Analysis of Optical and Near-Infrared Luminescence of Er3+ and Er3+/Yb3+ Co-Doped Heavy Metal Borate Glasses for Optical Amplifier Applications

Abstract

For the near-infrared emission, Er³⁺ and Er³⁺/Yb³⁺ co-activated borate based glass hosts were synthesized by the method of melting andquenching. The emission intensity was maximum for 0.5 mol% Er³⁺ singly activated glass in the near-infrared (NIR) region covering the telecommunication window. The 2 mol% of Yb³⁺ co-doping enhanced the emission gain cross-section of the glass by two times contrast to 0.5 mol% Er³⁺ loaded glass. This enhancement shifted to lower spectral regions when P increased from 0 to 1. The effect of Yb³⁺ loading on the gain cross-section of the Er³⁺ co-activated glasses was analyzed using the McCumber theory. The results showed that the 0.5Er2Yb glass has a flat gain in the range of 1460–1640 nm, this suggest a lower pump threshold is enough to perform the laser functioning of a 1530 nm band and optical window of telecommunication applications.

1. Introduction

In the recent past, investigations on ionized rare earth (RE) ions incorporating glassy materials have received significant research interest, owing to their down-conversion and up-conversion (UC) features in infrared and infrared to visible spectral regions, which make them greatly utilized in optical amplifier, high-density optical storage, infrared converters, fiber optic communication and 3D display devices [1]. For decades, the preparation, characterization and property evaluation of REs, such as Nd³⁺ and Er³⁺ doped phosphate, borate and silicate glasses have been continued for optical gain medium application of solid-state and fiber near infra-red (NIR) lasers at 1064 and 1530 nm wavelengths [2]. These NIR lasers have been used as NIR light sources for medical as well as sensor equipment, such as LIDAR [3,4].

In particular, the trivalent erbium (Er³⁺) doped vitreous systems have received tremendous interest because of the photoluminescence (PL) emission at 1530 nm with the considerable emission cross-section and relatively long metastable time. Therefore, these Er³⁺ activated glasses are found to be best suitable in wavelength division multiplexing (WDM) systems, microchip lasers, fiber amplifiers (EDFAs), lidar transmitters, eye-safe laser systems and waveguides [5]. In addition, the tri-valent erbium ions display luminescence in red, green and blue in the visible regions of the electromagnetic spectrum. The NIR emission intensity and related parameters of the luminescence transitions of Er³⁺ can be improved through the enhancement of corresponding transition probability, which is dependent on the surrounding ligand field of RE ions [6] for the effective utilization in the aforementioned applications. Further, because of the rapid growth in information technology, flexible networks are very much needed. To this end, the Er³⁺ doped glasses are of significant interest since the glasses can be molded into any flexible shape and size along with enhanced PL properties [6]. Furthermore, to be specific, the borate-based vitreous materials or glasses are important, owing to their wide range transparency, less processing temperatures, great thermal withstanding and excellent solubility of RE ions (reported up to 20 mol% of solubility in aluminoborate glasses [7]) compared to silicate and phosphate glasses [6]. Nonetheless, the NIR emission efficiency is highly impacted by the glass host, i.e., the energy of the phonons present in the glasses [5]. The addition of heavy metal oxides, such as PbO, Sb₂O₃, Bi₂O₃, GeO₂, etc., resulted in the decrease of energy of the phonons of the glass network, thereby causing a reduction in the non-radiative relaxation rates, which this change leads to the NIR emission mechanism with ease [8]. In general, a high absorption cross-section of the absorption peaks leads to higher luminescence from the RE ion.

The weak absorption of Er³⁺ ions in near-infrared region hinders practical use in the large bandwidth NIR device fabrications. The tri-valent ytterbium ions (Yb³⁺) possess strong absorption in NIR region compared to the Er³⁺ ion. Hence, it is predicted as a sensitizer that highly improves the efficiency of the down-conversion process of Er³⁺ ions by energy transfer [9]. In the open literature, there are many investigations revealing the energy transfer mechanisms of Er³⁺ co-doped Yb³⁺ diverse glasses, for example [5,6,10,11,12]. Precisely, therefore, there are many attempts at improving the NIR emission of around 1500 nm by co-doping with Yb³⁺ ions in different glass hosts [8,9,11,13]. In view of this, heavy metal borate glass can play a significant role due to its chemical, thermal and structural versatility [14]. These glasses can be prepared at a low melting temperature and it offers a high refractive index, which minimizes phonon energy and the dispersion of light in the NIR region and offer excellent moisture resistance [15]. However, there are very few reports available on improving the NIR emission efficiency of Er³⁺ ions by co-doping of Yb³⁺ ions in borate-based glasses, particularly heavy metal borate glasses.

2. Experimental and Characterization

The glass batches prepared by melt-quenching method for the present work are mentioned below:

Batch 1: 15ZnO − 10Bi₂O₃ − (75 − x)B₂O₃ − xEr₂O₃ (where x = 0.1, 0.5, 1 and 2 mol%)

Batch 2: 15ZnO − 10Bi₂O₃ − (75 − x − y)B₂O₃ − xEr₂O₃ − yYb₂O₃ (where y = 0.5, 1, and 2 mol%).

For the preparation of Er₂O₃ (0.1, 0.5, 1 and 2 mol%) and Yb₂O₃ (0.5, 1 and 2 mol%) co-doped into 0.5 mol% Er³⁺ doped glasses, the molar percentage of the analytical grade oxides were weighed according to the glass batch formula mentioned above. Using agate mortar and pestle, samples were well-grounded for 30 min to homogenize the oxide mixture. Then, after, the glass mixture was transferred into a porcelain crucible and was placed inside the electrically heated muffle furnace. Initially, the furnace was set to 400 °C and then slowly raised to 1000 °C. For 1 h, the glass batch was heat soaked at 1000 °C inside the furnace to obtain bubble-free molten liquid. Then, after 2 h of melting, the liquid glass batch was quenched on pre-annealed brass mold to obtain bulk glass pieces. These glasses were then heat treated at 273 °C for 3 h and slowly cooled to standard temperature.. Later, these bulk glasses were polished to get 2 mm thicknesses and were labeled as 0.1Er, 0.5Er, 1.0Er, and 2.0Er for 0.1, 0.5, 1 and 2 mol% Er₂O₃ singly loaded glasses, and co-activated glasses were labeled as 0.5Er0.5Yb, 0.5Er1.0Yb, 0.5Er2.0Yb for Er³⁺: 0.5 mol % and Yb³⁺: 0, 0.5, 1.0, and 2.0 mol% loaded in borate based glasses, respectively. The well-polished glasses were used for optical measurements, such as absorption, photoluminescence and decay curves. All physical parameters, are presented in Table 1. The powder form of the same glasses was used for structural characterization, such as XRD and FT-IR using an X-ray diffractometer with a 2θ range 5° to 80° and FT-IR spectra were measured from 4000 to 400 cm⁻¹. The absorption, photoluminescence and decay curves were collected utilizing a Perkin Elmer make Lambda-750 S spectrophotometer.

3. Results and Discussion

The XRD profiles of Er³⁺ singly loaded glasses are shown in Figure 1. The XRD profiles of the glasses showed broad humps without any sharp crystallographic peaks. The absence of such crystallographic peaks insisted that the prepared glass samples possess an amorphous network in them [16].

The features of the FT-IR absorption spectra of the Er₂O₃ doped 15ZnO, 10Bi₂O₃, (75 − x)B₂O₃, and xEr₂O₃ were recorded with the resolution of 4 cm⁻¹. The powdered form of the samples was palletized using KBr as a binder and, then, it was used to measure the absorption mode of the FT-IR spectra in the infrared region, from 400 to 4000 cm⁻¹. Figure 2 consists of absorption broad bands of the vitreous network of Er³⁺ doped glasses. The demonstrated band in the spectra, around 441 to 579 cm⁻¹, was attributable to the formation of the octahedral BiO₆ group in the vitreous network [17,18]. Additionally, the formation of the BO₃ groups in the borate structure absorbed the energy for its in-plane bending vibrations at the same wavenumber, 441 to 579 cm⁻¹ [19]. The broad FT-IR band ranging from 638 to 746 cm⁻¹ is manifested to bending motion of B–O bonds exist in the BO₃ units [19]. The FT-IR signature between 787–1046 cm⁻¹, is caused because of the motion of B–O bonds’ in the BO₄ motifs [20]. The partial portion of the fourth FT-IR band, from 1144 to 1286 cm⁻¹, has owed to the B–O bond’s stretch in the (BO₃)³⁻ functional groups [20]. The other half of the band is in the range of 1301 to 1478 cm⁻¹ because of the stretch of B–O bonds of (BO₃)³⁻ groups, which are an integral part of the synthesized vitreous glass network [20]. The structure of bismuth zinc borate glasses has not been modified due to the addition of Er³⁺ concentration.

Linear absorption spectral results of Er³⁺ singly activated glasses depicted in Figure 3 for UV-visible region (upper figure) and NIR region (below figure). The Er³⁺ ions showed their electronic transitions from their lower energy level (⁴I_15/2) to the different higher energy levels. All the peaks observed for the singly Er³⁺ doped glass samples used in the current study are assigned by referring to the reference [21]. From the spectra, it can be seen that, the intensity of the bands is enhanced monotonously with respect to Er³⁺ content in the composition. Among all transitions, the ⁴I_15/2 → ²H_11/2 possess highest intensity and is hypersensitive transition [HST], whose intensity sensitive to the surrounding structure [22]. Figure 4 displays the optical absorption spectra of 0.5Er (single) and co-doped (Er/Yb) in UV-vis–NIR (350–1700 nm) regions. Figure 4 shows the additional intense absorption band at 977 nm and it was ascribed to the Yb³⁺: ²F_7/2 → ²F_5/2 transition in all co-doped glasses [23,24,25]. Absorption at 977 nm (²F_7/2 → ²F_5/2) significantly increased with the increment of Yb³⁺ ions from 0.5 to 2.0 mol% in the Er/Yb multiple RE ions doped glasses. Interestingly, the spectra revealed the broader absorption band around 880 to 1070 nm due to the overlap in the Yb³⁺ ions ²F_7/2 → ²F_5/2 transition with the Er³⁺ ions ⁴I_15/2 → ⁴I_11/2 transition. This specifies the potential of absorption efficiencies in the NIR region than the singly Er³⁺ doped glass under NIR excitation (λ_exc = 980 nm). The presence of co-dopant Yb³⁺ in the glass network increased the NIR, and the demonstrated broad bands are due to light absorption glass around 980 nm.

Further, oscillator strengths, both f_exp and f_ms of the Er³⁺ doped glasses were computed using the relations mentioned in the references [23,24,25] and are tabulated in Table 2. The Judd-Ofelt (JO) factors viz. Ω₂, Ω₄ and Ω₆ were evaluated be referring to the procedure explained in references [26,27]. Both f_exp and f_cal, along with their root mean square deviations (σ_rms) are furnished in Table 2. It is already proved that the JO factors describe local ligand environments around the dopants (Er³⁺ ions), and the strength of covalency between the ligand bonds. Thus, information about the site symmetry of Er³⁺ ions can be determined from Ω₂ and it is sensitive to HST, while Ω₄ and Ω₆ depend on the bulk property and viscosity of a host glass. The JO factors of singly Er-doped borate glasses are calculated and tabulated in Table 3. Among all, 0.5Er glass attain the higher values which suggest the strong covalency nature between Er-O. Further, an increase in doping of Er³⁺ into host glass reduced the strength of Ω₂. This paramount shift is attributed to the decrease in order of symmetry around the Er³⁺ ions in in the studied glasses [22,23,24]. The JO parameters of the present borate glasses are comparable with SANSCEr10 [5], PKSAEr10 [22], fluorotellurite [23], ELB [24], TBA1 [25], TZN [28], BLK1.0Er [29], CaBaPEr20 [30], TBL [31] and lead phosphate [32] of Er³⁺ doped different glass materials.

The NIR luminescence spectra of (0.1Er–2.0Er) doped zinc borate glasses are depicted in Figure 5. All samples emitted the broad NIR emission (1440–1680 nm) and a peak at 1529 nm (1529 nm due to electronic motion from ⁴I_13/2 level to ⁴I_15/2 level of Er³⁺. Thus, the NIR emission covering C and L bands of the telecommunication window thereby it can be utilized for optical amplifier applications.. Interestingly, the intensity of NIR emission enhanced with Er³⁺ doping into the glass, from 0.1 to 0.5 mol%, and beyond that intensity of the same band, was decreased. This type of decrement is caused because of agglomeration of Er³⁺ ions in the examined glass. Hence, Er³⁺ ion concentrations increase, resulting in the reduction of distance among the Er³⁺ ions and it causing the quenching process.

Further, using the JO factors, the lasing potentials, such as emission maxima (λ_p), effective line width (Δλ_eff), stimulated emission cross-section (σ_emi), branching ratio (β_R) and quantum efficiency (η) have been computed for the studied glasses by referring the procedure provided in the reference [23,24]. The resulted calculation shows values for σ_emi and A_T of 0.5Er glass as superior among the 0.1 to 1Er glasses. Their values are 1.52, 1.14, 0.82, 0.80 (×10⁻²¹ cm²) and 281.1, 488.14, 357.76, 304.43 (s⁻¹), respectively, corresponding to the 0.1Er, 0.5Er, 1.0Er, and 2.0Er glasses. The gain bandwidth (σ_emi × Δλ_eff) and optical gain for examined glasses are also evaluated and found to be decreased as the Er³⁺ concentration elevated to higher levels. Table 4 displays the radiative parameters of prepared glasses with other reported glasses [5,22,30,31,32]. The 0.5Er glasses σ_emi value is higher than that of reported different glass materials. Interestingly, the resulting other radiative parameters that use the emission spectra and JO parameters revealed that, the current glasses have substantial for 1530 nm broadband amplifiers and eye-safe efficient NIR lasers.

PL spectra for single (0.5Er) and co-doped samples presented in Figure 6 for an excitation of 980 nm. The spectra consist of the representative band at 1550 nm due to electronic motion from ⁴I_13/2 to ⁴I_15/2 levels of Er³⁺. The amplitude of this peak improved with elevation of Yb³⁺ content in the composition. Interestingly, in the co-doped glasses, Er³⁺ ions emission intensity was enhanced with the effect of Yb³⁺ ions sensitization. This enhancement is due to the strong absorption cross-section of Yb³⁺ contrast to Er³⁺ at the pumped spectral region. The pumping wavelength, energy levels and transitions profile are displayed in the energy level diagram (Figure 7).

Further, the absorption spectrum of 0.5Er glass was utilized to compute the absorption cross-section (σ_abs), whilst the stimulated emission cross-section (^Mσ_emi) was computed by following the McCumber theory (MC). The McCumber hypothesis is always referred to for explaining the overlap between the σ_abs and ^Mσ_emi cross-sections. The factor of ^Mσ_emi influences the operation of a laser and all sets of these properties were realized with the assistance of the equations provided in the references [5,29].

From McCumber’s theory, the σ_abs and σ_abs profiles of 0.5Er and 0.5Er2.0Yb co-doped glasses are shown in Figure 8a,b, respectively.

From Figure 8, σ_abs and σ_emi magnitudes found to be 3.334 × 10⁻²¹ cm² and 3.713 × 10⁻²¹ cm² respectively at ~1530 nm whereas which for 0.5Er2.0Yb glass the magnitudes respectively found to be 5.842 × 10⁻²¹ cm² and 7.283 × 10⁻²¹ cm². The σ_emi value is found to be the maximum (7.283 × 10⁻²¹ cm²) for 0.5Er2.0Yb co-doped glasses and was enhanced ~2 times compared that of 0.5Er glass which is attributed to the resonant transfer of energy from Yb³⁺ to Er³⁺ ions.. These values are comparable with the other reported phosphate (0.5Er/12Yb: σ_abs = 6.15 × 10⁻²¹ cm², σ_emi = 7.11 × 10⁻²¹ cm²) [33], and fluorophosphate glasses (3Er4Yb: σ_abs = 9.53 × 10⁻²¹ cm², σ_emi = 9.86 × 10⁻²¹ cm²) [34].

Optical gain cross-section (G(λ)) has been used to ascertain the laser media performance. The G(λ) for ~1530 nm emission transition of 0.5Er glasses was determined by following equation [29]:

(1)$G\left(\lambda ,N\right)=P {\sigma }_{emi}\left(\lambda \right)-\left(1-P\right){\sigma }_{abs } \left(\lambda \right)$

where factor P is the population rate. Figure 9 exhibits the spectra of the gain cross-section G(λ) of the 0.5Er and 0.5Er2.0Yb glasses. From the spectra, as the values of G(λ) increase, the gain band shifts toward the short wavelength side when N increases from 0 to 1. For ~1530 nm emission transition of Er³⁺:⁴I_13/2–⁴I_15/2, when N reaches 0.4, the G(λ) achieves a magnitude of 10⁻²¹ cm². The maximum G(λ) is found to be 3.713 × 10⁻²¹ cm² for 0.5Er and 7.2836 × 10⁻²¹ cm² for 0.5Er2.0Yb glasses. G(λ) values of 0.5Er2.0Yb glasses increased 2 times compared to 0.5Er glasses and were also related to the phosphate glasses in the range of 7.11 × 10⁻²¹ cm² [33], and are less than fluorophosphate glass (9.86 × 10⁻²¹ cm²) [34]. Hence, according to Figure 9, the synthesized co-doped glasses’ flat gain is in the range of 1460–1640 nm. This optimum performance describes the laser operation of the 1530 nm band at a lesser pump threshold, which is a prerequisite for laser operation [29]. Hence, the obtained result infers that Er³⁺ with Yb³⁺ co-doped bismuth zinc borate glasses are competing hosts as an optical medium for laser operation at 1530 nm [31].

The metastable lifetime of the Er³⁺ ions plays a significant role in the EDFA and solid-state laser gain medium applications. A higher metastable lifetime eases the population inversion condition of the doped glasses. However, the lifetime of the Er³⁺ can be decreased or increased with the change in the composition of glass, doping concentration of Er³⁺ and the transfer of resonant energy from trivalent ytterbium to trivalent erbium ions [35]. Thus, the decay profiles for 0.5Er and 0.5Er/(0.5, 1.0, and 2.0)Yb co-doped ZBB glasses for ⁴I_13/2 → ⁴I_15/2 transition under the excitation at 976 nm provided in Figure 10. The profiles of PL decay were well fitted to single-exponential, and the obtained lifetime values are 3.56 ms, 3.60 ms, 3.99 ms, and 4.03 ms for 0.5Er, 0.5Er0.5Yb, 0.5Er1.0Yb, and 0.5Er/2.0Yb glasses, respectively. The observed behavior analogous to other Er³⁺/Yb³⁺ glass matrices were as such: 65P₂O₅-13K₂CO₃-13BaCO₃-8Al₂O₃-2ZnO [33]; 75NaH₂PO₄-20ZnO-5Li₂CO₃-Er₂O₃ [36]; 44P₂O₅+23PbO+17K₂O+9Al₂O₃+6Na₂O [37]. The closeness between the energy levels of ⁴F_5/2 (Yb³⁺) to ⁵I_11/2 (Er³⁺) ions [36] led to a high population inversion at the ⁵I_11/2 level due to transfer of resonant energy from the Yb³⁺ to Er³⁺ ions when excited at 980 nm.

4. Conclusions

In this study, the absorption spectra of the glass were observed with 12 absorption lines, with an increase of intensity with respect to Er³⁺ doping from 0.1 to 2 mol%. The addition of Yb³⁺ ion into the glass network added an extra absorption transition at 980 nm was observed. The JO factors Ω₂ = 9.15 × 10⁻²⁰, Ω₄ = 4.07 × 10⁻²⁰, and Ω₆ = 3.31 × 10⁻²⁰ cm², were the highest for 0.5 mol% Er³⁺ loaded glass; which infers the bond between Er³⁺ to O²⁻ was covalent.. The NIR emission of the telecommunication window was highest in 0.5 mol% of Er³⁺ doped zinc bismuth borate glass. The obtained radiative transition probability (488.14 s⁻¹), branching ratio (1) stimulated emission cross-section (11.41 × 10⁻²¹ cm²), radiative lifetime (3.2 ms), gain bandwidth (984.86 × 10⁻²⁸ cm³) and an optical gain (39.48 × 10⁻²⁵ cm²−s) of 0.5 mol% Er³⁺ loaded in borate glass suggest potential use for the construction of 1.53 µm optical amplifiers and efficient NIR lasers. Along with emission intensity, 2 mol% of Yb³⁺ co-doping enhanced the emission gain cross-section (7.283 × 10⁻²¹ cm²) of the glass by two times when compared to the 0.5 mol% Er³⁺ singly doped glass network. This increase in gain cross-section shifted the gain band for lower spectral side when P increased from 0 to 1 and for the Er³⁺: ⁴I_13/2–⁴I_15/2 emission, and when P reached 0.4, the gain cross-section achieved a magnitude of 7.283 × 10⁻²¹ cm² in the 2 mol% of Yb³⁺ co-activated glass. The 0.5Er2Yb glass has a flat gain in the range of 1460–1640 nm and its behavior proved that the lower pump threshold is sufficient for laser operation within the 1530 nm band and optical window of telecommunication.

Author Contributions

V.H.: Conceptualization, Methodology, Data curation, Investigation, Writing—original draft; G.D.: Data curation, Writing—original draft; A.G.P.: Data curation, Formal analysis; S.B.K.: Data curation, Formal analysis; D.A.A.: Data curation, Writing—review & editing; A.H.A.: Data curation, Writing—review & editing; M.I.S.: Writing—review & editing; G.J.: Conceptualization, Methodology, Data curation, Writing—review & editing. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All the data have been reported in the manuscript.

Acknowledgments

The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project (PNURSP2022R57), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. XRD of Er2O3 doped ZBB glasses.

Figure 2. FT-IR spectral results of studied Er2O3 doped ZBB glasses.

Figure 3. Optical absorption spectra of UV-vis (350–700 nm) (upper) and NIR (700–1700 nm) (lower) of Er3+ singly activated ZBB glasses.

Figure 4. Linear absorption spectral outcomes of Er3+/Yb3+ ions co-doped ZBB glasses from UV-vis to NIR (350–1700 nm) region.

Figure 5. Near-infrared emission spectra of Er3+ doped ZBB glasses.

Figure 6. Near-infrared emission 0.5 mol% Er3+ ions and Yb3+ ions co-doped ZBB glasses.

Figure 7. Energy level scheme of Er3+ and Yb3+ ions in ZBB glasses.

Figure 8. Absorption and emission cross-section of 0.5Er doped (a) and 0.5Er2.0Yb co-doped (b) ZBB glasses.

Figure 8. Absorption and emission cross-section of 0.5Er doped (a) and 0.5Er2.0Yb co-doped (b) ZBB glasses.

Figure 9. Gain cross-section profile of 4I13/2 → 4I15/2 transition in the range of 1400–1650 nm of 0.5Er (upper) and 0.5Er2.0Yb (lower) glasses used in the current study.

Figure 10. Decay profiles of 4I13/2 → 4I15/2 transition of 0.5Er and Er3+/Yb3+co-doped ZBB glasses.

Table 1

The physical parameters of Er³⁺ singly loaded studied glasses.

Physical Parameters	0.1Er	0.5Er	1.0Er	2.0Er
Density (g/cm3)	3.31	3.45	3.59	3.70
Thickness (cm)	0.152	0.154	0.153	0.151
Refractive index (n)	1.621	1.625	1.628	1.632
Concentration N (Ions/c.c ×1020)	0.156	0.903	1.963	3.938

Table 2

Experimental (f_exp) and calculated (f_cal) oscillator strengths (10⁻⁶) of Er³⁺ loadedin ZBB glasses.

Transition	Energy (cm−1)	0.1Er		0.5Er		1Er		2Er
		fexp	fcal	fexp	fcal	fexp	fcal	fexp	fcal
4I13/2	6527	5.41	4.67	2.33	2.67	3.22	3.52	2.93	1.05
4I11/2	10,256	2.46	2.72	1.56	1.23	1.17	1.61	1.33	7.17
4I9/2	12,516	-	-	2.66	2.70	1.07	0.92	1.30	1.72
4F9/2	15,361	5.65	5.89	2.91	1.11	5.39	5.71	3.53	0.84
4S3/2	18,416	2.25	3.67	-	-	2.65	1.35	1.83	1.45
2H11/2	19,231	13.47	14.20	8.33	7.36	16.67	16.37	4.47	4.37
4F7/2	20,492	7.72	8.13	4.74	3.78	7.03	5.49	3.45	4.06
4F5/2	22,173	2.73	4.04	1.86	1.35	2.05	1.64	1.36	1.19
4F3/2	22,573	-	-	1.28	0.78	2.11	0.95	1.13	3.73
2G9/2	24,631	1.58	2.49	2.15	1.56	3.08	2.03	2.97	0.47
4G11/2	26,525	3.16	2.85	12.02	13.05	28.77	29.02	6.73	1.23
2G7/2	28,090	-	-	-	-	3.34	1.28	2.08	2.90
σ(N)a		±0.26 × 10−6		±0.85 × 10−6		±0.45 × 10−6		±0.69 × 10−6

σ(N)^a shows r.m.s deviation among the f_exp to f_cal values and ‘N’ tells the number of transitions used in the fitting procedure.

Table 3

The comparison of Judd-Ofelt parameters Ω_λ (λ = 2, 4 and 6 × 10⁻²⁰ cm²) of Er³⁺ ions in different glass networks.

Glass Composition	Ω2	Ω4	Ω6
0.1Er (Present work)	7.28	2.76	5.09
0.5Er (Present work)	9.15	4.07	3.31
1.0Er (Present work)	4.49	2.94	2.73
2.0Er (Present work)	1.42	1.99	2.91
SANSCEr10 [5]	7.04	1.71	1.39
PKSAEr10 [22]	6.14	0.61	1.40
Florotellurite [23]	3.60	1.26	0.77
Sodium-boro-Lanthanate (ELB-1) [24]	5.96	1.96	2.04
TBA1 [25]	5.99	2.69	1.05
TZN [28]	5.96	2.42	0.53
BLK1.0Er [29]	3.19	1.38	2.16
CaBaPEr20 [30]	7.44	2.52	4.34
TBL [31]	6.17	1.50	1.10
Lead-Phosphate [32]	4.79	0.79	1.22

Table 4

Radiative properties for ⁴I_13/2 → ⁴I_15/2 of Er³⁺ ions doped ZBB glasses along with other reported glasses.

Glass Sample	AR(s−1)	Δλeff (nm)	(βR)	σemi(×10−21 cm2)	τRad (ms)	(σemi × Δλeff) (×10−28 cm3)	(σemi × τRad) (×10−24 cm2s)
0.1Er (Present work)	281.1	88.98	1	15.200	3.557	1352.50	54.07
0.5Er (Present work)	488.14	86.30	1	11.412	3.284	984.86	37.48
1.0Er (Present work)	357.76	101.28	1	8.246	2.795	835.15	23.05
2.0Er (Present work)	304.43	95.75	1	8.016	2.058	767.53	16.50
SANSCEr10 [5]	193	53	1	9.8	5.18	519.4	50.76
PKSAEr10 [22]	134	34	1	6.03	7.430	204	44.02
BLK1.0Er [30]	141.89	81.21	1	8.215	7.047	667.14	57.89
CaBaPEr20 [31]	183.23	64	1	7.99	2.728	511	21.80
PKAPbNEr10 [32]	144	46	1	6.73	6.910	310	13.86

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