 (×10−20 cm2)	Ω4 (×10−20 cm2)	Ω6 (×10−20 cm2)	Reference
BGN	6.26	0.24	1.6	This work
BGF	5.15	1.01	1.25
silicate	3.40	0.46	0.66	16
Tellurite	3.20	2.01	1.83	29
Fluorophosphate	3.01	2.56	1.54	32
Germanate	3.93	1.1	1.1	35

As shown in Table 2, spontaneous emission probability (A) for Tm³⁺ can also be calculated by using J-O theory, which is related with the J-O parameters and the refractive-index of host glass. Total spontaneous emission probability (∑A) of Tm³⁺: ³F₄ level in BGN glass (454.8 s⁻¹) is higher than that in BGF glass (406.38 s⁻¹), so is the A_rad of transition Tm³⁺: ³H₄ → ³F₄. High A value in BGN suggests strong emission, especially the ~1.8 μm emission. Lower A and Higher τ in BGF are owing to the addition of fluoride could reduce the refractive-index and J-O parameters in bismuthate glass system. Compared with calculated radiative properties in germanate glasses³⁵, BGN and BGF samples have higher A_rad value for each transition.

Table 2. Calculated radiative properties in BGN and BGF samples.

Transition	λ (nm)	Arad (s−1)	BGN sample				BGF sample
			∑A (s−1)	β (%)	τ (ms)	Arad (s−1)	∑A (s−1)	β (%)	τ (ms)
3F4 → 3H6	1847	454.48	454.48	100	2.20	406.38	406.38	100.00	2.46
3H5 → 3F4	3563	27.5	609.08	4.53	1.64	21.45	507.51	4.23	1.97
→3H6	1216	581.51		95.47		486.07		95.77
3H4 → 3H5	2428	10.81	3679.83	0.29	0.27	26.49	2894.29	0.92	0.35
→3F4	1444	283.61		7.71		235.88		8.15
→3H6	810	3385.40		92.00		2631.92		90.93
3F3 → 3H4	5200	7.05	4938.24	0.14	0.20	7.00	4302.28	0.16	0.23
→3H5	1655	832.61		16.86		685.69		15.94
→3F4	1310	184.22		3.73		133.42		3.10
→3H6	701	3914.36		79.27		3476.17		80.80
3F2 → 3F3	20449	0.01	2155.96	0.00	0.46	0.01	1639.24	0.00	0.61
→3H4	4145	41.78		1.94		33.83		2.06
→3H5	1531	370.17		17.17		347.88		21.22
→3F4	10722	2.09		0.10		1.63		0.10
→3H6	678	1741.92		80.80		1255.88		76.61
1G4 → 3F2	1632	20.61	5445.72	0.38	0.18	24.28	4493.39	0.54	0.22
→3F3	1511	118.63		2.18		97.46		2.17
→3H4	1171	714.61		13.12		533.45		11.87
→3H5	790	1946.18		35.74		1434.64		31.93
→3F4	647	383.41		7.04		318.74		7.09
→3H6	479	2262.29		41.54		2084.82		46.40
1D2 → 1G4	1538	432.58	71946.23	0.60	0.01	374.52	62466.60	0.60	0.02
→3F2	792	1258.84		1.75		1569.68		2.51
→3F3	762	3113.90		4.33		2523.72		4.04
→3H4	665	5208.87		7.24		3930.55		6.29
→3H5	522	244.90		0.34		188.45		0.30
→3F4	455	55623.17		77.31		43031.91		68.89
→3H6	365	6063.96		8.43		10847.76		17.37
1I6 → 1D2	1424	0.00	25009.80	0.00	0.04	0.00	26885.62	0.00	0.04
→1G4	739	3182.74		12.73		3497.78		13.01
→3F2	509	2202.92		8.81		1707.47		6.35
→3F3	497	55.70		0.22		49.53		0.18
→3H4	453	3851.15		15.40		4264.61		15.86
→3H5	382	150.15		0.60		125.55		0.47
→3F4	345	14686.53		58.72		15939.71		59.29
→3H6	291	880.60		3.52		1300.96		4.84

∑A is the total spontaneous emission probability of each level, A_rad is the spontaneous emission probability of each transition, τ is the calculated radiative lifetime.

Emission properties

Figure 4 shows the ~1.47 μm and ~1.8 μm emission spectra in BGN and BGF samples under 808 LD pumped. After the BaF₂ introduced, peak intensity of the ~1.8 μm emission in BGF is 2 times higher than that in BGN, while the intensity of ~1.47 emission is only a little change between two samples. As shown in the insert Fig. 4, the large intensity ratio of ~1800 nm to ~1470 nm (I₁₈₀₀/I₁₄₇₀) is related to the cross-relaxation (CR, ³H₆ + ³H₄ → ³F₄ + ³F₄)³⁶.

Figure 4. Room temperature ~1.8 μm emission spectra obtained by exciting with a cw laser diode at 808 nm for the BGN and BGF glasses doped with 1 mol% of Tm₂O₃.

The inset is the energy level diagram and energy transfer sketch map of Tm³⁺ when pumped at 808 nm.

With the introduction of BaF₂, the maximum phonon energy of glass hosts lower accordingly, which can be seen from the measured Raman spectra shown in Fig. 5, the maximum phonon energy of BGN and BGF samples can be presumed about 746 cm⁻¹ and 730 cm⁻¹, respectively. The Raman scattering band higher than 700 cm⁻¹ is mainly caused by the vibration of the tetrahedron group, the peak bond located in 756 cm⁻¹ and 846 cm⁻¹, correspond to the structure unit vibration of Ge-O and Ga-O, respectively³⁴. For BGF sample, lower phonon energy is also a key factor for stronger ~1.8 μm emissions.

Figure 5. Raman spectra of BGN and BGF host glass samples in the range from 200 to 1200 cm⁻¹.

According to the Fuchtbauer-Ladenburg theory, ~1.8 μm emission cross section (σ_em) is calculated⁵.

where λ is the wavelength, A_rad is the spontaneous emission probability calculated by J-O theory, I(λ) is the fluorescence intensity, n is the refractive index of the glass, and c is the light speed. It is noted that σ_em mainly related to ~1.8 μm emission spectrum and radiative transition probability of Tm³⁺: ³F₄ → ³H₆, which is a normalized line-shape function, respectively. According to Eq. (3), the stimulated emission cross-sections (σ_em) of ~1800 nm calculated are shown in Fig. 6. It can be determined that σ_em of BGF sample performs a maximum 7.56 × 10⁻²¹ cm² at 1865 nm, which is higher than that of BGN sample (7.01 × 10⁻²¹ cm², centered at 1865 nm). For BGN and BGF samples, the values of the maximum stimulated emission cross-section at the wavelength of 1865 nm, which are larger than that of the fluorophosphate glasses³⁷, silicate glasses²,¹⁶,³¹ and germanate glasses³⁸, due to high refractive index, high J-O parameters and good emission, and are beneficial to ~1.8 μm laser action of Tm³⁺ ions.

Figure 6. Stimulated emission cross-section of Tm³⁺:³F₄→³H₆ transition in BGN and BGF glasses doped with 1 mol% Tm₂O₃.

The product of emission cross-section and radiative lifetime σ_em × τ_rad is an important parameter for laser materials to obtain high gain. As shown in Table 3, the calculated values σ_em × τ_rad of BGN and BGF samples are 15.42 × 10⁻²¹ cm² ms and 18.59 × 10⁻²¹ cm² ms, respectively, which are lower than silicate glass³¹ σ_em × τ_rad= 28.48×10⁻²¹ cm² ms. However, There are still larger than tellurite glass²⁴ σ_em × τ_rad = 14.00 × 10⁻²¹ cm² ms and germanate glasses³⁸ σ_em × τ_rad= 13.6 × 10⁻²¹ cm² ms.

Table 3. Calculated emission cross-sections σ_em, radiative lifetime τ_rad, and σ_em × τ _rad of Tm³⁺: ³F₄ → ³H₆ in BGN and BGF samples.

Glass	σem (×10−21 cm2)	τrad (ms)	σem × τrad (×10−21 cm2 ms)	Reference
BGN	7.01	2.25	15.42	This work
BGF	7.56	2.46	18.59
silicate	3.6	7.91	28.48	28
Tellurite	8.1	1.73	14.00	24
Germanate	7.7	1.77	13.60	37

Cross-relaxation process

Because of the cross-relaxation transfer process (³H₆ + ³H₄ → ³F₄ + ³F₄) is beneficial for the ~1800 nm emission⁵. It is necessary to study the cross-relaxation process between Tm³⁺ ions. According to the theory of Dexter and Forster, the cross-relaxation rate can be calculated by the integral overlap of absorption cross-sections and emission cross-sections³³, which belongs to a dipole–dipole interaction. The microscopic transfer probability can be expressed by³⁴

where R is the distance between donor and acceptor, C_D−A is the transfer constant defined as follows¹⁵ , where R_c is the critical radius of the interaction and τ_D is the intrinsic lifetime of the donor-excited level. The transfer constant can be obtained according to Eq. (4) when phonons participate in the process to balance the energy gap⁵.

where c is the light speed, n is the refractive index, is the degeneracy of the lower and upper levels of the donor, respectively, is the average occupancy of the phonon mode at temperature T, is the maximum phonon energy, m is the number of phonons that participate in the energy transfer, S₀ is Huang–Rhys factor (0.31 for Tm³⁺)⁵, and is the wavelength with m phonon creation. The caculated energy migration (EM, ³H₄ + ³H₆ → ³H₆ + ³H₄) and cross relaxation (CR, ³H₆ + ³H₄ → ³F₄ + ³F₄) processes in BG and BGF are listed in Table 4. Because of the transfer condition of C_D−D is much larger than C_D−A, the hopping model is fulfilled in both BGN and BGF. to evaluate the energy transfer rate W_ET³⁹,

Table 4. Energy transfer parameters of the energy migration and cross-relaxation processes in BGN and BGF samples.

Glass	EM		CR		WET(10−20 cm3/s)
	M% phonons	CD−D (10−40 cm6/s)	M% phonons	CD−A (10−40 cm6/s)
BGN	0, 1	35.4	0, 1, 2	16.0	938
	99.99, 0.01		12.78, 83.99, 3.23
BGF	0, 1	37.8	0, 1, 2	18.6	1020
	99.99, 0.01		16.07, 79.37, 4.56

where n_D is the concentration of donor. According to Eq. (5), W_ET is calculated to be 938 cm³/s and 1020 cm³/s in BGN and BGF, respectively.

Fluorescence lifetime

The fluorescence decays of the Tm³⁺: ³F₄ level at room temperature is shown in Fig. 7. It can be seen that the measured lifetime τ_mea in BGN and BGF are 1.63 ms and 2.25 ms, respectively. The quantum efficiency (η) of the ³F₄ → ³H₆ emission can be calculated by

Figure 7. Luminescence decay curves of the ³F₄ level of the Tm³⁺ ions obtained exciting resonantly the ³H₆ → ³H₄ absorption transition at 808 nm and monitoring the Tm^{3+ 3}F₄ → ³H₆ emission at 1865 nm in BGN and BGF glasses doped with 1 mol% Tm₂O₃.

where τ_mea is the measured fluorescence lifetime and τ_rad is calculated with the Judd–Ofelt formalism. According to Eq. (6), the values of quantum efficiency for BGN and BGF are 74.09% and 91.46%, respectively, which are higher than silicate glass (13%)³¹, germanate glasss (55.52%)⁵, and lower than 70TeO₂-20ZnO-10ZnF₂ glass (164%)⁴⁰. The larger radiative lifetime (τ_mea) of Tm³⁺: ³F₄ state is benefit for ~1.8 μm laser action. It can be seen that the measured lifetime is shorter than the calculated lifetime, due to nonradiative quenching³¹. The nonradiative decay caused from several mechanisms, such as energy transfer between the Tm³⁺ ions, multiphonon decay²⁹, quenching by impurities (OH⁻), etc. The total rate of the ³F₄ → ³H₆ transition can be evaluated by⁴¹,⁴²:

where 1/τ_cal is the spontaneous radiative probability A_rad, W_MPR is the nonradiative multiphonon relaxation rate, W_OH⁻¹ is the nonradiative transition probability due to the energy transfer to OH⁻ impurities and W_ET represents an additional nonradiative loss mechanism due to the energy transfer between the RE ions. In this study, the concentrations of Tm³⁺ ions for BGN and BGF are the same, this third process can be neglected.

The multiphonon relaxation W_MPR can be expressed⁴³:

where W₀ is an experimentally determined parameter which is independent of the particular RE ion. ∆E is the energy gap between the ³F₄ and ³H₆ levels. g is the electron-phonon coupling strength parameter, and ћω_max is the highest phonon energy obtained from Raman spectra and p = ∆E/ћω_max. Multiphonon decay depends on the number of phonons required to bridge the energy gap to the next lower lying manifold. The higher the ћω_max is, the larger the multiphonon relaxation is.

W_OH⁻ is proportional to the concentration of Tm³⁺ ions and the measured absorption coefficient of OH⁻ groups⁴²,⁴⁴. For BGF sample, after BaF₂ introduced, the α_OH⁻ shows a significantly decrease, W_OH⁻¹ is expected to decrease which results in a reduced nonradiative transition rate. Thus the lifetime is much longer while the quantum efficiency is higher in BGF. Generally, the relatively longer radiation lifetime is beneficial to reduce the laser oscillation threshold⁴⁵.

Conclusion

In conclusion, we reported on ~1.8 μm emission in Tm³⁺-doped Bi₂O₃-GeO₂-Ga₂O₃ glasses in absence and presence of BaF₂. The addition of BaF₂ not only influences the network of glass, but also effectively reduces the content of hydroxyls and maximum phonon energy. For BGF sample, it shows a better thermal stability, and a stronger ~1.8 μm emission than that in BGN sample. It is also found that BGF glass possesses relatively large ~1.8 μm emission cross-section σ_em (7.56 × 10⁻²¹ cm²), measured fluorescence lifetime τ_mea (2.25 ms) and figure of merit gain σ_em × τ_rad (14.69 × 10⁻²¹ cm² ms) corresponding to the Tm³⁺: ³F₄ → ³H₆ transition. Our results suggest that introduced the BaF₂ into the glass network structure, which paves a way to enhance the ~1.8 μm emission properties and improve the fluorescence lifetime of Tm³⁺: ³F₄ in Tm³⁺ doped bismuthate glass.

Additional Information

How to cite this article: Han, K. et al. Optical characterization of Tm³⁺ doped Bi₂O₃-GeO₂-Ga₂O₃ glasses in absence and presence of BaF₂. Sci. Rep. 6, 31207; doi: 10.1038/srep31207 (2016).