Luminescence and Gamma Spectroscopy of Phosphate Glass Doped with Nd³⁺/Yb³⁺ and Their Multifunctional Applications

Abstract

A new glass with a composition of 40P₂O₅-30ZnO-20LiCl-10BaF₂ (in mol%), doped with 3.5Nd₂O₃-3.5Yb₂O₃, was fabricated by the quenching melt technique. The luminescence (PL) and gamma spectroscopy of the glass were investigated systematically. The spectroscopic parameters of the prepared glass, such as the optical energy gap, Judd–Ofelt parameters Ω_k (where k = 2, 4 and 6), lifetimes and branching ratio of the Nd³⁺/Yb³⁺ level, were evaluated. Moreover, the shielding parameters, such as the linear and mass attenuation coefficients, mean free path and half-value layer, were evaluated. The prepared glass had a spectroscopic quality factor (Ω₄/Ω₆) of 0.84, which is about three-times larger than that of the most standard laser host, Nd³⁺:YAG. The energy of the 2P1/2 (Nd³⁺) level (~23,250 cm⁻¹) was twice the energy of the Yb³⁺ transition (~10,290 cm⁻¹). The value of the emission cross section (${\sigma }_{em}\left(\lambda \right)$) of Nd³⁺:⁴F_3/2→⁴I_9/2 and Yb³⁺:²F_5/2→²F_7/2 were 2.23 × 10⁻²⁴ cm² and 2.88 × 10⁻²⁴ cm², respectively. The fabricated glass had a high emission cross section and low mean free path parameters, which makes the fabricated glass a potential candidate for multifunctional applications, such as laser emissions for medical purposes.

1. Introduction

The codoped ions Nd³⁺ and Yb³⁺ are some of the best examined rare-earth elements and are used in fiber lasers. In both glasses and crystals, efficient energy transfer between Nd³⁺ and Yb³⁺ ions has been established. Nd³⁺/Yb³⁺ glasses are applied as compact sources in non-linear microscope technology in image processing with a THz frequency [1,2].

It is worth exploring the higher excited states of Nd³⁺ involved in the energy transfer from Nd³⁺ to Yb³⁺. The lanthanide ion Yb³⁺ emits a wavelength of approximately 1000 nm, which may be absorbed without losing any energy. Moreover, the longer lifetime and broader absorption and emission bands of Yb³⁺ ions allow greater energy-storage efficiency in comparison with other rare earth ions, namely the Nd³⁺ ions [3,4]. Although the lanthanide ion Yb³⁺ has just one excited state, around 10,000 cm⁻¹ above the ground state, the pump wavelength range of Yb³⁺ ions is limited to 980 nm by this simple energy level scheme. Down-conversion may occur if a suitable sensitizer with energy levels of 20,000 cm⁻¹, two times the energy of Yb³⁺, is used [5].

However, laser glasses have been specifically designed for photodynamic therapy surgery and medical radiation technology. Researchers investigated the optical and shielding properties of such glasses for their usefulness as a safety replacement device in medical workplaces, such as X-ray and atomic projects in the field of inventions, V-ray equipment, gamma camera rooms and examination workplaces for computed tomography (CT) [6,7]. The radiation protecting characteristics of Erbium Zinc–Tellurite glass were inspected to compare a vast range of radiation energies for health and medical imaging applications (20, 30, 40 and 60 keV) [8]. Furthermore, the laser diodes for fiber optical intercommunicating applications exhibit near-infrared (NIR) discharge at a wavelength of 1.54 μm that can be employed in armed forces, detective work and medical investigations facilities [9].

Therefore, we fabricated phosphate laser glass with the composition P₂O₅-ZnO-LiCl-BaF₂ (PZLB) as the host lattice due to the low matrix phonon energy codoped with Nd³⁺/Yb³⁺ ions, which decreases the non-radiative transition rate to lower states. This is beneficial for the cross-relaxation energy transfer between Nd³⁺ and Yb³⁺. Thus, the spectroscopic properties of this glass were comprehensively investigated; furthermore, the energy transfer efficiency from Nd³⁺ to Yb³⁺ is also discussed. In addition to that, we measured attenuation radiation parameters, such as the linear attenuation coefficient, LAC; the mass attenuation coefficient, MAC; half-value layer, HVL; and the mean free path, MFP, of the prepared glass.

2. Materials and Methods

A homogeneity Nd³⁺/Yb³⁺doped glass with the composition (in mol%) 40P₂O₅-30ZnO -20LiCl-10BaF₂-3.5Nd₂O₃-3.5Yb₂O₃, referred to as PZLBNdYb glass, was prepared by the melt quenching technique. We mixed the chemical very well in an alumina crucible. We placed it into a muffle furnace to be melted at 1200 °C for 1 h following the melt quenching technique. The molten chemical mixture was then quenched in a preheated copper mold. The quenched glass was heat-treated at 450 °C for 2 h at the beginning of the annealing process to eliminate any strain on sample molecules.

The density of the glass was measured using a gas pycnometer (Model: UltraPyc 1200e). The measured density of the PZLBNdYb glass sample was ρ = 4.426 ± 0.001 g/cm³. Using a UV-VIS-NIR spectrophotometer, the optical absorption spectra of the glasses were measured in the wavelength range of 190–2500 nm (JASCO, V-570).

The concentration of Nd³⁺ (or Yb³⁺) ions can be calculated by the following expression:

$$N_{N{d}^{3+}}=2\frac{3.5\rho A_{\upsilon }}{100M}$$

(1)

where M is the molecular weight of PZLBNdYb glass and A_ν is Avogadro’s number. The concentration of the dopant Nd³⁺ or Yb³⁺ in PZLBNdYb glass was N_Nd³⁺ = N_Yb³⁺ = 1.405 × 10²⁷ ions/m³.

The shielding parameters—the linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), half-value layer (HVL) and mean free path (MFP)—of the proposed sample were measured using the NaI detector system (SPECTECH-NaI 1.5 PX 1.5/2.0 IV, S/N 010723-6) connected to a computer-based multichannel analyzer (MCA). Different gamma sources (Am²⁴¹-5µCI-59.5 keV, Cs¹³⁷-5µCI-662 keV, Co⁶⁰-5µCI-1170 and 1330 keV) were used to produce a collimated beam at the detector level. Our group study, in Ref. [10], detailed the experimental setup utilized for detecting the incident and transmission radiation intensities in Figure 1.

The values of ${\mu }_m$, $\mu$, HVL and MFP parameters can be calculated using the following relations.

$$\begin{array}{l}\{\begin{array}{c}\mu =\frac{ln\frac{I_o}{I}}{x},\\ {\mu }_m=\frac{ln\frac{I_o}{I}}{\rho x},\\ HVL=\frac{0.693}{\mu },\end{array}\\ \hspace{1em}\hspace{1em}\hspace{1em}\mathrm{and} MFP=\frac{1}{\mu }\end{array}$$

(2)

In Ref. [10], we detailed the experimental setup utilized for detecting the incident and transmission radiation intensities in Figure 1.

3. Results and Discussion

Absorption Spectroscopy, Optical Energy Gap and Judd–Ofelt Analysis

The UV–Vis–NIR absorption spectra for the PZLBNdYb sample are recorded in Figure 2. The absorption spectra displayed seven bands centered around 352, 428, 470, 522, 580, 628, 682, 744, 802, 882 and 980 nm. All bands originated from the absorption transition from the ground state (⁴I_9/2) to different excited states of the Nd³⁺(⁴f₃) ion, except the 980 nm peak, which corresponds to the ²F_7/2→²F_5/2 absorption transition for ytterbium ions.

The Nd³⁺ ion bands detected are comparable to those previously described [11,12], except for minor changes in the peak positions and relative intensities. This can be attributed to the nature of various ligand fields of different glass matrixes [13]. The maximum absorption coefficient is observed at 590 nm wavelength, corresponding to the ⁴I_9/2→²G_7/2 + ⁴G_5/2 hypersensitive transition. In contrast, the absorption peak of ⁴I_9/2→²H_11/2 (at 628 nm) was the lowest and was weak enough to be considered in the computation.

The Stark structure was poorly resolved for all bands due to the inhomogeneous broadening, and nearby energy levels overlapped—appearing as a single peak in the measured spectra. The number of long orders in the host causes changes in the micro symmetry surrounding the Nd³⁺ ions, resulting in amplification of the absorption bands. In other words, the linewidth of the various transitions is a measure of the Stark splitting of the J-manifold. The inhomogeneous broadening is due to the site-to-site variation in the local field seen by the rare earth ion.

Extrapolation of the linear relation, Equation (3), of the plotted absorption curves yielded the optical energy gap, E_opt, which reflected the transition from localized states at the top of the valence band into localized ones in the conduction band or vice versa.

The optical energy gap, E_opt, was calculated by using the absorption spectra of the produced glass as follows [7];

$${\left[\alpha \left(𝜈\right)h𝜈\right]}^{\frac{1}{r}}=A\left(h𝜈-{{\rm E}}_{opt}\right)$$

(3)

where $\alpha \left(𝜈\right)$ is the absorption coefficient, A is a constant, $h𝜈$ is the incident radiation’s photon energy, and r is an index that varies depending on the transition type (direct or indirect). The best fit to the result obtaining that r = 2 indicated the indirect allowed transition in the gap. The optical band edge is obtained by extrapolating from the linear range in plots of ${\left(\alpha h𝜈\right)}^{\frac{1}{2}}$ versus $h𝜈$, as shown in Figure 3. The optical energy gap E_opt was 4.41 eV higher than phosphate glasses doped with rare earth [11,12,13,14,15,16,17]. This wide optical energy gap range shows that this glass is superior and a good medium as an acceptor of the rare earth donor from the optical fiber (non-linear/laser waveguide).

To determine the spectroscopic parameters of this glass system, the Judd–Ofelt (JO) analysis was applied to the absorption intensities of Nd³⁺ doped in PZLBNdYb. The detailed applications of the JO model can be found in the literature [17,18]. A brief outline of the JO analysis is given hereafter.

The measured line strength $S_{\exp }(J\to J{}^{\prime })$ of a given band is determined by the following expression:

$$S_{\exp }(J\to J{}^{\prime })=\frac{9n}{{(n^2+2)}^2}·4\pi {\epsilon }_0·\frac{3c·h·(2J+1)}{8{\pi }^3{e}^2}.\frac{2.303}{N·l·\lambda }·\Gamma (\lambda )$$

(4)

where c is the velocity of light, h is the Planck’s constant, e is the elementary charge, J is the angular momentum of the initial state, N is the density of Nd³⁺ ions, λ is the mean wavelength of the absorption bands, l is the thickness of the studied sample (l = 7.82 mm), and n is the refractive index dispersion. $\Gamma ={\displaystyle \int OD(\lambda )·d\lambda }$ is the total area under the absorbed band and can be used to calculate the experimental integrated optical density in the wavelength range.

The magnetic-dipole contribution has been ignored in this work as its impact on the measured line strength is relatively negligible for absorption transitions of Nd³⁺ ion [15,19,20].

The results of the intensity measurements and line strength calculations for transitions of Nd³⁺ ions are reported in

Table 1. The results of the intensity measurements and line strength calculations for absorption transitions of Nd³⁺ doped in PZLBNdYb glass, δ_rms = 1.019 × 10⁻²⁵ m².

Transitions: 4I9/2→	λ (nm)	ν (cm−1)	||U2||2	||U4||2	||U6||2	Γ (nm·cm−1)	Sexp (10−26 m2)	Scal (10−26 m2)
4D3/2 + 4D5/2 + 2I11/2 + 4D1/2	352	28,409	0.0050	0.5256	0.0478	7.8511	24.489	22.244
2P1/2 + 2D5/2	430	23,255	0.0000	0.0369	0.0021	0.5117	1.2993	1.4960
2K15/2 + 2G9/2 + 2D3/2 + 4G11/2	470	21,276	0.0010	0.0472	0.0364	3.1505	7.3169	3.4488
2K13/2 + 4G7/2 +4G9/2	524	19,083	0.0665	0.2182	0.1271	16.22	34.053	15.772
4G5/2 + 2G7/2 + 2H11/2	580	17,241	0.9737	0.5968	0.0777	27.298	51.294	52.438
4F9/2	682	14,662	0.0009	0.0092	0.0417	2.6065	4.1785	2.2393
4F7/2 + 4S3/2	744	13,440	0.0010	0.045	0.6598	25.624	37.600	31.252
4F5/2 + 2H9/2	802	12,468	0.0102	0.2451	0.5127	14.853	20.269	32.523
4F3/2	882	11,467	0.0000	0.2293	0.0548	2.0965	2.6098	11.164

.

On the other hand, in the Judd–Ofelt theory, the line strength $S_{cal}(J\to J{}^{\prime })$ between initial state J characterized by (S, L, J) and the final state J’ given by (S′, L′, J′) can be calculated by the following expression [17,18]:

$$S_{cal}(J\to J{}^{\prime })={\displaystyle \sum _{t=2, 4, 6}{\mathsf{\Omega }}_t}{\left|\langle SLJ\Vert U^{(t)}\Vert S{}^{\prime }L{}^{\prime }J{}^{\prime }\rangle \right|}^2$$

(5)

where Ω_t (t = 2, 4, 6) denote the Judd–Ofelt variables and ||U^(t)||² (t = 2, 4, 6) are the doubly reduced matrix elements.

The reduced matrix elements could be found in the literature [13,21,22,23]. For two or more manifolds, the reduced matrix elements are taken as the sum of the corresponding matrix elements. The values of matrix elements for each absorption band are given in Table 1.

Based on Equations (4) and (5), a fitting between experimental and calculated line strengths of the absorption transitions provides the values of the three JO parameters. A least squares fitting of $S_{\exp }$ to $S_{cal}$ values was used to compute the Ω_t (t = 2, 4, 6) parameters for the studied PZLBNdYb sample.

According to matrix element and S_exp values, one can notice that, principally, the Ω₂ parameter depends on ⁴I_9/2→⁴G_5/2 + ²G_7/2 + ²H_11/2 (580 nm) and ⁴I_9/2→⁴D_3/2 + ⁴D_5/2 + ²I_11/2 + ⁴D_1/2 (352 nm) peak intensities, Ω₄ also depends on this later peak, while Ω₆ depends on the ⁴I_9/2→⁴F_7/2 + ⁴S_3/2 (744 nm) absorbance. Thus, one can consider that the ⁴I_9/2→⁴D_3/2 + ⁴D_5/2 + ²I_11/2 + ⁴D_1/2 (352 nm) transition is the most influencing line in the Ω_t computation for Nd³⁺ doped glasses.

The obtained JO parameters of Nd³⁺ in PZLBNdYb glass are given in

Table 2. Comparison of Judd–Ofelt parameters (Ω_t, ×10⁻²⁰ cm²) of PZLBPr glass along with other systems.

Systems	Ω2	Ω4	Ω6	Trend	χ
PZLBNdYb [Present Work]:	0.269	0.379	0.447	Ω2 < Ω4 < Ω6	0.84
LGBaBNd05 [12]	6.10	6.85	9.83	Ω2 < Ω4 < Ω6	0.69
YAG:Nd3+ [24]	0.20	2.70	5.00	Ω2 < Ω4 < Ω6	0.54
LHG-750 [25]	4.60	4.80	5.60	Ω2 < Ω4 < Ω6	0.85
PKFBAN10 [26]	4.92	3.67	5.26	Ω4 < Ω2 < Ω6	0.70
ZnBBi [27]	3.56	4.30	4.87	Ω2 < Ω4 < Ω6	0.88
Nd3+:fluorotellurite(n = cst) [11]	4.21	5.97	5.45	Ω2 < Ω6 < Ω4	1.09
Nd3+:fluorotellurite(n ≠ cst) [11]	4.51	6.34	6.16	Ω2 < Ω6 < Ω4	1.02
Nd3+ doped Y2O3 ceramic [22]	8.84	9.82	4.44	Ω6 < Ω2 < Ω4	2.21
75NaPO3-24CaF2-1NdF3 [28]	2.78	4.16	5.56	Ω2 < Ω4 < Ω6	0.74
3000 ppm Nd3+/Yb3+ in phosphate [13]	1.897	0.820	1.834	Ω4 < Ω6 < Ω2	0.44
30,000 ppm Nd3+/Yb3+ in phosphate [13]	0.2339	0.6437	0.9598	Ω2 < Ω4 < Ω6	0.67
NCB:Nd glasses [14]	1.50	0.93	2.39	Ω4 < Ω2 < Ω6	0.39
PMZ1.5 Nd [15]	4.69	4.72	2.98	Ω6 < Ω2 < Ω4	1.58
AEBTNd0.1 [16]	3.694	2.865	2.548	Ω2 < Ω4 < Ω6	1.12
P2O5-Li2O3-GdF3-Nd2O3 [29]	8.55	11.54	10.25	Ω2 < Ω6 < Ω4	1.13
Nd3+ doped zinc phosphate [30]	4.67	5.53	5.77	Ω2 < Ω4 < Ω6	0.95

with those for Nd³⁺ doped in other hosts. For Yb³⁺, it is not possible to determine the three Ω_t intensity parameters because only one transition (corresponding to the ²F_7/2→²F_5/2 transition at 980 nm) can be observed.

The calculated Judd–Ofelt parameters are in good agreement with literature values for Nd³⁺ doped glasses. The JO intensity parameters for this PZLBNdYb glass followed the trend Ω₆ > Ω₄ > Ω₂. This trend is similar to that of commercial laser glasses [25], YAG:Nd³⁺ [24], as well as LGBaBNd [12], 30,000 ppm Nd³⁺/Yb³⁺ phosphate [13], AEBTNd0.1 [16], ZnBBi [27], 75NaPO₃-24CaF₂-1NdF₃ [28] glasses (see Table 2).

The intensity parameter, Ω₂, strongly correlated with the local structure of the rare earth ions and the covalency degree lanthanide–O bonds, which is equivalent to the dynamic polarization of the ligands. In comparison, the Ω₄ and Ω₆ parameters depend upon the rigidity and viscosity of the host glasses [16,31,32]. Similar to the other reported work (mentioned in Table 2), the larger Ω₆ in the present glass indicates its high rigidity, and the lower Ω₂ indicates the higher asymmetry and lower covalency between the Nd-O group in this PZLBNdYb glass.

The obtained Ωt values are used to recalculate the transition line strengths Scal of the absorption bands from Equation (5) and deduce the rms deviation. The root-mean-square (rms) deviation of the fit between experimental and calculated oscillator strengths is deduced by the expression. ${\delta }_{rms}={({\displaystyle \sum _{}(S_{\exp }-S_{cal}})}^2/(N_{trans}-3){)}^{1/2}$

The value of the rms deviation calculated in the present work is equal 1.019 × 10⁻²⁵ m². This slightly elevated value of rms deviation can be explained by overlaps of absorption bands in the UV region.

The spectroscopic quality factor, χ = Ω₄/Ω₆, is an important characteristic in predicting the stimulated emission cross section for the laser active media. In the case of Nd³⁺, it is indicated that the smaller the ratio, the more intense the laser ⁴F_3/2→⁴I_11/2 transition. Due to the decreased matrix element’s zero value, this occurs $\langle {}^{4}F_{\mathrm{3/2}}{\Vert U^{(t)}\Vert }^2{}^{4}I_J\rangle$ of Nd³⁺ ion [33,34,35].

For this PZLBNdYb glass, the spectroscopic quality factor (Ω₄/Ω₆) was 0.84, which is about three-times larger than that of the standard laser host Nd³⁺:YAG. Usually, χ is in the range from 0.22 to 1.5 for Nd³⁺ in several host materials (see Table 2).

According to the absorption spectrum of Figure 2, the emission band ⁴F_3/2→⁴I_9/2 of Nd³⁺ partially overlapped with the absorption band ²F_5/2→²F_7/2 of Yb³⁺, which ensures that the Yb³⁺ ion absorbs the NIR light very effectively. The wideness and lowness of the Yb³⁺ absorption peak ascribe to the Nd³⁺→Yb³⁺ energy transfer. However, the short separation distance between ions, estimated as d = (3/4πN)^1/3 = 7Å, confirms an efficient Nd³⁺→Yb³⁺ energy transfer.

It is worth noting that systems based on Nd³⁺/Yb³⁺ energy transfers are interesting because they combine the Yb³⁺ ion’s good laser emission characteristics with the Nd³⁺ ion’s multiple intense absorption bands, which could be used for pumping with a variety of sources (laser diodes, flash lamps, solar radiation, etc.).

The ⁴F_3/2 level for Nd³⁺ ions is the only exciting J manifold that did not relax predominantly by a multiphonon process. This level fluoresces in the four bands ascribed to ⁴F_3/2→⁴I_9/2 at 882 nm, ⁴F_3/2→⁴I_11/2 around 1056 nm, ⁴F_3/2→⁴I_13/2 at 1318 nm and ⁴F_3/2→⁴I_15/2 at 1870 nm. The emission line strengths attributed to the transition from ⁴F_3/2 to ⁴I_J manifolds were computed through Equation (5) using the Ω₂, Ω₄ and Ω₆ parameters. The Nd³⁺→Yb³⁺ energy transfer competes with the self-quenching of Nd³⁺ emission due to the cross-relaxation of the resonant process (⁴F_3/2 + ⁴I_9/2→⁴I_15/2 +⁴I_15/2) or phonon-assisted process (⁴F_3/2 + ⁴I_9/2→⁴I_15/2 +⁴I_13/2) between the Nd³⁺ ions.

The spontaneous emission probability A_JJ′ for a transition from a J-multiplet to a lower J′-multiples is calculated as:

$$A_{J\to J{}^{\prime }}=\frac{1}{4\pi {\epsilon }_0}\frac{64{\pi }^4 e^2 {\upsilon }^3 n{(n^2+2)}^2}{27h(2J+1)}{S}_{cal}$$

(6)

$S_{cal}$ is the corresponding emission line strength.

The radiative lifetime τ for electric dipole transitions between an excited state (J) and the lower-lying terminal manifolds (J′) could also be estimated as follows:

$$\tau =\frac{1}{{\displaystyle \sum _{J{}^{\prime }}{A}_{J\to J{}^{\prime }}}}$$

(7)

The sum is taken over all final states J′. The fluorescence branching ratio is a critical parameter to the laser designer; it might be calculated by predicting the relative strength of lines from certain excited states and describing the possibility of achieving stimulated emission from a specific transition. It is determined by:

$$\beta =A_{J\to J{}^{\prime }}.\tau$$

(8)

Table 3. Spectroscopic parameters of the PZLBNdYb glass system.

Transition	Energy (cm−1)	A (s−1)	Τ (ms)	Β (%)
4F3/2→4I9/2	882	253.24	1.644	41.639
4F3/2→4I11/2	1051	294.29		48.389
4F3/2→4I13/2	1329	57.675		9.4834
4F3/2→4I15/2	1827	2.9709		0.4884
4I15/2→4I9/2	1626	1.6995	118.78	20.187
4I15/2→4I11/2	2478	4.5382		53.905
4I15/2→4I13/2	4878	2.1812		25.909
4I13/2→4I9/2	2440	5.935	126.42	75.028
4I13/2→4I11/2	5040	1.9754		24.972
4I11/2→4I9/2	4730	2.5817	387.34	100

shows the radiative transition probabilities ($A_{J\to J{}^{\prime }}$), radiative lifetimes (τ) and branching ratios (β) of energy levels ⁴I_9/2,⁴I_11/2, ⁴I_13/2, ⁴I_15/2 and ⁴F_3/2 of Nd³⁺ ion in the PZLBNdYb glass.

A critical factor in the success of the Nd³⁺ amplifier is the long lifetime of the ⁴F_3/2 metastable state that permits the required high population inversion to be obtained. The radiative lifetime of the ⁴F_3/2 state was calculated to be 1.644 ms, which is an essential metric to consider when considering the pumping need for the laser action threshold. The trend of lifetimes appears to be decreasing as ⁴I_11/2 > ⁴I_13/2 > ⁴I_15/2 > ⁴F_3/2. The branching ratios for emission transitions are steadily decreasing as follows: ⁴I_13/2→⁴I_9/2 > ⁴I_15/2→⁴I_11/2 > ⁴F_3/2→⁴I_11/2 > ⁴F_3/2→⁴I_9/2 > ⁴F_3/2→⁴I_13/2 > ⁴F_3/2→⁴I_15/2. A similar tendency of branching ratios was noticed by Zamen et al. [12] and James et al. [14].

In order to understand the probability of lasing action between ⁴F_3/2→⁴I_11/2 and ⁴F_3/2→⁴I_9/2 of Nd³⁺ ion, the essential parameters, such as the peak wavelength (λ), transition probability (A) and branching ratio (β) for the ⁴F_3/2→⁴I_11/2 and ⁴F_3/2→⁴I_9/2 transitions of different Nd³⁺-doped glasses are collected in Table 4.

The branching ratios of ⁴F_3/2→⁴I_9/2 and ⁴F_3/2→⁴I_11/2 transition in the PZLBNdYb glass was ~41% and 48%, respectively, which is comparable to BSKNLNd10 and PNbKA [36,37], PZLNNd1.0 [38], phosphate [14] and Nd³⁺-doped P₂O₅-Li₂O₃-GdF₃ [29] glasses (see Table 4).

Table 4. Peak position (λ, nm), radiative transition probabilities (A, s⁻¹), calculated branching ratios (β) and radiative lifetime (τ, ms) for ⁴F_3/2→⁴I_9/2 and ⁴F_3/2→⁴I_11/2 transitions of Nd³⁺-doped phosphate glasses.

Host	Transition	Wavelength (nm)	A (s−1)	Τ (ms)	Β (%)
PZLBNdYb [PW]	4F3/2→4I9/2	882	253.24	1.644	41
	4F3/2→4I11/2	1051	294.29		48
P2O5-Li2O3-GdF3-Nd2O3 [29]	4F3/2→4I9/2	874	2917	0.151	44
	4F3/2→4I11/2	1065	3091		47
PZLNNd1.0 [38]	4F3/2→4I9/2	873	398		41
	4F3/2→4I11/2	1052	342		53
3000 ppm Nd3+/Yb3+ in phosphate glasses [14]	4F3/2→4I9/2	896	403.8	0.77	31
	4F3/2→4I11/2	1056	716.2		55
30,000 ppm Nd3+/Yb3+ in phosphate glasses [13]	4F3/2→4I9/2	896	280.2	0.13	36
	4F3/2→4I11/2	1056	395.1		51

Table 4. Peak position (λ, nm), radiative transition probabilities (A, s⁻¹), calculated branching ratios (β) and radiative lifetime (τ, ms) for ⁴F_3/2→⁴I_9/2 and ⁴F_3/2→⁴I_11/2 transitions of Nd³⁺-doped phosphate glasses.

Host	Transition	Wavelength (nm)	A (s−1)	Τ (ms)	Β (%)
PZLBNdYb [PW]	4F3/2→4I9/2	882	253.24	1.644	41
	4F3/2→4I11/2	1051	294.29		48
P2O5-Li2O3-GdF3-Nd2O3 [29]	4F3/2→4I9/2	874	2917	0.151	44
	4F3/2→4I11/2	1065	3091		47
PZLNNd1.0 [38]	4F3/2→4I9/2	873	398		41
	4F3/2→4I11/2	1052	342		53
3000 ppm Nd3+/Yb3+ in phosphate glasses [14]	4F3/2→4I9/2	896	403.8	0.77	31
	4F3/2→4I11/2	1056	716.2		55
30,000 ppm Nd3+/Yb3+ in phosphate glasses [13]	4F3/2→4I9/2	896	280.2	0.13	36
	4F3/2→4I11/2	1056	395.1		51

The proposed glasses have suitable spectroscopic quality factors, radiative lifetime and branching ratio values for lasing materials in the infrared region. In both glasses and crystals, efficient energy transfer between Nd³⁺ and Yb³⁺ ions has been established. The Nd³⁺ energy diagram, presented in Figure 4, shows the grouping of levels. The gap between gathering levels guarantees a large radiative probability of transition among both groups. By contrast, the small energy gap between the levels inside each group favors the multiphonon relaxation process.

According to Figure 4, the energy of the ⁴F_3/2 emitting level of Nd³⁺ is located slightly higher than the ²F_5/2 emitting level of Yb³⁺; thus, an Nd³⁺→Yb³⁺ energy transfer could take place via a phonon-assisted process (⁴F_3/2, ²F_7/2→⁴I_9/2, ²F_5/2 exothermic nonresonant transfer) and (⁴F_3/2, ²F_7/2→⁴I_11/2, ²F_5/2 endothermic nonresonant transfer). Furthermore, it was suggested that only a negligible resonant Yb³⁺→Nd³⁺ back transfer occurred. However, the phonon-assisted energy transfer from Nd³⁺ to Yb³⁺ as the way of quantum cutting is noticed. The energy of the ²P_1/2(Nd³⁺) level (~23,250 cm⁻¹) was approximately twice the energy of the Yb³⁺ transition (~10,290 cm⁻¹) and the phonon-assisted energy transfer can be described as follows: Nd³⁺ emission: ²P_1/2(Nd³⁺)→⁴I_9/2(Nd³⁺); Yb³⁺ absorption: 2 ²F_7/2 (Yb³⁺)→2 ²F_5/2(Yb³⁺).

Normally, the ²F_7/2 and ²F_5/2 Stark levels of Yb³⁺ ions split into several sublevels due to the crystal field effect [36]. Here, the absorption spectrum was fitted by Lorentz fitting, shown in Figure 5.

From Figure 5, the spectrum fits two absorption bands attributed to transitions between the ground state of ²F_7/2 and two Stark-splitting levels of ²F_5/2. In principle, I₉₇₄/I₉₂₈ 3; however, in our case, this ratio is reduced to ~1.5, which is related to the Nd³⁺→Yb³⁺ energy transfer.

The absorption and emission cross sections must be calculated to determine the lasing performance. The absorption cross section of a transition may be calculated as:

$${\sigma }_{abs}\left(\lambda \right)=\frac{2.303}{Nl}\times D\left(\lambda \right)$$

(9)

where D(λ) is the optical density, l is the thickness of the sample, and N is the ion concentration in the sample. Furthermore, the emission cross section, ${\sigma }_{em}\left(\lambda \right),$ of Nd³⁺: ⁴F_3/2→⁴I_9/2 and Yb³⁺:²F_5/2→²F_7/2 can be calculated from the absorption cross section by:

$${\sigma }_{em}\left(\lambda \right)={\sigma }_{abs}\left(\lambda \right)·\frac{Z_l}{Z_u}·exp\left[hc·{\left(kT\right)}^{-1}·[{\left({\lambda }_{ZL}\right)}^{-1}-{\left(\lambda \right)}^{-1}\right]]$$

(10)

where the lower and upper levels of the optical transition are Z_l and Z_u. T is the temperature, k is the Boltzmann constant, and Z_ZL is the wavelength at which the lower Stark sublevels of emitting multiplets and receiving multiplets intersect at this transition (zero-phonon line). However, at high temperatures, the partition function ratios of the lower and higher states Z_l/Z_u simply degenerate into a weighting of the two states. The precise Z_l/Z_u glass value is not known. The zero-phonon line was considered to be 882 nm for Nd³⁺ and 972 nm for Yb³⁺ in the following calculation, which assumes a Z_l/Z_u ratio of 10/4 for Nd³⁺ and 8/6 for Yb³⁺.

Figure 6 shows the Absorption and emission cross section of prepared glass PZLBNdYb. The computed σ_{Yb abs} at (λ_p = 980 nm) of Yb³⁺:²F_5/2→²F_7/2 was 2.01 × 10⁻²⁴ cm², and that of Nd³⁺ for ⁴I_9/2→⁴F_3/2 at σ_{Nd abs}(λ_p = 882 nm) was 1.71 × 10⁻²⁴ cm². The σ_{Yb abs} was larger than that of Nd³⁺ σ_{Nd abs} in the NIR region, confirming that the Nd³⁺→Yb³⁺ dominates the Nd³⁺→Nd³⁺ energy transfer. Since the absorption cross section of Yb³⁺ is larger than that of Nd³⁺ at equal densities, it can be considered that Yb³⁺ acts as an acceptor, while Nd³⁺ is the donor in this NIR region. The values of ${\sigma }_{em}\left(\lambda \right)$ of Nd³⁺: ⁴F_3/2→⁴I_9/2 and Yb³⁺:²F_5/2→²F_7/2 are equal to 2.23 × 10⁻²⁴ cm² and 2.88 × 10⁻²⁴ cm², respectively. The larger cross sections of the emission transitions indicate that the intense NIR emitting can be conditioned.

Figure 7a,b shows the measured MAC and LAC at 59.5, 622, 1170 and 1330 keV. The recorded values of MAC and LAC for the proposed sample at 662 keV were 0.081 ± 0.03 and 0.225 ± 0.13 in cm²/g, respectively. These values were better than commercially available glass shielding materials, such as RS253 and G18 [39]. The measured half-value layer, HVL; and mean free path, MFP; at the same specific energies 59.5, 622, 1170 and 1330 keV were obtained; Figure 7c,d. The values for HVL and MFP of the present glass at 662 keV were 2.20 ± 0.82 and 3.17 ± 1.18 cm, respectively.

The HVL signifies the material thickness that reduces the intensity of radiation to half. HVLs are reported for commercial materials, such as windows glass (4.73 cm), serpentine (4.07 cm), concrete (3.87 cm), SCHOOT glass RS253 (3.65 cm), hematite serpentine (3.6 cm), Ilmenite (2.63 cm) and SCHOOT glass RS323 (2.48 cm) [40,41]. Thus, our glass had a lower HVL, which is better than commercial material. It was correlated with codoped heavy compounds of Nd³⁺/Yb³⁺ ions in its structure of the host glass 40P₂O₅-30ZnO-20LiCl-10BaF₂ to increase interaction probability, and more electrons are effectively available at low energy levels.

4. Conclusions

The incorporated double ions of Nd³⁺/Yb³⁺ into 40P₂O₅-30ZnO-20LiCl-10BaF₂ glass increase the optical energy gap (4.41eV), which is a suitable active medium for laser glasses. We found that the JO intensity parameters of the produced glass follow the trend Ω₆ > Ω₄ > Ω₂, which has a high spectroscopic quality factor (Ω₄/Ω₆) equal to 0.84. This is larger than standard laser host Nd³⁺:YAG.

The fabricated glass had a large value of ${\sigma }_{em}\left(\lambda \right),$ 2.23 × 10⁻²⁴ cm², with the corresponding transition level Nd³⁺: ⁴F_3/2→⁴I_9/2 and was 2.88 × 10⁻²⁴ cm², attributable to Yb³⁺:²F_5/2→²F_7/2. Moreover, the gamma spectroscopic properties of the present glass showed a low half-value layer, which increases the interaction probability and creates more effective electrons at low energy. We conclude that the investigated glass has unique luminescence/gamma spectroscopic properties; hence, it can be used in photodynamic therapy surgery as a laser material in radiology rooms.