Samarium-Doped Lead Phosphate Glass: Optical Experiments and Calculations Using the Judd–Ofelt Theory

Abstract

In this work, Sm³⁺-activated lead phosphate glass has been studied using spectroscopic methods. Based on absorption spectrum measurements, the oscillator strengths for Sm³⁺ ions were determined and compared to those calculated from the Judd–Ofelt theory. This procedure was applied to evaluate some radiative parameters (radiative transition rates, emission branching ratios, radiative lifetime) of Sm³⁺ ions in lead phosphate glass. Further luminescent studies indicate that lead phosphate glass doped with Sm³⁺ emits intense reddish-orange light due to ⁴G_5/2 ⟶ ⁶H_7/2 transition, for which several important spectroscopic parameters like emission linewidth and lifetime, quantum efficiency, peak stimulated emission cross-section, and figure of merit for laser gain were determined. The factors for Sm³⁺ ions in lead phosphate glass are as follows: η = 53%, FWHM = 10.5 nm, τ_exp = 1.925 ms, σ_em = 7.6 × 10⁻²² cm², σ_em × τ_exp = 14.6 × 10⁻²⁵ cm²s. The experimental and theoretical results suggest that samarium-doped lead phosphate glass can be successfully used as a reddish-orange-emitting component in photonic devices.

1. Introduction

Samarium-doped inorganic glasses, due to their enhanced luminescent transition ⁴G_5/2 ⟶ ⁶H_7/2 (Sm³⁺), are known as promising reddish-orange emitting materials useful in solid-state lighting (SSL) technology and photonic devices [1,2,3,4,5]. Emission properties have been examined for numerous glass systems doped with Sm³⁺ ions, i.e., silicate [6,7,8,9,10], germanate [11,12,13], tellurite [14,15,16], and multicomponent mixed network-former glasses [17,18,19,20,21,22,23,24,25,26,27]. Luminescence behavior of Sm³⁺ ions in non-oxide glasses (chalcogenide, fluoride) has also been explored [28,29,30,31]. A great attention has been paid to borate [32,33,34,35,36,37,38,39,40] and phosphate [41,42,43,44,45,46,47,48,49] glasses containing Sm³⁺ ions. The impact of fluoride and oxide network modifiers on local structure and physicochemical properties (especially luminescence) of Sm³⁺-doped glasses has been analyzed in detail [50,51,52,53]. From numerous literature data, it is also well-known that trivalent samarium ions play an important role as an excellent acceptor in Dy³⁺/Sm³⁺ [54,55,56,57,58,59] and Tb³⁺/Sm³⁺ [60,61,62,63,64,65] co-doped glass systems through the excitation energy transfer processes.

Among inorganic glass systems, rare-earth-activated lead phosphate glasses represent a family of heavy metal glass (HMG) systems [66,67,68,69,70,71,72], and they are really attractive for optical applications. Recent studies concerned with rare-earth-activated lead phosphate-based glasses emitting visible light [73,74,75,76] and near-infrared radiation [76,77,78,79]. Owing to the hygroscopic nature of the main component P₂O₅, the procedure for glass synthesis should be strongly restrictive, i.e., glass samples should be synthesized in a glove-box in order to eliminate hydroxyl groups, which quench emission from excited states of rare earths [80]. Our previous investigations for rare-earth-activated lead phosphate glasses revealed that the intensities of the IR band assigned to the vibration of the hydroxyl groups were significantly lower for glasses fabricated in a glove box than in open air [81]. Thus, luminescence characteristics and spectroscopic parameters for rare earths are enhanced significantly, which is extremely important from the optical point of view.

In this work, lead phosphate glass based on PbO-P₂O₅-Ga₂O₃-Sm₂O₃ composition has been studied using optical spectroscopy. The introduction of the third component Ga₂O₃ to several glass host matrices increases their thermal stability [82]. It was also confirmed for lead phosphate glasses, for which the thermal stability increases with increasing Ga₂O₃ content [83]. The Sm³⁺ concentration was close to 0.5 mol%. From the luminescent studies published previously, low-concentrated (0.5 mol%) Sm³⁺ doped glasses [84,85,86,87,88,89] showed optical maximum emission intensity in the reddish-orange spectral region. Above 0.5 mol% of Sm³⁺, the activator concentration effects in glass samples are clearly observed due to cross-relaxation processes occurring between samarium ions [90,91,92]. Based on the optical experiments (absorption and emission spectra measurements) and calculations using the standard Judd–Ofelt theory [93,94], several spectroscopic and laser parameters of samarium ions in lead phosphate glass were determined. At this moment, it should be pointed out that the Judd–Ofelt calculation strategy was greatly developed, and some calculation routes were established in recent years. The Judd–Ofelt parameters of rare earths have been determined according to the excitation spectrum [95]. Luo et al. [96] have established a fluorescence decay route to calculate the Judd–Ofelt parameters of rare earth ions. In the current work, measured and calculated spectroscopic parameters were compared to the previous results published for similar Sm³⁺-doped glasses. The optical results indicate that Sm³⁺-activated lead phosphate glass is promising for reddish-orange emission applications.

2. Materials and Methods

Lead phosphate glass with the following chemical formula given in mole percent (mol%) 45PbO-45P₂O₅-9.5Ga₂O₃-0.5Sm₂O₃ was prepared by mixing and melting amounts of P₂O₅ and appropriate metal oxides. Oxide components of high purity (99.99%, Aldrich Chemical Co., St. Louis, MO, USA) were used to prepare a glass sample in a glove box, where a homogeneous mixture was heated in a protective atmosphere of dried argon (99.99%). In our case, the argon is necessary, contrary to the cheaper, but strongly reducing atmosphere of nitrogen, which can effectively reduce Sm³⁺ to Sm²⁺ ions. Reagents were melted in a Pt crucible at T = 1100 °C for 0.5 h.

In order to characterize the prepared glass, the XRD pattern (X’Pert Pro diffractometer, Panalytical, Almelo, The Netherlands), the DSC curve (Perkin Elmer differential scanning calorimeter, Shelton, CT, USA), and the Raman spectrum (Thermo Scientific^TM DXR^TM2xi Raman imaging microscope, Waltham, MA, USA) were measured, whereas the Metricon 2010 prism coupler (Pennington, NJ, USA) using λ = 632.8 nm was used to estimate the refractive index. Absorption and emission spectra were measured using a UV-VIS-NIR spectrophotometer (Cary 5000, Agilent Technology, Santa Clara, CA, USA) and a PTI QM40 spectrofluorometer (Photon Technology International, Birmingham, NJ, USA). Details for the equipment of the spectrofluorometer are given in previous work [97]. Resolution for the absorption and emission spectra was ±0.1 nm. The decay emission curve was measured with an accuracy of ±1 μs. All measurements were carried out at room temperature.

3. Results

Figure 1 presents the XRD pattern, DSC curve and Raman spectrum for Sm³⁺-activated lead phosphate glass. The X-ray diffraction analysis indicated that the studied sample is fully amorphous without narrow diffraction lines characteristic of crystalline systems. However, we do not exclude the presence of several small crystalline particles inside the glass that cannot be detected due to the resolution limit. The DSC curve was registered for the glass sample up to 600 °C, because the operating temperature range of the calorimeter is limited. Based on the DSC curve measurement, the glass transition temperature T_g was estimated, and its value is equal to 435 °C. Owing to the lack of the exothermic peak in the temperature range between T_g and T = 600 °C, we suggest that Sm³⁺-activated lead phosphate glass exhibits relatively good thermal stability (ΔT larger than 165 °C) against devitrification. The Raman spectrum shows that several vibration modes related to the characteristic phosphate groups are involved in the studied glass. The assignments of the unresolved bands for lead fluorophosphate glass were reported earlier by Kesavulu and Jayasankar [98]. The Raman bands centered at about 1050 cm⁻¹ and 1107 cm⁻¹ are due to symmetric stretching vibration of diphosphate and metaphosphate groups, whereas the shoulders near 900 cm⁻¹ and 1250 cm⁻¹ correspond to the symmetric (PO₄ groups) and asymmetric (PO₂ groups) stretching vibrations, respectively. Additionally, the broad Raman band located at about 750 cm⁻¹ (not presented here) is assigned to P–O–P stretching vibration [98]. Phonon energy of the studied glass (mode with maximum energy) obtained from the Raman spectrum measurements is equal to nearly 1107 cm⁻¹. For that reason, it was suggested that lead phosphate glass belongs rather to a medium-phonon system located between high-phonon borate-based glasses (hω = 1300 ÷ 1400 cm⁻¹) and low-phonon tellurite or germanate glass matrices (700 ÷ 800 cm⁻¹), respectively.

The Raman results are well correlated with the following value 1117 cm⁻¹, which was obtained for Eu³⁺-activated lead phosphate glass from the phonon sideband excitation spectrum measurements [99]. Selected physicochemical properties of Sm³⁺-activated lead phosphate glass are summarized in

Table 1. Some physicochemical properties of Sm³⁺-activated lead phosphate glass.

Parameters	Lead Phosphate Glass
Chemical composition (molar%)	45PbO-45P2O5-9.5Ga2O3-0.5Sm2O3
Average molecular weight (M g mol−1)	183.9
Density (d g cm−3)	5.12
Activator (Sm3+) content (molar %)	0.5
Sm3+ ion concentration (N × 1020 ions cm−3)	1.68
Refractive index (n)	1.75
Phonon energy (hω cm−1)	1107
Glass transition temperature (Tg °C)	435

.

In the next step, the absorption spectrum of Sm³⁺-doped lead phosphate glass was measured in the UV-VIS and NIR spectral range. The cut-off wavelength is close to 304 nm (UV range). The spectrum consists of bands characteristic of the 4f⁵-4f⁵ electronic intraconfigurational transitions of samarium ions. Absorption bands are assigned to transitions originating from ⁶H_5/2 ground state to the following excited states of Sm³⁺: ⁴D_7/2, ⁴D_3/2, ⁴D_1/2 + ⁶P_7/2, ⁶P_3/2, ⁶P_5/2, ⁴M_17/2, ⁴M_15/2 + ⁴I_J/2 (J = 9, 11, 13, 15), ⁴G_7/2, ⁴F_3/2, ⁴G_5/2 (UV-VIS absorption range) and ⁶F_11/2, ⁶F_9/2, ⁶F_7/2, ⁶F_5/2, ⁶F_3/2, ⁶H_15/2 and ⁶F_1/2 (NIR absorption range), respectively. The absorption spectrum for Sm³⁺-doped lead phosphate glass is presented in Figure 2. Then, the standard Judd–Ofelt framework [93,94] was used to calculate the theoretical oscillator strengths for each transition of Sm³⁺ ions in lead phosphate glass, which were compared to the measured oscillator strengths estimated by measuring the areas under the absorption bands (Figure 2). The absorption bands from the ⁶H_5/2 ground state to the ⁶F_J excited states with the spin selection rule ΔS = 0 were taken into account in the Judd–Ofelt calculation, because these transitions are allowed and their intensities are relatively strong [20]. The absorption transitions in the UV-VIS region are overlapped, and the energy states are lying very close to each other, thus the Judd–Ofelt calculations become more complicated. The calculation procedure using the Judd–Ofelt theory has been successfully applied to numerous Sm³⁺-activated inorganic glass systems [100,101,102,103,104,105,106,107].

The experimental and theoretical oscillator strengths of Sm³⁺ ions were determined using the following relations:

$${\mathrm{P}}_{\mathrm{meas}}=4.318\times 10^{-9}{\displaystyle \int \mathsf{\epsilon }(\mathsf{\nu })\mathrm{d}\mathsf{\nu }}$$

(1)

where ∫ε(ν)dv is the area under the absorption band and ε(ν) = A/c × l. In this relation, A, c and l denote the absorbance, the Sm³⁺ concentration and the optical path length.

$${\mathrm{P}}_{\mathrm{calc}}={\displaystyle \frac{8{\mathsf{\pi }}^2\mathrm{mc}{({\mathrm{n}}^2+2)}^2}{3\mathrm{h}\mathsf{\lambda }(2\mathrm{J}+1)\cdot 9\mathrm{n}}}\times {\displaystyle \sum _{\mathrm{t}=2,4,6}{\mathsf{\Omega }}_{\mathrm{t}}}{(<4{\mathrm{f}}^{\mathrm{N}}\mathrm{J}\Vert {\mathrm{U}}^{\mathrm{t}}\Vert 4{\mathrm{f}}^{\mathrm{N}}{\mathrm{J}}^{\prime }>)}^2$$

(2)

where m, c, h and λ denote the electron mass, the light velocity, the Planck constant and the mean wavelength of each transition. Here, ║U^t║² for samarium ions was adopted from Ref. [108]. The experimental and theoretical oscillator strengths for samarium ions in lead phosphate glass are given in

Table 2. Measured and calculated oscillator strengths (P × 10⁻⁶) for lead phosphate glass with Sm³⁺.

Level	Energy (cm−1)	Pmeas	Pcalc	Pmeas − Pcalc *
6F1/2	6300	0.257	0.262	0.005
6F3/2	6750	0.880	0.877	0.003
6F5/2	7257	1.510	1.528	0.018
6F7/2	8130	3.950	3.905	0.045
6F9/2	9276	2.850	2.916	0.066
6F11/2	10,600	0.495	0.484	0.011

* rms = (∑(P_meas − P_calc)²/N)^1/2 = ±0.34 × 10⁻⁶, N—the number of transitions.

. Small deviation of root mean square value (rms = ±0.34 × 10⁻⁶) between P_meas and P_calc suggests good fitting between them.

Based on comparison of the experimental and theoretical oscillator strengths for Sm³⁺ ions, the Judd–Ofelt intensity parameters Ω_t (where t = 2, 4, 6) were determined and compared to some glass systems [109,110,111,112]. The results are shown in

Table 3. Judd–Ofelt parameters for Sm³⁺ in lead phosphate glass compared to some glass systems.

Glass Host	Judd–Ofelt Parameters Ωt (in 10−20 cm2 Units)			Trend	Ref.
	Ω2	Ω4	Ω6
45PbO-45P2O5-9.5Ga2O3-0.5Sm2O3	0.76 ± 0.19	2.43 ± 0.09	2.98 ± 0.05	Ω2 < Ω4 < Ω6	this work
68H3BO3-30PbO-2Sm2O3	0.75	2.67	3.01	Ω2 < Ω4 < Ω6	[109]
67H3BO3-12Li2CO3-20Cs2CO3-1Sm2O3	0.81	3.22	4.28	Ω2 < Ω4 < Ω6	[110]
67B2O3-12Li2O-20K2O-1Sm2O3	0.88	3.93	4.66	Ω2 < Ω4 < Ω6	[111]
67B2O3-12Li2O-20Na2O-1Sm2O3	0.77	6.39	7.09	Ω2 < Ω4 < Ω6	[111]
67B2O3-12Na2O-20K2O-1Sm2O3	1.47	2.00	3.09	Ω2 < Ω4 < Ω6	[111]
30PbF2-30TeO2-39H3BO3-1Sm2O3	0.21	1.42	1.8	Ω2 < Ω4 < Ω6	[112]

.

In the following step, the factors Ω_t were applied to obtain the radiative transition rates and emission branching ratios using the following relation:

$${\mathrm{A}}_{\mathrm{J}}={\displaystyle \frac{64{\mathsf{\pi }}^4{\mathrm{e}}^2}{3\mathrm{h}(2\mathrm{J}+1){\mathsf{\lambda }}^3}}\times {\displaystyle \frac{\mathrm{n}{({\mathrm{n}}^2+2)}^2}{9}}\times {\displaystyle \sum _{\mathrm{t}=2,4,6}{\mathsf{\Omega }}_{\mathrm{t}}}{(<4{\mathrm{f}}^{\mathrm{N}}\mathrm{J}\Vert {\mathrm{U}}^{\mathrm{t}}\Vert 4{\mathrm{f}}^{\mathrm{N}}{\mathrm{J}}^{\prime }>)}^2$$

(3)

$$\mathsf{\beta }={\displaystyle \frac{{\mathrm{A}}_{\mathrm{J}}}{{\displaystyle \sum _{\mathrm{i}}{\mathrm{A}}_{\mathrm{J}\mathrm{i}}}}}$$

(4)

The radiative transition rates and emission branching ratios for samarium in lead phosphate glass are presented in

Table 4. Radiative transition rates and emission branching ratios for Sm³⁺-activated lead phosphate glass.

Transition	λ (nm)	AJ (s−1) *	β
4G5/2 ⟶ 6F11/2	1460	0.34	0.11
4G5/2 ⟶ 6F19/2	1198	0.96	0.35
4G5/2 ⟶ 6F7/2	1038	2.60	0.94
4G5/2 ⟶ 6F5/2	953	6.82	2.48
4G5/2 ⟶ 6F3/2	908	0.82	0.30
4G5/2 ⟶ 6H15/2	902	0.50	0.18
4G5/2 ⟶ 6F1/2	893	0.66	0.24
4G5/2 ⟶ 6H13/2	795	7.16	2.60
4G5/2 ⟶ 6H11/2	710	32.87	11.93
4G5/2 ⟶ 6H9/2	648	70.47	25.58
4G5/2 ⟶ 6H7/2	596	145.84	52.94
4G5/2 ⟶ 6H5/2	560	6.46	2.35

* A_TOTAL = ∑A_J = 275.5 s⁻¹, τ_rad = 1/A_TOTAL = 3.63 ms.

. The total radiative transition rate, defined as the sum of the A_J values calculated for each transition from the ⁴G_5/2 excited state to the lower lying states of Sm³⁺ ions, is equal to A_TOTAL = 275.5 s⁻¹, whereas the radiative lifetime τ_rad for the state ⁴G_5/2 (Sm³⁺) as an inverse of A_TOTAL is close to 3.63 ms. Details for the Judd–Ofelt analysis and calculations using relations (1)–(4) are given elsewhere [97].

In the next step, emission properties have been examined in detail. The emission spectrum of Sm³⁺-activated lead phosphate glass is presented in Figure 3.

The results well demonstrated that the emission intensity is higher for the glass sample excited at 402 nm (⁶P_3/2 state) than 470 nm (multiband due to ⁴M_15/2 + ⁴I_J/2 (J = 9, 11, 13, 15) states), respectively. Four emission bands correspond to ⁴G_5/2 ⟶ ⁶H_J/2 (where J = 5, 7 9, 11) transitions of samarium. Reddish-orange emission at 596 nm due to the ⁴G_5/2 ⟶ ⁶H_7/2 transition of samarium ions is the most intense. The inset shows a decay curve for the ⁴G_5/2 state of samarium ions in lead phosphate glass. Luminescence lifetime was estimated based on the decay curve measurement. Its experimental value τ_exp for the excited state ⁴G_5/2 (Sm³⁺) is close to 1.925 ms. Four emission lines are illustrated schematically on the energy level diagram of Sm³⁺ ions in Figure 4.

The experimental emission lifetime τ_exp as well as the radiative lifetime τ_rad and the radiative transition rate A_J from the Judd–Ofelt framework were used to calculate the quantum efficiency η and the peak stimulated emission cross-section σ_em. The appropriate relations (5) and (6) are given below:

$$\mathsf{\eta }={\displaystyle \frac{{\mathsf{\tau }}_{\exp }}{{\mathsf{\tau }}_{\mathrm{rad}}}}\times 100\%$$

(5)

$${\mathsf{\sigma }}_{\mathrm{em}}={\displaystyle \frac{{\mathsf{\lambda }}_{\mathrm{p}}^4}{8\mathsf{\pi }\mathrm{c}{\mathrm{n}}^2\mathsf{\Delta }\mathsf{\lambda }}}{\mathrm{A}}_{\mathrm{J}}$$

(6)

In relation (6), n is the refractive index, and its value is close to 1.75 (Table 1), λ_p is the peak emission wavelength, whereas Δλ is the effective linewidth defined as full width at half maximum (FWHM).

Spectroscopic parameters for samarium ions in lead phosphate glass are given in

Table 5. Spectroscopic parameters for Sm³⁺ ions in lead phosphate glass and other glass systems.

Glass Composition (mol%)	λp (nm)	FWHM (nm)	τexp (ms)	τrad (ms)	η (%)	σem (cm2 × 10−22)	Ref.
45PbO-45P2O5-9.5Ga2O3-0.5Sm2O3	596	10.50	1.925	3.630	53	7.60	this work
10Li2O-10PbO-9Al2O3-70B2O3-1Sm2O3	597	10.59	0.966	1.600	60.4	7.23	[113]
15PbF2-59TeO2-25WO3-1Sm2O3	600	-	0.620	1.360	45.6	6.26	[114]
26.66B2O3-52.33PbO-16GeO2-4Bi2O3-1Sm2O3	601	15.03	1.392	2.580	54	6.08	[115]
55P2O5-39PbO-5Nb2O5-1Sm2O3	598	10.40	1.896	3.268	58	6.76	[116]
55P2O5-14K2O-6KF-15BaO-9Al2O3-1Sm2O3	597	12	2.400	4.290	56	5.92	[117]
58.5P2O5-15K2O-16.5MgO-9Al2O3-1Sm2O3	598	11.20	1.800	3.140	57	5.80	[118]
44P2O5-17K2O-9Al2O3-23PbF2-6Na2O-1Sm2O3	601	13.96	1.580	2.04	77	8.98	[119]
41P2O5-17K2O-8Al2O3-23ZnF2-10LiF-1Sm2O3	601	14.63	1.690	2.124	80	9.53	[120]
44P2O5-17K2O-9Al2O3-23PbO-6Na2O-1Sm2O3	598	11.20	1.570	1.880	83.5	11.50	[121]
44P2O5-17K2O-9Al2O3-29Nb2O5-1Sm2O3	602	15.07	1.175	-	98	11.52	[122]
45P2O5-45Na2O-2Al2O3-8BaO-0.5Sm2O3	600	-	2.400	2.710	88	12.36	[123]

. The results are compared to the previously published data for similar phosphate-based glass systems and heavy metal glasses containing lead [113,114,115,116,117,118,119,120,121,122,123].

4. Discussion

The physicochemical results obtained using XRD, DSC and Raman methods (Figure 1) confirmed that Sm³⁺-doped lead phosphate glass is fully amorphous, thermally stable and belongs to medium-phonon glass matrices (Table 1). Based on the absorption spectrum recorded in the UV-VIS and NIR ranges (Figure 2) and relations (1)–(4) from the Judd–Ofelt theory, several radiative parameters for samarium ions in lead phosphate glass were obtained. The measured and calculated oscillator strengths for transitions of Sm³⁺ ions were compared (Table 2), and the Judd–Ofelt parameters Ω_t (t = 2, 4, 6) were achieved. The following trend Ω₄ > Ω₆ > Ω₂ or Ω₆ > Ω₄ > Ω₂ is usually observed for Sm³⁺ ions in inorganic glasses [124]. In our case, the Judd–Ofelt intensity parameters for Sm³⁺ ions are changed in direction Ω₆ > Ω₄ > Ω_2, and this trend is similar to the results obtained earlier for other systems (Table 3). Moreover, the Judd–Ofelt intensity parameter Ω_2, exhibiting the degree of bonding (covalent/ionic) between samarium ions and ligands is low. Its value is equal to 0.76 × 10⁻²⁰ cm². It suggests absolutely more ionic bonding in character between samarium ions and their nearest surroundings confirming previous Judd–Ofelt results obtained for phosphate-based glasses doped with Sm³⁺ [125,126,127].

The Judd–Ofelt parameters Ω_t were used to obtain the radiative transition rates, emission branching ratios and radiative lifetime (Table 4). In particular, the luminescence properties of Sm³⁺-doped lead phosphate glass have been examined in detail. Luminescence spectrum (Figure 3) consists of four bands, which are associated with the following transitions: ⁴G_5/2 ⟶ ⁶H_5/2, ⁴G_5/2 ⟶ ⁶H_7/2, ⁴G_5/2 ⟶ ⁶H_9/2 and ⁴G_5/2 ⟶ ⁶H_11/2 centered at 560 nm, 596 nm, 648 nm and 710 nm, respectively. All transitions are indicated on the energetic diagram of samarium ions (Figure 4). Lead phosphate glass with Sm³⁺ emits reddish-orange light related to the most intense ⁴G_5/2 ⟶ ⁶H_7/2 transition at 596 nm. Based on emission spectrum and its decay from the ⁴G_5/2 (Sm³⁺), and the appropriate relations (5) and (6), several spectroscopic parameters for trivalent samarium ions in lead phosphate glass were determined. The results are summarized in Table 5.

The main spectroscopic parameters for Sm³⁺ ions in PbO-P₂O₅-Ga₂O₃ glass system are as follows: the peak emission wavelength λ_p = 596 nm, the luminescence linewidth FWHM = 10.5 nm, the ⁴G_5/2 theoretical radiative lifetime τ_rad = 3.63 ms, the experimental luminescence lifetime of ⁴G_5/2 state τ_exp = 1.925 ms, the stimulated emission cross-section σ_em = 7.6 × 10⁻²² cm² and the quantum efficiency ⁴G_5/2 (Sm³⁺) η = 53%. The latter parameter, i.e., the quantum efficiency η is larger than 50% suggesting that Sm³⁺-activated lead phosphate glass is also a potential laser material emitting in the reddish-orange region. Interestingly, the quantum efficiency for the ⁴G_5/2 (Sm³⁺) state in lead phosphate glass is smaller than the η value (60.4%) obtained for Sm³⁺ ions in heavy metal oxide glass based on Li₂O-PbO-Al₂O₃-B₂O₃ [113] but higher than η = 45.6% for Sm³⁺ in heavy metal oxyfluoride glass based on PbF₂-TeO₂-WO₃ [114]. In fact, the quantum efficiency agrees with the results (54–58%) for multicomponent heavy metal oxide glass [115] and phosphate-based glasses with the presence [116] and absence [117,118] of lead. Contrary to η values, the peak stimulated emission cross-section σ_em for the main ⁴G_5/2 ⟶ ⁶H_7/2 reddish-orange transition of trivalent samarium ions in lead phosphate glass is higher compared to the values (σ_em = 5.8 ÷ 7.23 × 10⁻²² cm²) obtained for heavy metal glass systems as well as phosphate-based glasses [113,114,115,116,117,118]. At this moment, it should also be noted that both spectroscopic parameters seem to be smaller compared to the values η (77 ÷ 98%) and σ_em (9 ÷ 12.4 × 10⁻²² cm²) reported for some phosphate-based glasses with Sm³⁺ [119,120,121,122,123].

Finally, the figure of merit for laser gain defined as σ_em × τ_exp was determined for the ⁴G_5/2 ⟶ ⁶H_7/2 transition of Sm³⁺ ions in lead phosphate glass at 596 nm. Relatively large values of σ_em × τ_exp product are necessary to generate laser action in glass systems. In our case, the figure of merit for laser gain is close to 14.6 × 10⁻²⁵ cm²s and its value is higher compared to the following results: 8.51 × 10⁻²⁵ cm²s for PbF₂-TeO₂-WO₃ [114], 10.4 × 10⁻²⁵ cm²s for P₂O₅-K₂O-MgO-Al₂O₃ [118], 11.7 × 10⁻²⁵ cm²s for Li₂O-PbO-Al₂O₃-B₂O₃ [113], as well as 12.8 × 10⁻²⁵ cm²s for P₂O₅-PbO-Nb₂O₅ [116], respectively. The σ_em × τ_exp product for trivalent samarium ions in lead phosphate glass ranges between 13.54 × 10⁻²⁵ cm²s for P₂O₅-K₂O-Al₂O₃-Nb₂O₅ [122] and 16.1 × 10⁻²⁵ cm²s for P₂O₅-K₂O-Al₂O₃-PbF₂-Na₂O [119], even though these Sm³⁺-doped glass systems exhibit higher values of η and σ_em compared to our glass, as mentioned above. It suggests that the figure of merit for laser gain can be useful in comparison to reported laser phosphate glass systems with Sm³⁺ ions [119,120,121,122,123]. According to the previous results for PbO-P₂O₅-Ln₂O₃ (Ln = Sm, Gd) glass without Ga₂O₃, the lifetimes and the quantum efficiencies depend significantly on the Sm³⁺ content as well as on the heating time of glasses melted at high temperature [128]. On the other hand, thermal stability increases with increasing Ga₂O₃ concentration in lead phosphate glass, as mentioned in the Section 1 [83]. Therefore, we can conclude based on the spectroscopic results shown in Table 5 that the thermally stable samarium-doped lead phosphate glass modified by Ga₂O₃ is suitable for the applications of reddish-orange visible light. It can be successfully used as a glass component in photonic devices similar to other Sm³⁺-doped glass host matrices published recently, which seem to be excellent reddish-orange-emitting candidates for numerous luminescence applications [129]. For example, borosilicate glasses modified by alkaline/alkali (CaF₂, NaF) fluorides [87] or mixed alkali (Li₂O, Na₂O) oxides [130] playing the role as the glass-network-modifiers are attractive for luminescence applications after Sm³⁺ ion doping. Based on the structural, thermal and optical studies, it was suggested that borosilicate-based glasses doped with Sm³⁺ ions are promising for radiation protection and photonic display devices [87] and luminescence applications in art and decoration [130].

5. Conclusions

Optical experiments and the Judd–Ofelt calculations have been successfully applied to Sm³⁺-doped lead phosphate glass, which emits intense reddish-orange light related to ⁴G_5/2 ⟶ ⁶H_7/2 transition at 596 nm. Several spectroscopic factors for trivalent Sm³⁺ were determined. The following spectroscopic parameters the for ⁴G_5/2 ⟶ ⁶H_7/2 transition of samarium in lead phosphate glass were achieved: the quantum efficiency η = 53%, the emission linewidth FWHM = 10.5 nm, the experimental emission lifetime τ_exp = 1.925 ms, the peak stimulated emission cross-section σ_em = 7.6 × 10⁻²² cm² and the figure of merit for laser gain σ_em × τ_exp = 14.6 × 10⁻²⁵ cm²s, respectively. The results compared to heavy metal glass systems and phosphate-based glasses published previously. The theoretical and experimental studies demonstrate that Sm³⁺-activated lead phosphate glass is a promising reddish-orange laser gain media operated at 596 nm.