Enhanced emission in the NIR range by Nd³⁺ doped borosilicate glass for lasing applications

Abstract

Borosilicate glasses were prepared via melt quench technique with different concentration of Nd³⁺ ions. X-ray diffraction (XRD) was performed for the prepared glass to study the amorphous structure. The glass stability was studied by Thermo-gravimetric Analysis (TGA). Spectroscopic analysis of the prepared glasses was done through absorption, excitation, emission and decay measurements. Absorption spectra was used to evaluate the J-O parameters. Radiative parameters are evaluated with the help of application of J-O theory. Emission spectra show three prominent bands in NIR region arising from ⁴F_3/2 → ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2 centered around 910, 1068 and 1339 nm accordingly, with the most intense being the one at 1068 nm. Stimulated emission cross section, branching ratio and quantum efficiency for ⁴F_3/2 → ⁴I_11/2 transition is very high and is suitable for lasing applications. Dipole–dipole interaction is observed among activator ions on the basis of Dexter theory. The optimized Nd³⁺ doped glass (NBS10) possess maximum value for all radiative parameters and hence can be best suited for applications in the area of lasers and fiber amplifiers.

1 Introduction

Hyaline substances doped with a rare earth (RE) ions find vast usage in numerous optoelectronic devices like light emitting diodes (LEDs), fiber amplifiers, solid state lasers, optical waveguides, temperature sensors, etc. [1,2,3,4,5]. Intense lasing emissions in NIR range for Nd³⁺ places it as most famous RE ion for luminescence based characteristics [6, 7]. The transition at 1068 nm is sharpest and hence, is vastly explored for usage in high power lasers. Also, it can be observed easily at room temperature [8, 9]. While the one associated with 1340 nm finds huge utility in enhancing the O-band optical signal and provides a window in telecommunication transition, the emission centered around 900 nm provides a window for forging a device that could produce blue emission via monolithic integration of emission from a powerful diode laser [10, 11].

Various glassy systems like silicate, borates, phosphates, tellurites, chalcogenides and fluorides have been explored for the NIR range luminescence via Nd³⁺ ions [7, 10, 12,13,14,15]. Among these, borosilicate, a combination of borate and silicate glass systems, provides fine RE ion solubility, good mechanical strength, thermal and chemical durability [16]. Further, luminescence characteristics can be enhanced by reducing the phonon energy in the glass host, which in turn produces further utility for fiber amplifiers and high efficiency lasers [16, 17]. Phonon energy in this system can be lowered upon introduction of heavy metal oxide (PbO) which also increases the refractive index for the glass system. It further helps in reduction of transition temperature and allows for a wider spectral transmission window. Incorporation of ZnO, a nontoxic and non-hygroscopic oxide in the host matrix paves the way for better optical, magnetic and electrical characteristics. ZnO also possess some unique properties like direct wide band gap, large intrinsic emitting and higher exciting binding energy which in turn helps the glass system to find applications in solar energy converters, optoelectronic devices and gas sensors. By taking up the tetrahedral and octahedral positions in the host matrix, the addition of Al₂O₃ enhances its chemical and thermal stability as well as its mechanical strength, emission characteristics, and solubility of RE ions. It also decreases crystallization. The inclusion of alkali oxides (Li₂O, Na₂O, etc.) in the borate matrix can change the three coordinated boron atoms in the system into four coordinated tetrahedral structure, which improves chemical stability and causes non-bridging oxygens (NBO) to be produced [18,19,20,21,22]. As compared to phosphors, glasses possess easier fabricating technique and lower melting temperature leading to better incorporation in the optical devices [10, 23].

Nd³⁺ ions populate the ⁴F_5/2 level via pumping and later decay to ⁴F_3/2 state via non-radiative transition (multi phonon relaxation). Subsequently, the ions decay to ⁴I_13/2, ⁴I_11/2 and ⁴I_9/2 levels from ⁴F_3/2 emitting radiation in NIR range at 900, 1068 and 1340 nm respectively. These NIR range emissions have two major setbacks. Firstly, nearby Nd³⁺ ions tend to suffer cross relaxation mechanism, leading to quenching thereby mandating an optimized concentration of Nd³⁺ ions [24, 25]. Secondly, to acquire a rapid multi phonon relaxation rate of Nd³⁺ ions from the ⁴F_5/2 (²H_9/2) to ⁴F_3/2 level when excited by 585 nm, the ambient phonon energy possessed by glass host should be close to the bridge energy gap (~1000 cm⁻¹). Minimum non radiative transition produced by multiphonon relaxation provides a good window for quantum yield and hence can be better used as laser amplifiers.

Great interest by numerous researchers has been observed in studying the physical, absorption and fluorescence properties of Nd³⁺ doped glass matrix and it can be improvised by selecting appropriate glassy system [26,27,28]. In the present study, we aim to prepare Nd³⁺ ions doped borosilicate glass and hence to identify the improvised NIR lasing band obtained upon the introduction of optimized Nd³⁺ content. On account of above scientific parameters, we prepared a borosilicate glass with Li₂O, PbO, ZnO and Al₂O₃ as intermediates for enhanced thermal and mechanical strength. Dwelling upon the aforementioned utilities, we intend to state a pertinent examination of lithium lead zinc alumino borosilicate glass doped via various concentrations of Nd³⁺ ions figuring out optimized content of the RE ion for intense laser emission at 1068 nm.

2 Experimental procedure

With the help of melt quench technique Nd³⁺ doped glasses were prepared according to the following glass composition:

10Li₂O–5PbO–(5−x)ZnO–10Al₂O₃–10SiO₂–60B₂O₃–xNd₂O₃, where, x = 0.1, 0.5, 1.0, 1.5, 2.0 and 2.5 mol%. For the ease of recognition, these samples were tagged as NBS01, NBS05, NBS10, NBS15, NBS20 and NBS25 accordingly. The starting reagents i.e. H₃BO₃, SiO₂, PbO, ZnO, Al₂O₃, Li₂O and Nd₂O₃ of high purity (98–99.99%) were taken. A batch of 7.0 g of ingredient chemicals were measured and then grounded finely via agate mortar so as to obtain homogeneous mixture. This mixture was transferred to an alumina crucible and then placed in an electric furnace at 1100 °C for 3 h. The melt so obtained was suddenly quenched by decanting it on a preheated brass plate and pressing with a similar one. The obtained glass samples were further annealed in a muffle furnace at 350 °C for about 4 h. This process helps in releasing internal mechanical stress which avoids cracking and bubbles formation in the glass samples. Figure 1 shows the photograph of Nd³⁺ ions doped NBS glasses. These samples were then characterized at room temperature (RT). Archimedes’ principle and Brewster’s method was used to estimate the densities and refractive indices respectively of NBS glasses using xylene as the immersion liquid. Using an XPERT-PRO diffractometer, the XRD spectral recordings were made with a step size of 0.02 and a 2θ angle that ranged from 10° to 75°. JASCO V-670 model UV–vis–NIR spectrophotometer was used to record the optical absorption spectra of the samples. Hitachi-F7000 fluorescence spectrofluorometer was used to record photoluminescence (PL) excitation, emission spectra and fluorescence decay.

Fig. 1

Nd³⁺ ions doped NBS glass samples

3 Results and discussion

3.1 Physical properties and XRD

Density is a useful tool for examining changes in coordination, the degree of structural compactness, the geometrical topologies of the glass network, and the dimensions of interstitial holes. The values of density measured for the present glass system are 2.64, 2.66, 2.67, 2.69, 2.73 and 2.76 g/cm³ as the mol% of Nd³⁺ ions increased from 0.1 to 2.5 mol% respectively. The refractive index of optical materials is another crucial parameter. The values of refractive index measured for the 0.1 to 2.5 mol% of Nd³⁺ ions doped NBS glasses are 2.42, 2.47, 2.51, 2.54, 2.59 and 2.62 respectively. The calculated values of molar volume for the 0.1 to 2.5 mol% of Nd³⁺ ions doped NBS glasses are 3062, 3077, 3114, 3138, 3139 and 3151 cm³ respectively. Figure 2 shows that the refractive index, density and molar volume of the glasses which increase as the concentration of Nd³⁺ ions rises, signifying the addition of Nd₂O₃ in place of B₂O₃. These increasing values of density and molar volume suggest that there are more non-bridging oxygen molecules (NBOs) in the glass network. Since Nd₂O₃ enters the glass network as a network modifier, occupies an interstitial space within the network and ultimately produces NBOs in the glass structure, the glass network grows with the addition of Nd₂O₃.

Fig. 2

Variation of refractive index, density and molar volume with the concentration of Nd³⁺ ions in NBS glass samples

Figure 3 depicts the XRD pattern of the un-doped NBS glass. It shows the amorphous behaviour of the as-synthesized glass. The broad hump signifies absence of long range order in the glass lattice.

Fig. 3

XRD pattern of undoped NBS glass

3.2 Thermal analysis

The TGA curve was utilized to calculate the weight loss and identify the weight loss mechanisms of the powder precursors to form pure NBS glass. As seen in Fig. 4, the TGA curve illustrates weight loss across three separate stages from 21 to 800 °C. Evaporation of the absorbed water from the sample's surface causes a weight loss of 4.09% during the first stage, which is observed between 21 and 102 °C. The exhaustion and breakdown of remaining oxides in the sample is represented by the second stage (102–334 °C), which has a weight loss of 8.59%. The presence of combustibles in the sample is the reason of the third stage, which is between 334 and 768 °C and has a weight loss of 3.83%. The evaporation of various gases and the exhaustion of organic species cause a total weight loss of around 16.51%. Therefore, it is evident from Fig. 4 that the glass sample have a lesser mass loss at high temperatures and is thermally more stable.

Fig. 4

TGA curve for the undoped sample

3.3 Absorption spectrum and Judd–Ofelt parameters

Absorption spectra for Nd³⁺ doped NBS glass is shown in Fig. 5 for the wavelength range of 300–1100 nm. The figure comprises of various peaks of f–f electronic transitions belonging to Nd³⁺ ions from their ground state. The transitions found in the UV–vis–NIR range are from ⁴I_9/2 → ⁴F_3/2, ⁴F_5/2, ⁴F_7/2 + ⁴S_3/2, ⁴F_9/2, ²H_11/2, ⁴G_5/2, ⁴G_7/2, ⁴G_9/2 + ²(D+P)_3/2 and ²P_1/2 which are centered at 876, 800, 743, 680, 628, 582, 525, 470 and 429 nm respectively. These transitions are quite identical to other reported Nd³⁺ doped glasses excluding the minor changes in band positions and respective intensities, on account of the present glass system possessing diverse ligand fields having corresponding nature [7, 29]. As the intensity for all bands increases on increasing the Nd³⁺ content in the glass, it can be concluded that the Nd³⁺ ions are very well homogeneously dissolved in the glass matrix.

Fig. 5

Absorption spectra of Nd³⁺ ions in NBS glasses

Nephelauxetic ratio (β) and bonding parameter (δ%) help in determination of the type of Nd³⁺ ligand bond [16].

$$\upbeta = \frac{{\Upsilon}_{a}}{{\Upsilon}_{b}} * 100$$

(1)

here, ${\Upsilon}_{a}$, ${\Upsilon}_{b}$ represents the energies for the transitions in complex and free ion or aqua ion respectively as given in Carnall paper [30]. From all calculated β values respective to the transitions occurring in absorption spectra, $\overline{\upbeta }$ the average value was calculated, which further helps in determination of the bonding parameters by using following expression:

$$\delta \%=\left[\frac{1-\overline{\upbeta } }{\overline{\upbeta } }\right]\times 100$$

(2)

Bonding parameter value is either positive or negative corresponding to covalent or ionic bonding of the RE ions with the local host in glassy system. Hence, as the values obtained for the bonding parameters are positive for all Nd³⁺ doped NBS glasses, we can conclude that the bonding between the ions is covalent in nature. The values of nephelauxetic ratios and bonding parameters of all the samples are tabulated in Table 1.

Table 1 Experimental (f_exp) (×10^–6), calculated (f_cal) (×10^–6) oscillator strengths, r.m.s deviation (${\delta }_{rms}$), nephelauxetic ratio ($\overline{\upbeta }$) and bonding parameters (δ %) of Nd³⁺ ions in NBS glasses

Various important parameters like experimental oscillator strength, Judd–Ofelt parameters, various radiative properties such as transition probability, radiative lifetime and fluorescence branching ratio rely upon the data from the absorption spectra. The area under the curve for each transition occurring in absorption band is used to estimate the experimental oscillator strength (f_exp) of f–f induced electric -dipole transitions by the following expression [1, 8]:

$${\text{f}}_{\text{exp}}= 4.32 \times {10}^{-9} {\int }_{\nu 1}^{\nu 2}\varepsilon (\nu )d\nu$$

(3)

Here, for the wavenumber (cm⁻¹), $\varepsilon (\nu )$ represents the molar extinction coefficient while $d\nu$ represents the half-bandwidth corresponding to the absorption band. If Gaussian shapes do occur for the absorption bands, then for such circumstances oscillator strength could be easily determined by half width technique according to the relation [1, 8]:

$${\text{f}}_{\text{exp}} = 4.32 \times {10}^{-9} \sum \Delta \nu$$

(4)

Here, $\Delta \nu$ (cm⁻¹) represents the width of the band at half the intensity of the peak. However Gaussian shape does not occur for glasses generally and bands suffer from inhomogeneous broadening which forces us to not use the latter technique, as it would give inaccurate results. For the present study, intensities for all absorption bands have been determined via area method. Calculated oscillator strength (f_cal) are evaluated in accordance with the Judd–Ofelt (J–O) theory, for f–f intensity model with the help of least square fit analysis from initial to final state [31]. Proper relation for estimating the f_cal was used from literature [32, 33]. Root mean square deviation (δ_rms) is used to estimate the goodness of fit among f_exp and f_cal by the equation:

$$\delta \text{rms}={\left[\frac{{\sum \left({f}_{exp}-{f}_{cal}\right)}^{2}}{p}\right]}^{1/2}$$

(5)

The number of energy levels in totality for present fitting technique are represented by p. The experimental and calculated oscillator strengths along with δ_rms are shown in Table 1 for all Nd³⁺ doped NBS glasses. Smaller values of δ_rms signifies the precision of estimation used. Applying least square fitting procedure provided in literature [34], the three J–O intensity parameters Ω_t (t = 2, 4, 6) for Nd³⁺ ions doped NBS glasses have been determined and are listed in Table 2 with other reported JO parameters [35,36,37,38]. The trend followed by JO parameters for Nd³⁺ doped NBS glasses is Ω₆ > Ω₂ > Ω₄ and these values increase upto 1 mol%. Beyond this concentration, the values for these three parameters decrease. As similar dopant sites are occupied, the JO intensity characteristics ideally do not need to vary with concentration in the same host. However, if the clustering of dopant ions occurs, then variation in JO intensity parameters is observable, like the one noticed in the present work [39]. These three parameters are concerned with numerous physical and structural characteristics of glasses. Ω₂ is highly sensitive to the RE ions surroundings and is associated with the lack of symmetry with respect to coordination structure, type of bonding and polarizability of ligand ions. Since Ω₂ is correlated with the asymmetry of the immediate environment around the Nd³⁺ sites, it demonstrates the reliance of the covalence between Nd³⁺ ions and ligand anions. The ion site becomes less centro symmetrical and forms a stronger ionic chemical interaction with the ligands when the Ω₂ parameter values increase. The current investigation reveals that the values of Ω₂ changes from 5.8593 to 5.7406 and then increases to 6.4213 as the concentration of Nd³⁺ ions increases from 0.1, to 0.5 and to 1.0 mol%, respectively, indicating a rise in the covalent nature of the Nd–O bond. The values obtained in the present study are higher than the values reported in the different composition, presented in the Table 2 [35,36,37,38]. Ω₄ is the parameter which defines the bulk characteristics such as rigidity and viscosity of the host glass system comprising of the RE ions. Ω₆ is inversely proportional to the covalency of Nd–O bonds and this can be altered on modification of the host glass structure or composition [40, 41]. J-O intensity parameters for NBS10 glass shows the highest value among the six prepared glasses by varying Nd³⁺ ion content, so we can say that NBS10 possess more asymmetry, high covalency, and maximum rigidity as compared with the other Nd³⁺ doped NBS glasses.

Table 2 Judd–Ofelt parameters (${\Omega }_{\lambda } \times$ 10⁻²⁰cm²) and their spectroscopic quality factor (χ = ${\Omega }_{4}/{\Omega }_{6}$) of Nd³⁺ ions in NBS glasses along with various reported hosts

Hypersensitive transition for Nd³⁺ doped NBS glasses is ⁴I_9/2 → ⁴G_5/2 situated around 582 nm in Fig. 5. This transition is entirely influenced by the RE ion-ligand surrounding and obeys the selection rule ΔS = 0, ΔL ≤ 2 and ΔJ ≤ 2. Along with this, the ⁴I_9/2 → ⁴G_5/2 transition possess maximum values for oscillator strengths and matrix elements ||U²||², showing an association with hypersensitivity and Ω₂ parameter (both are directly proportional). Ω₄ and Ω₆ help in calculating the radiative analysis like stimulated emission cross section, transition probability and branching ratio for the active ions. Ω₄ and Ω₆ are quite impactful in considering the neodymium emission intensity. For the present case, ⁴F_3/2 → ⁴I_9/2 transition is dependent upon Ω₄ while Ω₆ is accountable for ⁴F_3/2 → ⁴I_11/2 transition. Spectroscopic quality factor (χ), a ratio between Ω₄ and Ω₆, thats helps in recognizing the path way for the excited metastable state ⁴F_3/2 to decay to ground state. Smaller the value of χ, better will be the probability for lasing in NIR corresponding to ⁴F_3/2 → ⁴I_11/2 transition. According to relation between χ and NIR transitions (⁴F_3/2 → ⁴I_9/2 and ⁴I_11/2), if its values are less than 1 then ⁴F_3/2 → ⁴I_11/2 transition has higher efficiency and is better for lasing. While if its values are more than one then, ⁴F_3/2 → ⁴I_11/2 transition efficiency is reduced and ⁴F_3/2 → ⁴I_9/2 transition efficiency is increased [42]. For the present case study, NBS10 possess minimum value of χ as 0.168 (however, usual reported values are in the range 0.22–1.5) and is shown in Table 2 [43].

3.4 Emission and radiative characteristics

Photoluminescene excitation spectra for 1 mol% (NBS10) Nd³⁺ doped NBS glass at 1068 nm emission wavelength is shown in Fig. 6. Eleven bands arising from ⁴I_9/2 → ²I_11/2, ⁴D_3/2, ²P_1/2, ²K_15/2, (⁴G_9/2, ²K_13/2), (⁴G_7/2, ⁴G_5/2), ²H_11/2, ⁴F_9/2, (⁴S_3/2, ⁴F_7/2), ²H_9/2 and ⁴F_5/2 which are centered around 293, 358, 431, 475, 526, 585, 627, 683, 738, 800 and 825 nm in UV–vis–NIR range can be seen. Among all the transitions, 585 nm was the most intense peaks observed. Therefore, the emission spectra of all the prepared glass samples were recorded at this excitation wavelength. Figure 7 shows the emission spectra with three peaks in NIR range, arising from the transitions ⁴F_3/2 → ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2 centered around 910, 1068 and 1339 nm respectively. Among these bands, the most intense one is at 1068 nm and so, is best suited for laser transition. In the inset diagram of Fig. 7 the variation of intensity for ⁴F_3/2 → ⁴I_11/2 transition with the concentration of Nd³⁺ ions as shown in the form of bar graphs. The observed intensity of ⁴F_3/2 → ⁴I_11/2 transition increases till 1 mol% of the RE ion beyond which, the intensity of the band decreases. This decrement is ascribed due to increased interaction among Nd³⁺—Nd³⁺ ions and also among Nd³⁺-host defects, resulting in the cross-relaxation process in the effective ion centres through concentration quenching. Figure 8 depicts the diagram for energy level transitions of the Nd³⁺ ions in the NBS glasses emphasizing upon the excitation, emission and cross- relaxation processes. As the Nd³⁺ ions are excited from ⁴I_9/2 ground state to ⁴F_5/2 excited state, they decay to a metastable state ⁴F_3/2 via a non-radiative decay. This ⁴F_3/2 level gets strongly populated by Nd³⁺ ions resulting in three radiative transitions: ⁴F_3/2 → ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2. The transition corresponding to ⁴I_11/2 is most intense. When the Nd³⁺ ions content is increased in the host glass system, it leads to reduction in the separation between Nd³⁺ ions resulting in increased cross- relaxation mechanism among the Nd³⁺ ions. These processes cumulatively depopulate the Nd³⁺ ions situated at ⁴F_3/2 energy level. Cross relaxation channels involved in the process is ⁴F_3/2 + ⁴I_9/2 → ⁴I_15/2 + ⁴I_15/2 result in loss of energy through non-radiative mechanism. The non radiative energy transfer can occur by either exchange interaction or multipolar interaction. The kind of inter-ionic interaction between the dopant ions can be accessed via Dexter Theory. The interactions can be grouped as dipole–dipole (d–d), dipole–quadrupole (d–q) and quadrupole—quadrupole (q–q). Based upon the relation between emission intensity and concentration of the activator ions, a graph can be plotted using the following relation [16]:

Fig. 6

Excitation spectra of Nd³⁺ ions in NBS10 glass monitored at 1068 nm emission

Fig. 7

Emission spectra of Nd³⁺ ions in NBS glasses under 585 nm excitation (Inset Variation of ⁴F_3/2 → ⁴I_11/2 transition with the concentration of Nd³⁺ ions)

Fig. 8

Partial energy level diagram showing excitation, emission and cross-relaxation mechanism for Nd³⁺ ions in NBS glasses

$$\text{log }\frac{I}{c}=\text{log}f- \frac{slog (c)}{d}$$

(6)

Here I, c, f and d are emission intensity, concentration of activator ions, a constant which is independent of activator ions concentration and dimension of the compound (=3) respectively. Interaction between the closest neighbouring ions is predicted by s, where s = 6, 8 and 10 for d-d, d-q and q-q interaction respectively [16]. The plot between log (I/c) and log (c) is presented in Fig. 9 which shows the value of slope (s/d) to be 1.86, hence the calculated data for s = 1.86 *3 = 5.6. Here the obtained data for s is approximately equal to 6 indicating towards dipole–dipole interaction among the activator ions. Hence in the NBS glasses, dipole–dipole interaction is responsible for non-radiative energy transfer among Nd³⁺ ions. Moreover, this non radiative energy transfer leads to the concentration quenching effect in the emission spectra.

Fig. 9

Plot of log(I/c) v/s log(c) of Nd³⁺ ions in NBS glasses

The radiative parameters like transition probability (A_R), total transition probability (A_T), radiative lifetime (τ_R) and branching ratio (β_R) corresponding to ⁴F_3/2 → ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2 transitions for Nd³⁺ ions doped NBS glasses with the help of relations provided in literature were also calculated [44] and are represented in Table 3. From the data represented in Table 3, we can observe that the values of branching ratio (β_R) for NBS10 glass are maximum among all prepared Nd³⁺ doped NBS glasses corresponding to ⁴F_3/2 → ⁴I_11/2 transition. The values for total radiative transition probability increase upto 1 mol% of Nd³⁺ ions and then decrease upon further increment of the RE ions concentration. The total radiative transition probability for ⁴F_3/2 → ⁴I_11/2 is highest which is the most intense peaks. The fluorescence branching ratio is an important parameter in identifying the intensity for laser transition ascribed to electric dipole transitions of various excited and lower energy levels. If the value of β_R is ≥ 0.5 then it is very well suited for the lasing job. In the present study the value of β_R is above 0.5 for ⁴F_3/2 → ⁴I_11/2 energy level for all Nd³⁺ ions doped NBS making it as possible candidate for the lasing field applications. For further analyzing the utility as an appropriate lasing host, stimulated emission cross-section (σ_se) of the glass should be of high value. The value of stimulated emission cross-section suggests the behavior of energy extraction from optical material and is evaluated with the help of relation [1, 11]:

$${\sigma }_\text{se}=\left[\frac{{\lambda }_{p}^{4}}{8\pi c{n}^{2}\Delta {\lambda }_{p}}\right]\text{ A}_{R}$$

(7)

where, the ${\lambda }_{p}$ and $\Delta {\lambda }_{p}$ represent the wavelength corresponding to most intense band and linewidth (FWHM). Table 4 shows all the calculated values for stimulated emission cross-sections (${\upsigma }_{se}$), emission peak wavelength (${\lambda }_{P}$), line widths ($\Delta {\lambda }_{P}$), gain band width (${\upsigma }_{se}\times \Delta {\lambda }_{P}$) and optical gain parameter (${\upsigma }_{se}\times {\uptau }_{\text{R}}$) parameters for the emission transitions for Nd³⁺ ions in NBS glasses. The value of stimulated emission cross-section for NBS10 glass is maximum, making it superior host for lasing and optical fiber amplifier applications.

Table 3 Transition probability (A_R) (s⁻¹), measured and experimental branching ratio (β_exp $and {\beta }_{R}$), total transition probability (A_T) (s⁻¹) and radiative lifetime (τ_R) (µs) for the observed emission transitions of Nd³⁺ ions in NBS glasses

Table 4 Emission peak wavelength (${\lambda }_{P}$) (nm), linewidths ($\Delta {\lambda }_{P}$) (nm), stimulated emission cross-sections (${\upsigma }_{se}$) (cm²), gain band width (${\upsigma }_{se}\times \Delta {\lambda }_{P}$) (cm³) and optical gain parameter (${\upsigma }_{se}\times {\uptau }_{\text{R}}$) (cm² s) parameters for the emission transitions for Nd³⁺ ions in NBS glasses

3.5 Decay spectral examination

Figure 10 shows the fluorescence decay curves for the Nd³⁺ ions in NBS glasses at 1068 nm emission wavelength for ⁴F_3/2 → ⁴I_11/2 transition under 585 nm excitation. The measured decay curves for the Nd³⁺ doped NBS glasses show single exponential fit behavior for all concentrations. The experimental decay time ${(\uptau }_{\text{exp}}$) for the Nd³⁺ doped NBS glasses are calculated initially by applying e-folding time of the intensity for decay curves and with the help of equation provided in literature which are shown in Table 5 [8, 11, 22]. The values of ${\uptau }_{\text{exp}}$ are found to be decreasing with increment in concentration of Nd³⁺ ions for NBS glasses which may be attributed to concentration quenching effect among the Nd³⁺ ions. The ${\uptau }_{\text{exp}}$ values are also lower than the corresponding ${\uptau }_{\text{R}}$ obtained via J–O theory, which may be ascribed due to specific the non-radiative decay mechanism (W_NR). Quantum efficiency ($\eta$), which is the ratio between emitted and absorbed light intensity, is an important parameter that describes the utility of the material for lasing applications. Higher the value of quantum efficiency, better will be the lasing properties of studied glass matrix. Following equations are used to determine the values of $\eta$ and W_NR given in literature and are shown in Table 5 [8, 11]:

Fig. 10

Decay profiles of Nd³⁺ ions in NBS glasses for ⁴F_3/2 → ⁴I_11/2 transition under 585 nm excitation

Table 5 Experimental lifetime (τ_exp) (µs), radiative lifetime (τ_R) (µs), quantum efficiency (η), and non-radiative decay rates (W_NR) (s⁻¹) for Nd³⁺ ions in NBS glasses

$$\upeta = \frac{{\uptau }_{\text{exp}}}{{\uptau }_{\text{R}}} x 100{\%}$$

(8)

$$\text{W}_{NR }= \left(\frac{1}{{\uptau }_{\text{exp}}}- \frac{1}{{\uptau }_{R}}\right)$$

(9)

From the obtained values we can see that the highest quantum efficiency and lowest non radiative decay rate is for 1 mol% of Nd³⁺ ions doped NBS glasses, which further ascertains its suitability for NIR laser emission at 1068 nm [45, 46].

The values of important parameters, such as stimulated emission cross-section, gain band width, optical gain, experiment decay time, quantum efficiency and non-radiative decay rate, of NBS glass are compared to other Nd³⁺-doped glasses and are shown in Table 6, along with the other reported glasses doped with Nd³⁺ ions. The measured values for optimized NBS10 glasses are maximum from all the other prepared glass as well as other reported values, which marks towards more suitability in various lasing applications.

Table 6 Stimulated emission cross-sections (${\upsigma }_{se}$× 10^–22) (cm²), gain band width (${\upsigma }_{se}\times \Delta {\lambda }_{P}$) (× 10^–28) (cm³), optical gain parameter (${\upsigma }_{se}\times {\uptau }_{\text{R}}$) (× 10^–25) (cm² s), experimental lifetime (τ_exp) (µs), radiative lifetime (τ_R) (µs), quantum efficiency (η), and non-radiative decay rates (W_NR) (s⁻¹) for (⁴F_3/2 → ⁴I_11/2) transition of Nd³⁺ ions in NBS glasses along with other reported values

4 Conclusions

Nd³⁺doped NBS glasses were prepared via a melt quench technique. The X-ray diffraction pattern shows the amorphous behavior of the undoped glass. The Thermo-gravimetric analysis shows stability of the glass. A thorough spectroscopic analysis of the samples was done via characterization techniques like UV–VIS-NIR absorption, photoluminescence excitation and emission and time decay measurements. Judd–Ofelt analysis was conducted and three intensity parameters Ω₂, Ω₄ and Ω₆ were obtained for all the prepared glass samples from the absorption data. Various important radiative parameters were calculated to help assess the suitability of the glasses in lasing applications. Emission of the Nd³⁺ doped NBS glasses was found in NIR range with three prominent transitions corresponding to ⁴F_3/2 → ⁴I_9/2, ⁴I_11/2 and ⁴I_13/2, wherein ⁴F_3/2 → ⁴I_11/2 transition centered at 1068 nm had the maximum intensity. This transition possesses the maximum value of spectroscopic quality factor, branching ratio, stimulated emission cross section and quantum efficiency for the optimized glass (NBS10). Interaction among the activator ions was predicted to be of dipole–dipole nature by utilizing the Dexter theory. The decay curves for NBS glasses show single exponential for all concentrations. The aforementioned results are encouraging enough to ascertain that the 1 mol% of Nd³⁺ ions doped NBS glass is ideal for laser and fiber amplifier applications.