Judd–Ofelt Analysis and Emission Properties of Dy3+ Ions in Borogermanate Glasses

Borogermanate glasses singly doped with Dy3+ ions were synthesized and then studied using the absorption and luminescence spectra. Spectroscopic changes of Dy3+ ions have been examined for compositional-dependent glasses with various molar ratios GeO2:B2O3. In this work, several spectroscopic parameters of Dy3+ ions were obtained experimentally and compared to the calculated values from the Judd–Ofelt theory. Luminescence spectra measured for borogermanate glasses consist of blue, yellow and red bands, which correspond to 4F9/2 → 6H15/2, 4F9/2 → 6H13/2 and 4F9/2 → 6H11/2 transitions of Dy3+, respectively. Luminescence lifetimes for the 4F9/2 excited state are reduced, whereas the stimulated emission cross-sections for the most intense 4F9/2 → 6H13/2 yellow transition of Dy3+ increase with increasing GeO2 and decreasing B2O3 concentrations in glass-hosts. Quantum efficiency of the 4F9/2 (Dy3+) excited state is nearly independent on molar ratios GeO2:B2O3. Attractive spectroscopic properties related to the 4F9/2 → 6H13/2 transition of Dy3+ ions are found for borogermanate glasses implying their potential utility for yellow laser action and solid-state lighting technology.


Introduction
Judd [1] and Ofelt [2] published their pioneering scientific works concerning the absorption intensities of rare earths 60 years ago. Based on the Judd-Ofelt (J-O) framework, several spectroscopic parameters for the optically active ions from the lanthanide series can be determined, which are really important from the optical and laser points of view. The most important of which are the radiative transition probability, the luminescence branching ratio and the radiative lifetime for the upper laser state of rare earth ions. The radiative transition probability and spectral linewidth for luminescent transition of rare earth ions can be used to calculate the peak stimulated emission cross-section, whereas measured emission lifetime and radiative lifetime calculated from the J-O framework are usually applied to estimate the quantum efficiency of the excited state. As a result, many glass matrices doped with rare earths can be quite well evaluated for a variety of possible applications such as for optical components and devices. Therefore, the J-O theory made a huge contribution to the development of optical and laser glasses in modern photonics. Since then, numerous published papers have been devoted to the study of glasses, glass-ceramics and other inorganic compounds singly or doubly doped with rare earth ions [3][4][5][6][7][8] using the theory on the intensities of 4f-4f electronic transitions introduced by Judd and Ofelt in 1962. In particular, the Judd-Ofelt analysis was performed for trivalent Nd 3+ [9][10][11][12][13][14][15][16][17], Er 3+ [18][19][20][21][22][23][24][25][26][27][28][29][30], Sm 3+ [31][32][33][34][35], Pr 3+ [36][37][38][39][40], Tm 3+ [41][42][43][44], Ho 3+ [45][46][47][48][49][50] and Dy 3+ [51][52][53][54][55][56][57][58] ions in various inorganic glasses. The later trivalent rare earth ions, i.e., Dy 3+ ions, were successfully used as an optical probe to study the luminescence behavior of inorganic glasses [59]. Recently, systematic investigations indicate that dysprosium doped glasses are excellent candidates for solid-state yellow lasers, white LEDs and other photonic device applications [60][61][62][63]. Their luminescence properties depend strongly on glass-network-modifiers [64], excitation wavelength and activator concentration [65]. Glass samples were synthesized using a melt-quenching technique. Starting components of high purity 99.99% (Aldrich Chemical Co., St. Louis, MO, USA) were used for glass synthesis. All oxide components were mixed in an agate mortar for homogenization. Then, glass batches were placed in an Al 2 O 3 crucible and melted at temperature T = 1250 • C for t = 45 min in an electric furnace. The received glass samples were cooled to room glass synthesis. All oxide components were mixed in an agate mortar for homogenization. Then, glass batches were placed in an Al2O3 crucible and melted at temperature T = 1250 C for t = 45 min in an electric furnace. The received glass samples were cooled to room temperature and then polished for optical measurements. Photographs of the Dy 3+ doped glass samples are shown in Figure 1. The refractive indices of glass series were determined using the Metricon 2010 prism coupler at a wavelength of 632.8 nm. The optical absorption spectra measurements were performed using the UV-VIS-NIR spectrophotometer (Cary 5000, Agilent Technology, Santa Clara, CA, USA). The emission spectra and decays were recorded using laser equipment, which consists of a Photon Technology International (PTI) Quanta-Master 40 (QM40) UV/VIS Steady State Spectrofluorometer (Photon Technology International, Birmingham, NJ, USA) with a xenon lamp as an excitation source, Nd:YAG laser (Opotek Opolette 355 LD, OPOTEK, Carlsband, CA, USA) with a tunable pulsed optical parametric oscillator, double 200 mm monochromator and multimode UVVIS PMT R928 detector (PTI Model 914). Resolution for emission spectra measurements was 0.1 nm, whereas decays were measured with an accuracy of 1 µ s.

Theoretical Background
The measured oscillator strengths of transitions were obtained from the absorption bands of Dy 3+ ions. They were estimated by measuring the areas under the absorption bands of Dy 3+ ions using the equation: where: ∫ε(ν) represents the area under the absorption line and ε(ν) = A/(c × l), A indicates the absorbance, c is the concentration of the Dy 3+ ion (in mol × l −1 ) and l denotes the optical path length. The theoretical oscillator strengths for each absorption transition of Dy 3+ ions were calculated using the Judd-Ofelt theory [1,2]. The theoretical oscillator strength is defined as follows: where λ denotes the mean wavelength of each transition, whereas m, c, h and n are the mass of the electron, the velocity of light, the Planck constant and the refractive index of the medium, respectively. In this relation, ║U t ║ 2 represents the square of the matrix elements of the unit tensor operator U t . The values of ║U t ║ 2 used for Dy 3+ were adopted from Ref. [86]. The theoretical oscillator strengths were compared to the experimental values obtained from the optical absorption spectra of Dy 3+ ions in borogermanate glasses and the phenomenological intensity parameters Ωt (where t = 2, 4, 6) were determined. The fit quality was expressed by the magnitude of the root-mean-square deviation. It was defined by rms =  (Pmeas − Pcalc) 2 . These three Judd-Ofelt intensity parameters Ωt (t = 2, 4, 6) were used to calculate the radiative transition probabilities, the luminescence branching ratios The refractive indices of glass series were determined using the Metricon 2010 prism coupler at a wavelength of 632.8 nm. The optical absorption spectra measurements were performed using the UV-VIS-NIR spectrophotometer (Cary 5000, Agilent Technology, Santa Clara, CA, USA). The emission spectra and decays were recorded using laser equipment, which consists of a Photon Technology International (PTI) Quanta-Master 40 (QM40) UV/VIS Steady State Spectrofluorometer (Photon Technology International, Birmingham, NJ, USA) with a xenon lamp as an excitation source, Nd:YAG laser (Opotek Opolette 355 LD, OPOTEK, Carlsband, CA, USA) with a tunable pulsed optical parametric oscillator, double 200 mm monochromator and multimode UVVIS PMT R928 detector (PTI Model 914). Resolution for emission spectra measurements was 0.1 nm, whereas decays were measured with an accuracy of 1 µs.

Theoretical Background
The measured oscillator strengths of transitions were obtained from the absorption bands of Dy 3+ ions. They were estimated by measuring the areas under the absorption bands of Dy 3+ ions using the equation: where: ε(ν) represents the area under the absorption line and ε(ν) = A/(c × l), A indicates the absorbance, c is the concentration of the Dy 3+ ion (in mol × l −1 ) and l denotes the optical path length. The theoretical oscillator strengths for each absorption transition of Dy 3+ ions were calculated using the Judd-Ofelt theory [1,2]. The theoretical oscillator strength is defined as follows: where λ denotes the mean wavelength of each transition, whereas m, c, h and n are the mass of the electron, the velocity of light, the Planck constant and the refractive index of the medium, respectively. In this relation, U t 2 represents the square of the matrix elements of the unit tensor operator U t . The values of U t 2 used for Dy 3+ were adopted from Ref. [86]. The theoretical oscillator strengths were compared to the experimental values obtained from the optical absorption spectra of Dy 3+ ions in borogermanate glasses and the phenomenological intensity parameters Ω t (where t = 2, 4, 6) were determined. The fit quality was expressed by the magnitude of the root-mean-square deviation. It was defined by rms = Σ (P meas − P calc ) 2 . These three Judd-Ofelt intensity parameters Ω t (t = 2, 4, 6) were used to calculate the radiative transition probabilities, the luminescence branching ratios and the radiative lifetimes. The radiative transition probabilities A J for the excited states of Dy 3+ ions were calculated using the relation given below: The luminescence branching ratio β is related to the relative intensities of transitions from the excited state to all terminal states of Dy 3+ ions.
The radiative lifetime τ rad is the inverse of the total radiative transition probability (the sum of the A J terms). Its value was compared to the experimental lifetime received from the luminescence decay curve. Both calculated and measured lifetimes were applied to determine the quantum efficiency of an excited state η. The appropriate relations are given below: Finally, the emission linewidth ∆λ referred as full width at half maximum (FWHM) and the radiative transition probability A J were successfully used to calculate the peak stimulated emission cross-section σ em using the following expression: where λ p is the peak emission wavelength for the electronic transition of Dy 3+ . All theoretical and experimental spectroscopic parameters for Dy 3+ ions in the studied borogermanate glasses are summarized in Table 2.

Results and Discussion
Judd-Ofelt analysis of Dy 3+ ions in mixed borogermanate glasses with various GeO2:B2O3 molar ratios equal to 11:1, 5:1, 2:1, 1:1, 1:2 and 1:5 was carried out. Theoretical and experimental results were compared to GeO2-BaO-Ga2O3 and B2O3-BaO-Ga2O3 glasses. Absorption and emission properties have been examined for glass samples, where the concentration of Dy 3+ ions was the same (0.5 mol%). Firstly, the absorption spectra measurements for Dy 3+ ions in borogermanate glasses were carried out at room temperature. The absorption spectra of borogermanate glasses doped with Dy 3+ ions were measured in the UV-visible and near-infrared spectral ranges, respectively. The spectra consist of inhomogeneously broadened absorption bands characteristic for 4f 9 -4f 9 electronic transitions of Dy 3+ . The absorption bands correspond to transitions originating from the 6 H15/2 ground state to the following excited states: 6 H11/2, 6 F11/2, 6 F9/2, 6 F7/2, 6 F3/2, 4 F9/2, 4 I15/2, 4 G11/2, 4 I13/2, 4 F7/2, ( 4 M19/2+ 4 D3/2+ 6 P5/2), 6 P7/2 and 6 P3/2. The later transition, i.e., 6 H15/2 → 6 P3/2 transition, is clearly visible for GeO2-BaO-Ga2O3 glass contrary to B2O3-BaO-Ga2O3 glass. For mixed borogermanate glasses, the 6 H15/2 → 6 P3/2 transition of Dy 3+ lies on the absorption edge. This indicates that the absorption edge is shifted to longer wavelengths from GeO2-BaO-Ga2O3 glass via mixed B2O3-GeO2-BaO-Ga2O3 compositions to B2O3-BaO-Ga2O3 glass, respectively. The absorption spectra are presented in Figure 2. From the optical absorption spectra, the experimental oscillator strengths for Dy 3+ ions have been determined. Owing to the standard procedure, the x-axes of absorption spectra were converted to wavenumbers (given in cm −1 ). In the next step, the baseline was From the optical absorption spectra, the experimental oscillator strengths for Dy 3+ ions have been determined. Owing to the standard procedure, the x-axes of absorption spectra were converted to wavenumbers (given in cm −1 ). In the next step, the baseline was fitted individually to each absorption band. The integrated areas of absorption bands were calculated. The intensities of absorption lines of Dy 3+ ions presented in Figure 2 were estimated by measuring the areas under the bands, and then applied to determine the experimental oscillator strengths using relation (1). The commercially available software OriginPro was used during the calculation procedure.
The theoretical oscillator strengths for each transition of Dy 3+ ions were calculated from the J-O framework (Part 3) using relation (2). In order to perform the analysis, the refractive index of the medium was used for calculations. The refractive index is changed OriginPro was used during the calculation procedure.
The theoretical oscillator strengths for each transition of Dy 3+ io from the J-O framework (Part 3) using relation (2). In order to perfor refractive index of the medium was used for calculations. The refractiv from 1.736 for GeO2-BaO-Ga2O3 glass to 1.605 for B2O3-BaO-Ga2O3 g indices for the studied glass samples are schematized in Figure 3. The experimental oscillator strengths from the absorption spectra cillator strengths were compared. They are shown in Tables 3 and 4.  The experimental oscillator strengths from the absorption spectra and theoretical oscillator strengths were compared. They are shown in Tables 3 and 4.  The main calculation process is related to three phenomenological Judd-Ofelt intensity parameters Ω t (t = 2, 4, 6), which were obtained by comparison of the experimental oscillator strengths from the absorption spectra with the theoretical oscillator strengths from Equation (2) of the Judd-Ofelt framework (Part 3) using the fitting procedure. The quality of the fit shown in Tables 3 and 4 expressed by the rms deviation defined by Σ(P meas − P calc ) 2 (see Part 3) is quite good. The rms deviations for the studied glass systems varying with GeO 2 /B 2 O 3 molar ratios are in the range 0.23-0.58 (×10 −6 ). The error is within the acceptable range compared to similar glass doped with Dy 3+ [70], which was studied using the Judd-Ofelt framework. The three Judd-Ofelt intensity parameters Ω t (t = 2, 4, 6) are necessary to calculate some spectroscopic parameters such as the radiative transition probabilities and the luminescence branching ratios, and then the radiative lifetimes, the quantum efficiencies of excited states and the peak stimulated emission crosssections for electronic transitions of Dy 3+ ions. The three Judd-Ofelt intensity parameters Ω t (t = 2, 4, 6) for Dy 3+ ions in borogermanate glasses are given in Table 5.  [87] and Na 2 O-ZnO-PbO-GeO 2 -TeO 2 composition (Ω 2 = 7.34 × 10 −20 cm 2 ) referred to as NZPGT [88] as well as obtained for similar borate glasses based on the B 2 O 3 -CaF 2 -CaO-BaO-Al 2 O 3 system (Ω 2 = 5.98 × 10 −20 cm 2 ) referred to as CFB [89] and B 2 O 3 -ZnO-Al 2 O 3 -Bi 2 O 3 (Ω 2 = 6.20 × 10 −20 cm 2 ) referred to as ZnAlBiB [90]. Following that, the Judd-Ofelt intensity parameters Ω 4 and Ω 6 are structuredependent, i.e., the parameter Ω 4 describes the viscosity of the glass medium while the parameter Ω 6 is connected with the rigidity of the glass medium. Interestingly, GeO 2 -BaO-Ga 2 O 3 glass and borogermanate glasses with lower B 2 O 3 content (GeO 2 :B 2 O 3 from 11:1 to 2:1) exhibit Ω 4 > Ω 6 , whereas B 2 O 3 -BaO-Ga 2 O 3 glass and borogermanate glasses with relatively higher B 2 O 3 content (GeO 2 :B 2 O 3 = 1:2 and 1:5) possess Ω 4 < Ω 6 ( Table 3). The same situation was observed earlier for germanate, germanate-tellurite and tellurite glasses [87,87,91], where Ω 4 > Ω 6 contrary to borate or phosphate glasses [90,92,93], where Ω 4 < Ω 6 . However, further investigations for borate-based glasses suggest that Ω 4 < Ω 6 can be changed to Ω 4 > Ω 6 with decreasing Dy 3+ concentration [94]. For glass with GeO 2 :B 2 O 3 = 1:1 both the Judd-Ofelt parameters Ω 4 and Ω 6 are nearly the same as Dy 3+ doped silicate glass based on SiO 2 -Al 2 O 3 -PbF 2 -AlF 3 -YbF 3 -DyF 3 composition [95].
It was concluded that the intensity parameters Ω 4 and Ω 6 depend not only on the viscosity and rigidity, but they are also affected by the acidity and basicity of the glass-host, i.e., the highest Ω 4 and Ω 6 indicates the lowest basicity of the glass and the highest hardness [83]. In particular, the parameter Ω 6 is reduced systematically with increasing basicity and decreasing rigidity of the glass [96]. The calculation results given in Table 5 clearly indicate that the intensity parameter Ω 6 increases from GeO 2 -BaO-Ga 2 O 3 glass to B 2 O 3 -BaO-Ga 2 O 3 glass. The values of Ω 6 are larger for glass samples containing higher B 2 O 3 concentrations suggesting their lower basicity and higher rigidity. Further studies suggest that the Judd-Ofelt intensity parameters Ω 4 and Ω 6 not only influence the physicochemical properties of glasses but also strongly affect the radiative transition probabilities as a result of the interaction between trivalent dysprosium ions and their nearest environments [97].
Following that, the spectroscopic quality parameter χ referred to as the magnitude of Ω 4 /Ω 6 belongs to important factors characterizing the optical potential of the currently prepared glass. It was presented and discussed in detail for several glass systems doped with Dy 3+ ions [91]. For borogermanate glass systems, the values of χ are relatively large, which demonstrates quite well the intense luminescent transitions of Dy 3+ ions. Luminescence studies for multicomponent glass based on B 2 O 3 -Bi 2 O 3 -SrO-Al 2 O 3 -PbO-Dy 2 O 3 revealed that the spectroscopic quality factor χ ≥ 0.50, can be suggested as a good optical candidate for the lasing action of dysprosium ions [80].
The three phenomenological J-O intensity parameters Ω t (t = 2, 4, 6) were applied to calculate the radiative transition probabilities and the luminescence branching ratios using the appropriate Relations (3) and (4)  and 1495 s −1 for GeO 2 -BaO-Ga 2 O 3 glass, respectively. In all cases, the luminescence branching ratio is the highest for the 4 F 9/2 → 6 H 13/2 electronic transition of Dy 3+ ions at 573 nm. Its value changed from 69.1% to 74.5% depending on the chemical composition of the glass-host. The calculation results suggest that the studied borogermanate glass systems are promising for yellow emission independently on molar ratios GeO 2 :B 2 O 3 . The luminescence spectra measurements confirm this hypothesis.  Figure 4 presents the luminescence spectra of Dy 3+ ions in borogermanate glasses. The spectra for glasses based on B 2 O 3 -BaO-Ga 2 O 3 and GeO 2 -BaO-Ga 2 O 3 are also indicated. The emission spectra show three characteristic bands of Dy 3+ ions located at blue, yellow and red spectral range. These luminescence bands are attributed to 4 F 9/2 → 6 H 15/2 (blue), 4 F 9/2 → 6 H 13/2 (yellow) and 4 F 9/2 → 6 H 11/2 transitions of trivalent dysprosium. In previous work [85], the influence of glass former (GeO 2 ), oxide (CaO/SrO/BaO) and fluoride (CaF 2 /SrF 2 /BaF 2 ) glass modifiers on spectral properties, the yellow-to-blue luminescence intensity ratios and CIE coordinates of Dy 3+ in borate-based glasses have been examined in detail. The studies revealed that the CIE chromaticity coordinates (x, y) are changed significantly with molar ratios GeO 2 :B 2 O 3 in glass composition. The CIE coordinates are changed from (x = 0.405, y = 0.452) to (x = 0.430, y = 0.472) with increasing GeO 2 content, which contributes to color modification of the borogermanate glass system from greenish to yellowish. These experimental results are presented and discussed in the previously published work [85]. The luminescent transitions of Dy 3+ ions are indicated in the energy level diagram shown in Figure 5.  The luminescent results presented in Figure 4 indicate that the intensities are the highest for yellow bands related to the 4 F9/2 → 6 H13/2 transition of Dy 3+ , independently on GeO2:B2O3 ratios. In addition, the 4 F9/2 → 6 H13/2 transition of Dy 3+ ions is so-called hypersensitive transition, which follows the selection rules S = 0, ΔL  2 and ΔJ  2. The emission intensities as well as the spectral profiles and positions are very sensitive to even small changes of the nearest environment around dysprosium ions. The same situation is observed for the absorption band centered near 1250 nm due to transition originating from the 6 H15/2 ground state to the 6 F11/2 state. Figure 6 shows hypersensitive absorption and emission transitions of Dy 3+ varying with GeO2:B2O3 molar ratios. In order to compare the spectral profile and position of hypersensitive transitions, the spectra were normalized. Spectroscopic analysis indicates that the spectra are broader with increasing B2O3 content. These effects are significantly stronger for absorption than emission bands.   The luminescent results presented in Figure 4 indicate that the intensit highest for yellow bands related to the 4 F9/2 → 6 H13/2 transition of Dy 3+ , indepe GeO2:B2O3 ratios. In addition, the 4 F9/2 → 6 H13/2 transition of Dy 3+ ions is so-ca sensitive transition, which follows the selection rules S = 0, ΔL  2 and Δ emission intensities as well as the spectral profiles and positions are very sensit small changes of the nearest environment around dysprosium ions. The same observed for the absorption band centered near 1250 nm due to transition origin the 6 H15/2 ground state to the 6 F11/2 state. Figure 6 shows hypersensitive abso emission transitions of Dy 3+ varying with GeO2:B2O3 molar ratios. In order to co The luminescent results presented in Figure 4 indicate that the intensities are the highest for yellow bands related to the 4 F 9/2 → 6 H 13/2 transition of Dy 3+ , independently on GeO 2 :B 2 O 3 ratios. In addition, the 4 F 9/2 → 6 H 13/2 transition of Dy 3+ ions is so-called hypersensitive transition, which follows the selection rules |S| = 0, |∆L| ≤ 2 and |∆J| ≤ 2. The emission intensities as well as the spectral profiles and positions are very sensitive to even small changes of the nearest environment around dysprosium ions. The same situation is observed for the absorption band centered near 1250 nm due to transition originating from the 6 H 15/2 ground state to the 6 F 11/2 state. Figure 6 shows hypersensitive absorption and emission transitions of Dy 3+ varying with GeO 2 :B 2 O 3 molar ratios. In order to compare the spectral profile and position of hypersensitive transitions, the spectra were normalized. Spectroscopic analysis indicates that the spectra are broader with increasing B 2 O 3 content. These effects are significantly stronger for absorption than emission bands. Further luminescent studies suggest that yellow-to-blue factor Y/B (Dy 3+ ) due to the ratio of the integrated emission intensities ( 4 F9/2 → 6 H13/2)/( 4 F9/2 → 6 H15/2) is changed significantly with molar ratios GeO2:B2O3 in glass composition. The values of Y/B (Dy 3+ ) are reduced from 4.22 for GeO2-BaO-Ga2O3 glass to 2.80 for B2O3-BaO-Ga2O3 glass with increasing B2O3 concentration suggesting more ionic bonding between Dy 3+ ions and surrounding ligands. The results are in a good agreement with the calculated values of the intensity parameters Ω2, which decrease from 8.73 for GeO2-BaO-Ga2O3 glass to 5.92 for B2O3-BaO-Ga2O3 glass indicating more ionic bonding in character. It was schematized on Figure 7.
The same situation is also observed for the peak stimulated emission cross-section calculated from equation (7) in Part 3 for the 4 F9/2 → 6 H13/2 transition of Dy 3+ at 573 nm, which is decreased with increasing B2O3 content (Figure 7).
Finally, luminescence decays from the 4 F 9/2 state of Dy 3+ ions have been analyzed in detail. Decay curves for the 4 F 9/2 (Dy 3+ ) state in borogermanate glasses were measured under excitation 454 nm and monitoring emission wavelength 573 nm. The luminescence decay curves for Dy 3+ are presented in Figure 8. The obtained results clearly demonstrated that decays are longer with increasing B 2 O 3 concentration in glass composition.
(Equation (5), Part 3) calculated from the J-O theory. Both me lifetimes were used to calculate quantum efficiency (Equation lifetimes and quantum efficiencies for the 4 F9/2 state of Dy 3+ var ratios are schematically shown in Figure 9.  . The 4 F 9/2 lifetime of Dy 3+ ions is the highest (τ m = 513 µs) for B 2 O 3 -BaO-Ga 2 O 3 glass. In contrast to the dependences of luminescence intensity ratio Y/B and the peak stimulated emission cross-section for the 4 F 9/2 ® 6 H 13/2 transition (Figure 7), the luminescence lifetime for the 4 F 9/2 state of Dy 3+ increases with increasing B 2 O 3 content. It is experimentally evidenced that the non-radiative multiphonon relaxation probabilities of rare earth ions are increased significantly with increasing phonon energy from GeO 2 to B 2 O 3 . Glass based on GeO 2 -BaO-Ga 2 O 3 (~800 cm −1 ) has relatively smaller phonon energy than B 2 O 3 -BaO-Ga 2 O 3 glass (~1400 cm −1 ). Thus, the measured lifetimes of rare earth ions are reduced from GeO 2 to B 2 O 3 because multiphonon relaxation probabilities become higher with increasing B 2 O 3 content. For example, this situation is observed for Er 3+ ions, where the energy separation between the excited state 4 I 13/2 and next lower-lying ground state 4 I 15/2 is relatively small and non-radiative multiphonon relaxation provides an important contribution to the total relaxation process. The opposite effects are observed for other rare earth ions such as Tb 3+ , Eu 3+ or Dy 3+ , where the energy gaps between the interacting levels are relatively large and non-radiative relaxation probabilities are negligibly small. Thus, luminescence lifetimes 4 F 9/2 (Dy 3+ ) are nearly equal to radiative lifetimes calculated from the J-O theory and their experimental values increase from GeO 2 -BaO-Ga 2 O 3 glass to B 2 O 3 -BaO-Ga 2 O 3 glass. It was also confirmed earlier by the measurements of luminescence decay curves for rare earth ions in heavy metal oxide glasses referred to as HMOG. Previously published work clearly demonstrated that the dependence of experimental luminescence lifetimes on the phonon energies of HMOG glass systems is completely different for the 5 D 0 state of Eu 3+ than for the 4 I 13/2 state of Er 3+ [100].
Further studies indicate that the quantum efficiency of excited state 4 F 9/2 (Dy 3+ ) is almost unchanged with increasing B 2 O 3 concentration. The quantum efficiency for the 4 F 9/2 state of Dy 3+ in mixed borogermanate glasses seems to be 47 ± 1%, independently of GeO 2 :B 2 O 3 molar ratios. For GeO 2 -BaO-Ga 2 O 3 glass (η = 52%) the quantum efficiency is above 50%. The results obtained for borogermanate glasses singly doped with Dy 3+ ions suggest their potential luminescent applications in the yellow spectral range [71,101].

Conclusions
Borogermanate glasses doped with Dy 3+ have been studied experimentally and theoretically using the Judd-Ofelt framework. Based on absorption and emission spectra measurements, several spectroscopic parameters for Dy 3+ ions were determined, such as the measured and calculated oscillator strengths, the Judd-Ofelt intensity parameters, the radiative transition probabilities, the luminescence branching ratios, the peak stimulated emission cross-sections, the measured and radiative (calculated) luminescence lifetimes and the quantum efficiencies of excited state. They have been examined as a function of GeO 2 :B 2 O 3 molar ratios in glass composition. The systematic investigations demonstrated that the peak stimulated emission cross-sections for the most intense 4 F 9/2 → 6 H 13/2 yellow transition of Dy 3+ ions decrease, whereas the 4 F 9/2 luminescence lifetimes are enhanced with increasing B 2 O 3 concentration. The quantum efficiencies for the 4 F 9/2 state of Dy 3+ ions are close to η = 47 ± 1% and their values are nearly independent of GeO 2 :B 2 O 3 ratios. It was suggested that the results for borogermanate glasses doped with Dy 3+ are attractive for yellow luminescence, providing an important contribution to the development of optical glasses and celebrating the 60th anniversary of the Judd-Ofelt theory.

Data Availability Statement:
The data presented in this study are available on request from the author.