Thermal and luminescent properties of 2 μm emission in thulium-sensitized holmium-doped silicate-germanate glass

Table 1. Compositions of the Prepared Glasses

Samples	Glass Compositions (mol%)
S0	60 SiO2-20(CaO+Li2O)-5Nb2O5-15BaO
SG	30 SiO2-30 GeO2-20(CaO+Li2O)-5Nb2O5-15BaO
SGT1	30 SiO2-30 GeO2-20(CaO+Li2O)-5Nb2O5-15BaO-0.5Tm2O3
SGT2	30 SiO2-30 GeO2-20(CaO+Li2O)-5Nb2O5-15BaO-1.5Tm2O3
SGTH1	30 SiO2-30 GeO2-20(CaO+Li2O)-5Nb2O5-15BaO-1Ho2O3-0.5Tm2O3
SGTH2	30 SiO2-30 GeO2-20(CaO+Li2O)-5Nb2O5-15BaO-1Ho2O3-1.5Tm2O3

B. Measurements

The density of the samples was measured using Archimedes’ water-immersion method on an analytical balance. Refractive index was measured at room temperature by the prism minimum deviation method. The characteristic temperatures (temperature of glass transition $T_{g}$ and onset crystallization peak $T_{x}$ ) were tested by a differential scanning calorimeter (DSC). Absorption spectra were recorded at room temperature in the wavelength range of 350–2200 nm with a Perkin Elmer Lambda 900UV-VIS-NIR spectrophotometer. The Raman spectrum of glass sample was measured with an FT Raman spectrophotometer (Nicolet MODULE) in the spectral range of $60 - 1100 {cm}^{- 1}$ , which has a resolution of $4 {cm}^{- 1}$ . The fluorescence spectra were measured with a computer-controlled Triax 320 type spectrometer upon excitation at 808 nm. The fluorescence lifetimes of ${}^{3}{F_{4}}$ level were recorded with an HP546800B 100-MHz digital oscilloscope and pumped by 800 nm LD. All the measurements were done at room temperature.

3. RESULTS AND DISCUSSION

A. Physical and Thermal Property

The physical and thermal property results of the analyzed glasses are listed in Table 2. For the investigated samples from Table 2, the density of the germanium-oxide-free sample is found to be $3.16 g / {cm}^{3}$ . Subsequently, it is observed that the density increased after introducing ${GeO}_{2}$ into the glass contents. The reason for increment in density is due to the large molecular weight $M$ of ${GeO}_{2}$ . Additionally, the refractive index for the studied compositions also increased with increasing ${GeO}_{2}$ contents. The present silicate-germanate glasses have a high refractive index ( $n = 1.70$ ) compared with fluorophosphate ( $n = 1.56$ ) ^[8] or silicate ( $n = 1.48$ ) glasses ^[22]. The rare-earth-ions’ electric dipole transition rate $A_{rad}$ increases with the increase of refractive index according to $A_{rad} \sim {(n^{2} + 2)}^{2} / n$ . Thus a higher value of the refractive index ( $n$ ) increases the spontaneous emission probability ( $A_{rad}$ ) and consequently provides a better opportunity to obtain laser actions in the laser medium.

Table 2. Physical and Thermal Properties of Silicate-Germanate Glasses

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Table 2. Physical and Thermal Properties of Silicate-Germanate Glasses

Sample Parameter Value
S0 Density ρ (g/cm3) 3.36
Refractive index nD 1.61
SG Density ρ (g/cm3) 3.56
Refractive index n 1.69
SGTH Refractive index n 1.70
Tg (°C) 585
Tx (°C) 740
ΔT (°C) 155
Sample thickness (mm) 1.50

At the same time, Table 2 shows the characteristic temperatures (containing temperatures of glass transition $T_{g}$ and onset crystallization $T_{x}$ ) of the prepared host glass. From Table 2, it can be seen that the present silicate-germanate glass possesses a larger $T_{g}$ value compared with germanate (596°C) ^[23] and fluorogallate (640°C) glass ^[24]. According to previous reports, glass hosts have a high $T_{g}$ value, which can make it achieve good thermal stability to resist thermal damage at high pumping power ^[25]. The difference between $T_{g}$ and $T_{x} (Δ T = T_{x} - T_{g})$ ^[26] of glass is also given in Table 2. Generally, it is desired that $Δ T$ is as large as possible to achieve a wide range of working temperature during the fiber fabricating. Because fiber fabricating is a reheating process, any crystallization during the process will affect the optical properties ^[27]. The larger $Δ T$ is, the better thermal stability the glasses will have ^[28]. According to Table 2, the $Δ T$ of silicate-germanate glass is 155°C, which is significantly higher than that of germanate (111°C) ^[23] and fluoride (90°C) glass ^[29]. Thus, the results show that the ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glass has good thermal stability, which is helpful for the construction of optical fibers.

B. Raman Spectrum

In the last decades, the structure of niobium silicate glasses ^[30,31] and alkali germanaosilicate glasses ^[32] has been reported by the Raman spectroscopic technique. However, few papers, to the best of our knowledge, have reported on the Raman spectra of niobium silicate-germanate glass. Figure 1 presents the vibrational spectra of an investigated silicate-germanate glass sample. It can be seen that the maximum phonon energy of the present sample is located at $804 {cm}^{- 1}$ , which is lower than that of sodium germanosilicate glass ( $862 {cm}^{- 1}$ ) ^[33]. For the sake of detailed analysis, the Gaussian deconvolution procedure is utilized to fit multipeaks ^[34], and the result is showed in Fig. 1. It can be found that the bands of five peaks are around at 325, 552, 784, 804, and $973 {cm}^{- 1}$ . According to the reported literatures, the low frequency region at around $\sim 325 {cm}^{- 1}$ is related to the chains of ${GeO}_{4}$ tetrahedra connected by six coordinated Ge units within the network ^[32]. Meanwhile, the weak peak at around $\sim 552 {cm}^{- 1}$ was observed, which has been attributed to the presence of germania, related to the Ge-O-Nb bonds, a structural network formed by ${GeO}_{4}$ tetrahedra and ${NbO}_{6}$ octahedra according to ^[35,36]. In the high-frequency region, the band at $784 {cm}^{- 1}$ is assigned to ${NbO}_{6}$ octahedra ^[36]. The latter intensity band centered near $804 {cm}^{- 1}$ should be assigned to the Nb-O bonds because, as the polarizability of Nb-O bonds is higher than that of Si-O bonds on the Raman spectra, the bands related to Si-O vibrations usually cannot be seen ^[31]. Compared with the structure of ${SiO}_{2}$ glass ^[37] and the alkali germanate compositions ^[32], the new shoulder is observed at $\sim 973 {cm}^{- 1}$ in the silicate-germanate glass, which should be related to the vibrational modes of Ge-O-Si linkages ^[35].

Figure 1.Deconvolution of Raman spectrum of SG glass using symmetric Gaussian functions.

C. Absorption Spectra

In order to better understand the properties of glass, some important optical parameters were calculated for our samples. Figure 2 shows optical absorption spectra of ${Tm}^{3 +}$ single doped, and ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glasses at room temperature in the wavelength range from 400 to 2200 nm. The length of samples is 10 mm for the measurement of the absorption spectra. The spectra shapes of single-doped or co-doped glass samples are similar, and the absorption intensity is proportional to the mol content of ${Tm}^{3 +}$ and ${Ho}^{3 +}$ ions.

Figure 2.Absorption spectra of ${Tm}^{3 +}$ single-doped and ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glasses in the range of 400–2200 nm.

From the absorption spectra, several inhomogeneously broadened absorption peaks can be observed, which are assigned to the transition from the ground-state level to the excited states of 4f configuration of ${Tm}^{3 +}$ and ${Ho}^{3 +}$ ions, respectively. Some important absorption bands are labeled in the spectra. It can be seen that the 808 or 980 nm LD is not applicable to ${Ho}^{3 +}$ ions. Nevertheless, levels ${}^{3}{H_{4}}$ of the ${Tm}^{3 +}$ ions can be excited at 808 nm. The intense absorption band centered at nearly 800 nm of the ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped sample from absorption curve, which indicates ${Tm}^{3 +}$ can function as an absorber to increase the absorption of the 808 nm pumping energy. Additionally, in comparison to single-doped and co-doped glass samples, it can be found that the shape and peak positions of each transition are similar, and there is no shift of the absorption peaks. This result indicates that there is no apparent cluster in the local ligand field, and both ${Ho}^{3 +}$ and ${Tm}^{3 +}$ ions are homogeneously incorporated into the glassy network. Meanwhile, Figure 2 shows the absorption peak intensity with ${Tm}^{3 +}$ ions at different concentrations, in which a significant increase of absorption with increased ${Tm}^{3 +}$ ions concentrations is clearly observed when concentrations of ${Ho}_{2} O_{3}$ remained constant.

D. J-O Analysis and Radiative Properties

To the best of our knowledge, J-O theory ^[38,39] has been often used to discuss the radiative properties of rare-earth ions within the host matrix from the absorption spectra. According to J-O theory, the J-O intensity parameters $Ω_{2}$ , $Ω_{4}$ , and $Ω_{6}$ for 4f–4f transitions of ${Ho}^{3 +}$ ions in the glass samples were computed from the measured absorption spectra. Afterward, these parameters $Ω_{t}$ ( $t = 2$ , 4, 6) were used to evaluate radiative properties of the main laser emitting levels of ${Ho}^{3 +}$ in silicate-germanate glass, such as radiative transition probability ( $A_{rad}$ ), fluorescence branching ratios ( $β$ ), and radiative lifetime ( $τ_{rad}$ ). The parameters $Ω_{λ}$ are important for the investigation of the local structure and bonding in the vicinity of rare-earth ions. The J-O intensity parameters of glass in this paper are compared with those obtained from various other ${Ho}^{3 +}$ doped glasses, as listed in Table 3. It should be noted that the five absorption bands— ${}^{5}{I_{6}}$ , ${}^{5}{F_{5}}$ , ${}^{5}{F_{4}} + {}^{5}{S_{2}}$ , ${}^{5}{F_{1}} + {}^{5}{G_{6}}$ , and ${}^{5}{G_{5}}$ —were used for the calculation in this process because the transition ${}^{5}{I_{8}} \to {}^{5}{I_{7}}$ has a substantial magnetic dipole component. From Table 3, it is observed that the oxide glasses have large $Ω_{2}$ and small $Ω_{6}$ values. The $Ω_{2}$ parameter of silicate-germanate glass follows the trend $Ω_{2} > Ω_{4} > Ω_{6}$ . This trend is consistent with the one observed for other glasses, such as silicate, germanate, fluorophosphate, and phosphate glasses; however, it differs from those of fluoride and tellurite glasses, as shown in Table 3. The root mean square deviation $δ_{rms}$ was calculated to be $1.31 \times 10^{- 6}$ . According to previous studies, $Ω_{2}$ is related with some factors such as the ligand symmetry of host glass, the degree of covalency of the chemical bonds between rare-earth ions and its nearest neighbor atoms of a glass. $Ω_{4}$ and $Ω_{6}$ are related to the covalency of the medium in which the rare-earth ions are situated. And $Ω_{6}$ reflect the bulk properties of the host such as rigidity and viscosity ^[8], which can be adjusted by the composition or structure of the glass host. It is also found that $Ω_{2}$ for ${Ho}^{3 +}$ in this work is larger than that of silicate ^[40], fluoride ^[41], fluorophosphate ^[42], tellurite ^[14], and phosphate ^[40] glass hosts. A large $Ω_{2}$ value is probably due to relatively high covalency of the chemical bond between rare-earth and oxygen ions. But the value of $Ω_{2}$ is smaller than that in germanate ^[43] glass. Thus the result indicates that ligand asymmetry around the rare-earth ions in ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped germanate glass is stronger than those in silicate-germanate glass. The smaller the $Ω_{6}$ value is, the stronger covalence between anions and rare-earth ions. It can be seen clearly that the $Ω_{6}$ of studied glass is smaller than that of various other glasses, as shown in Table 3. The J-O analysis indicated a strong asymmetry and covalent environment between the rare-earth ions and the ligand in the present matrix.

Table 3. J-O intensity Parameters ( $Ω_{λ}$ , $λ = 2$ , 4, 6) ( $\times 10^{- 20} {cm}^{2}$ ) of ${Ho}^{3 +}$ Ions in Various Glass Hosts

Table 3. J-O intensity Parameters ( $Ω_{λ}$ , $λ = 2$ , 4, 6) ( $\times 10^{- 20} {cm}^{2}$ ) of ${Ho}^{3 +}$ Ions in Various Glass Hosts

Samples	Ω2	Ω4	Ω6	Trend	Reference
SGTH2	6.5	2.61	0.33	Ω2>Ω4>Ω6	This work
Tellurite	5.21	2.28	2.18	Ω2>Ω6>Ω4	[14]
Silicate	5.20	1.80	1.20	Ω2>Ω4>Ω6	[40]
Phosphate	3.33	3.01	0.61	Ω2>Ω4>Ω6	[40]
Fluoride	1.86	1.90	1.32	Ω2>Ω6>Ω4	[41]
Fluorophosphate	3.23	2.71	1.82	Ω2>Ω4>Ω6	[42]
Germanate	6.60	1.75	0.99	Ω2>Ω4>Ω6	[43]

Furthermore, the spontaneous transition properties of the ${Ho}^{3 +}$ are shown in Table 4, including the spontaneous transition probability $A_{rad}$ , branching ratio $β$ , and radiative lifetime $τ_{rad}$ of different emission states of ${Ho}^{3 +}$ ions in silicate-germanate glass, which were evaluated using the three intensity parameters through J-O theory. Table 4 shows that the values of $A_{rad}$ for the ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ transition and $τ_{rad}$ of the ${}^{5}{I_{7}}$ level of ${Ho}^{3 +}$ are $103.46 s^{- 1}$ and 9.67 ms, respectively. The $A_{rad}$ value is larger than that of germanate, phosphate ^[41], silicate ^[44], and fluorophosphates ^[45] glasses. Higher $A_{rad}$ is beneficial in achieving intense infrared emissions. Consequently, this silicate-germanate glass can be considered as an appropriate host glass to achieve 2 μm laser from the ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ transition.

Table 4. Spontaneous Transition Probability $A_{rad}$ , Branching Ratio $β$ , and Radiative Lifetime $τ_{rad}$ for Different Excited Levels of ${Ho}^{3 +}$ in Silicate-Germanate Glass

Table 4. Spontaneous Transition Probability $A_{rad}$ , Branching Ratio $β$ , and Radiative Lifetime $τ_{rad}$ for Different Excited Levels of ${Ho}^{3 +}$ in Silicate-Germanate Glass

Transition	Energy (cm−1)	Arad (s−1)	β (%)	τrad (ms)
I75→I85	5139	103.46	100	9.67
I65→I85	8681	155.77	84.20	5.41
I65→I75	3321	29.23	–	–
I55→I85	11187	61.66	37.51	6.08
I55→I75	6046	82.36	–	–
I55→I65	2726	20.37	–	–
F55→I85	15528	2039.53	77.33	0.38
F55→I75	10384	1215.8	–	–
F55→I65	7067	178.8	–	–
F55→I55	4342	14.4	–	–

E. Fluorescence Spectra

Figure 3 shows ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glass fluorescence spectra in the range of 1600–2200 nm when excited by 808 nm LD at room temperature. From Fig. 3, it can be seen clearly that two emission peaks are centered near at 1.8 and 2 μm, which correspond to the ${Tm}^{3 +} : {}^{3}{F_{4}} \to {}^{3}{H_{6}}$ and ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ transition, respectively. Moreover, the 1.8 and 2 μm fluorescent intensity is in direct proportion to the ${Tm}_{2} O_{3}$ concentration, while, compared with the 2 μm emission, the emission intensity of 1.8 μm increased relatively little. Due to the intense energy transferring (ET) between the ${}^{3}{F_{4}}$ state of ${Tm}^{3 +}$ and ${Ho}^{3 +} : {}^{5}{I_{7}}$ state and cross-relaxation (CR) of adjacent ${Tm}^{3 +}$ ions.

Figure 3.Fluorescence spectra of the ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glasses.

In order to explain the mechanism of strong 2 μm luminescence, Fig. 4 shows the simplified energy level diagrams of ${Tm}^{3 +}$ and ${Ho}^{3 +}$ ions identified from the absorption spectra. The locations of the energy levels are similar to those reported previously for bismuthate ^[9] and tellurite ^[11] glass hosts. And the detailed energy transfer paths between the two rare-earth ions can be illustrated. In Fig. 4, the start state ${}^{3}{H_{6}}$ of ${Ho}^{3 +}$ ions are initially excited to the excited state of the ${Ho}^{3 +} : {}^{3}{F_{4}}$ level when ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped glass is pumped by 808 nm LD. Afterward, part of the ions of ${Tm}^{3 +}$ in the ${}^{3}{H_{4}}$ state drop down to the ${}^{3}{F_{4}}$ state, then the ${Tm}^{3 +} : {}^{3}{F_{4}}$ level decays to the ${}^{3}{H_{6}}$ level emitting 1.8 μm fluorescence. While most of the excited ${Tm}^{3 +}$ ions in ${}^{3}{H_{4}}$ states are excited from the ${}^{3}{H_{6}}$ ground state to ${}^{3}{F_{4}}$ state via CR between ${Tm}^{3 +} : {}^{3}{H_{4}}$ level and ${Tm}^{3 +} : {}^{3}{H_{6}}$ level and multiphonon relaxation (MR) process. ${Tm}^{3 +}$ ions in the ${}^{3}{F_{4}}$ state transfer energy to the ${Ho}^{3 +}$ ions in ${}^{5}{I_{7}}$ state via the ET process. After that, once the ${Ho}^{3 +} : {}^{5}{I_{7}}$ state is populated, the 2 μm emission via ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ transition takes place. The detail transfer mechanism is described as follows: ${}^{3}{H_{6}} ({Tm}^{3 +}) + h v (808 nm) \to {}^{3}{H_{4}} ({Tm}^{3 +}) (GSA) {}^{3}{H_{4}} ({Tm}^{3 +}) + {}^{3}{H_{6}} ({Tm}^{3 +}) \to {}^{3}{F_{4}} ({Tm}^{3 +}) + {}^{3}{F_{4}} ({Tm}^{3 +}) (CR) {}^{3}{F_{4}} ({Tm}^{3 +}) \to {}^{3}{H_{6}} ({Tm}^{3 +}) + h v^{'} (1.8 μm) (emission) {}^{3}{F_{4}} ({Tm}^{3 +}) + {}^{5}{I_{8}} ({Ho}^{3 +}) \to {}^{3}{H_{6}} ({Tm}^{3 +}) + {}^{5}{I_{7}} ({Ho}^{3 +}) (ET) {}^{5}{I_{7}} ({Ho}^{3 +}) \to {}^{5}{I_{8}} ({Ho}^{3 +}) + h v^{'} (2 μm) (emission)$

Figure 4.Energy level diagrams and energy transfer sketch map of ${Tm}^{3 +}$ and ${Ho}^{3 +}$ ions.

F. Absorption and Emission Cross Sections

The absorption and emission cross sections are two vital spectroscopic parameters and related to the optical gain of a laser material. The emission cross section ( $σ_{em}$ ) of ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ can be derived from Eq. (1) by using the McCumber theory ^[46]: $σ_{em} (λ) = σ_{abs} (λ) \times \frac{Z_{l}}{Z_{u}} \times \exp [\frac{h c}{k T} \times (\frac{1}{λ_{Z L}} - \frac{1}{λ})],$ (1)where $Z_{l} / Z_{u}$ is the partition functions ratio involved in the considered optical transition. Here $T$ is the room temperature, $k$ is the Boltzmann constant, and $λ_{Z L}$ is the wavelength for the transition between the lower Stark sublevels of the emitting multiplets and the lower Stark sublevels of the receiving multiplets. The $σ_{abs}$ is the absorption cross section of ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped sample, which is calculated from the absorption spectra by using Eq. (2): $σ_{abs} (λ) = \frac{2.303 \log (I_{0} / I)}{N l},$ (2)where $N$ is the concentration of ${Ho}^{3 +}$ ions, $l$ is the thickness of the glass samples, and $\log (I_{0} / I)$ is the absorptivity from absorption spectra, respectively.

Moreover, the emission cross section ( $σ_{em}$ ) also can be calculated from the fluorescence spectrum by the Fuchtbauer–Ladenburg equation in Eq. (3): $σ_{em} (λ) = \frac{λ^{4} A_{rad}}{8 π c n^{2}} \times \frac{λ I (λ)}{\int λ I (λ) d λ},$ (3)where $λ$ is the emission wavelength, $A_{rad}$ is the spontaneous radiative transition probability of ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ transition, $c$ is the velocity of light in vacuum, $n$ is the refractive index of glass host, $I (λ)$ is the fluorescence intensity, and $\int I (λ) d λ$ is the integrated fluorescence intensity.

Figure 5 shows the absorption and emission cross sections for ${Ho}^{3 +} : {}^{5}{I_{8}} \to {}^{5}{I_{7}}$ transition based on McCumber theory. According to the figure, it can be found that the peak absorption cross section of ${Ho}^{3 +} : {}^{5}{I_{8}} \to {}^{5}{I_{7}}$ transition in silicate-germanate glass reaches $2.77 \times 10^{- 21} {cm}^{2}$ near 1946 nm, and the emission cross section of ${Ho}^{3 +}$ is $4.78 \times 10^{- 21} {cm}^{2}$ at 2014 nm, respectively. The value of emission cross section is a little larger than that of fluoride glass ^[47] and silicate glass ^[44] but smaller than the value of germanate glass ^[48]. Compared with silicate ( $n = 1.48$ ) or phosphate ( $n = 1.52$ ) glasses ^[22], the prepared silicate-germanate glass has a high refractive index ( $n = 1.7$ ), the higher refractive index of the host glass induces the higher emission cross section of ${Ho}^{3 +}$ , due to the electric dipole transitions of rare-earth ions increasing as the refractive index of the glass increases ^[22]. It is worth noting that the emission cross section is as large as possible to obtain high gain for a laser medium ^[49]. Thus, ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glass could be a suitable candidate matrix for 2 μm optical fiber amplifier.

Figure 5.Emission cross sections of silicate-germanate glasses doped with 1.5 mol% ${Tm}_{2} O_{3}$ and 1 mol% ${Ho}_{2} O_{3}$ .

G. Laser Spectroscopic Properties

Table 5 shows the emission cross-section $σ_{e}^{peak}$ and the FWHM of the emission peak of ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ transition in different glass hosts. The $σ_{e}^{peak} \times FWHM$ is an important parameter in which to characterize the bandwidth properties of the optical amplifier materials, the larger value of which represents the wider gain bandwidth and the higher gain character ^[50]. The value of $σ_{e}^{peak} \times τ_{m}$ is another parameter that can be applied to evaluate the gain of bandwidth ^[51]. As the results show in Table 5, $σ_{e}^{peak} \times FWHM$ is $731.34 \times 10^{- 28} {cm}^{3}$ and $σ_{e}^{peak} \times τ_{m}$ is $46.22 \times 10^{- 21} {cm}^{2} \cdot ms$ in this work, respectively. Those values are much larger than those of various glasses, excluding fluoride ^[8] glass, as shown in Table 5. Therefore, it is desirable that the ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped silicate-germanate glass should become a suitable host material to be used as a candidate for broadband optical amplifiers or a 2 μm laser.

Table 5. Peak Cross Section $σ_{e}^{peak}$ , FWHM, Radiative Lifetime $τ_{m}$ , $σ_{e}^{peak} \times FWHM$ and $σ_{e}^{peak} \times τ_{m}$ of ${}^{5}{I_{7}} \to {}^{5}{I_{8}}$ Transition of ${Ho}^{3 +}$ in Different Glass Samples

Table 5. Peak Cross Section $σ_{e}^{peak}$ , FWHM, Radiative Lifetime $τ_{m}$ , $σ_{e}^{peak} \times FWHM$ and $σ_{e}^{peak} \times τ_{m}$ of ${}^{5}{I_{7}} \to {}^{5}{I_{8}}$ Transition of ${Ho}^{3 +}$ in Different Glass Samples

Glasses	FWHM(nm)	σepeak (10−21 cm2)	τm (ms)	σepeak×FWHM (10−28 cm3)	σepeak×τm (10−21 cm2·ms)	Reference
SGTH2	153	4.78	9.67	731.34	46.22	This paper
Silicate	82	7.0	0.32	574	2.24	[8]
Germanate	84	4.0	0.36	336	1.44	[8]
Gallate	141	3.8	8.2	535.8	31.16	[8]
Fluoride	118	5.3	26.7	625	141.51	[8]
Tellurite	–	10.7	2.2	–	23.54	[11]

H. Energy Transfer Efficiency

Figure 6 shows the decay curves of glass samples. By using the lifetime value of the ${Tm}^{3 +} : {}^{3}{F_{4}}$ energy level, the energy transfer efficiency from ${Tm}^{3 +} : {}^{3}{F_{4}}$ to ${Ho}^{3 +} : {}^{5}{I_{7}}$ in silicate-germanate glass can be estimated as follows ^[52]: $η = 1 - \frac{τ_{Tm / Ho}}{τ_{Tm}} .$ (4)

Figure 6.(a) Fluorescence decay curve of ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped glass sample from ${Tm}^{3 +} : {}^{3}{F_{4}} \to {}^{3}{H_{6}}$ . Inset shows the decay curve of ${Tm}^{3 +}$ singly doped glass sample. (b) Fluorescence decay curve of ${Tm}^{3 +} / {Ho}^{3 +}$ co-doped glass samples from ${Ho}^{3 +} : {}^{5}{I_{7}} \to {}^{5}{I_{8}}$ .