1 Introduction

Glasses doped with rare-earth (RE) ions are important for a wide range of scientific and industrial processes [1]. In the recent decades, extensive research work has been carried out on glasses and glass ceramics doped with rare-earth ions for their use in telecommunication system elements such as upconverters, fibers, optical amplifiers, solid-state lasers and 3D displays. In the last years, many researchers have been investigating different host glasses and glass ceramics doped with rare-earth ions and used it in different applications [2,3,4,5,6,7,8,9]. The application of rare-earth ions doped glasses for laser filed depends on the refractive index of the host materials, bonding of rare-earth ions and the energy of the emitted radiation [2,3,4,5,6,7]. When the host glass changed, the effect of the rare-earth ions is also changed. This is due to the change in the absorption and radiative properties; this effect can be studied using the Judd–Ofelt theory [8, 9]. In this respect, Er3+ ions are the most significant active ions due to their sole energy level structure which have the capability to deliver concurrent green, red emission along with mid IR emission (1530 nm) through both the up and down conversion optical processes.

This is due to the Er3+ ion transition around 1.5 µm, which is an eye-safe wavelength. Er-doped silicate, borosilicate, phosphate, and tellurite glasses exhibit superior spectral and laser properties [10,11,12,13,14,15,16,17]. Extraordinarily, Erbium ions doped glass or ceramic glass is more charming due to the band located at 1550 nm in the infrared region transition between (4I13/2 to 4I15/2). erbium doped glasses have numerous applications like microchip lasers [18, 19], amplifier in wavelength division multiplexing systems [18, 20], waveguide amplifiers [21] high-density optical storage and lidar transmitters [22,23,24,25,26]. Silicate glasses have many benefits, based on the availability of designing new types that are suitable for developing up-conversion waveguide laser [27]. The main purpose of this investigation is the preparation of cadmium lithium silicate host glass doped with gadolinium and erbium ions and to investigate its structure and optical properties.

2 Experimental procedures

The 50SiO2 -30Li2O- 1Gd2O3- (19 − x)CdO and x Er2O3; where (0 ≤ x ≥ 2.5), mol% glasses have been synthesized by conventional melting—quenching technique. Pure SiO2, Li2O, Gd2O3, CdO and Er2O3 at a purity of 99.9%, were ground to obtain a mixture for each of the glass samples. The powders produced were then melted in an electrically heated furnace at about 1473 K in regular atmospheric pressure in Pt crucibles, for 4 h to homogenize the melt, which was then added to a preheated mold. This mold was moved right away to a different furnace heated to 673 k for two hours to anneal the glass. Table 1 presents the starting mixtures, also known as nominal composition. The prepared samples’ thickness was 0.2 cm, and each was polished in accordance with its use to optical properties. The optical measurements have been studied using a UV spectrometer (JASCO 670).The states of the obtained glasses were identified by X-ray diffractometer. FTIR spectroscopy of the prepared glass samples has been studied at room temperature with the range 400–4000 cm−1 by spectrometer type JASCO 430. The experiential setup for measuring the emission spectra consists of a diode-pumped CW laser with emission wavelength of 355 nm as a pumping source, laser beam reshaping optics for collimating the laser beam, infinitely corrected objective and a UV–Vis spectrometer. The power of the diode-pumped CW laser is controlled by two means, first through the adjustment of the power of the pumping diode and second through a round variable neutral density filter. The laser beam passes through a 50/50 beam splitter to the sample and a power meter. The pumping laser spot is expanded collimation by a set of plano-concave and plano-convex cylindrical lenses [26].

Table 1 Chemical composition and preparation of glasses
Full size table

3 Results and discussion

3.1 XRD and FTIR analysis

Figure 1 shows that XRD of present prepared glass samples. It is shown that the curves confirm the glassy nature of the prepared glasses, where no distinguished peaks and no sharp lines, were observed.

Fig. 1
figure 1

XRD of the studied glasses

Full size image

Once upon a time the studies of IR spectroscopy on silicate glasses containing alkali have exposed that the glasses structure have not depend on the alkali oxide content and the rule retains the tetravalent valence for the silicon ion [28, 29]. The FTIR spectra of studied glasses are shown in Fig. 2 in the range of 4000–400 cm−1. FTIR spectra give more details about the main groups of the studied glass samples. The basic bands of these glasses are associated to the overlapping of some mono bands with each other. The separated peak has center (C) and its relative area (A). The center of the band is correlated to the vibrations of a specific structural group, while the area under peak is related to the content of these groups as listed in Table 2. Table 3 listed attribution of deconvoluted IR absorption peaks of studied glasses. The values of these parameters agreed well with previous work [30,31,32]. Figures 3, 4 and 5 presented the deconvoluted spectrum of the glass sample G1, G3& G5. The main absorption band of the studied glasses is identified as follows: [33,34,35,36,37,38,39,40,41,42,43,44,45] band at 464–494 cm−1 is associated to Cd–O stretching vibration and band at 494 cm−1 associated to the Er–O vibration. Band at range 400–600 cm−1 is generally correlated with Si–O–Si and O–Si–O bending modes of bridging oxygen in the glass network. Band around 524 cm−1 is ascribed to the vibrations of the Si–O–Si and O–Si–O bending modes of bridging oxygen and Er–O vibration in the glass network. Band at 600–800 cm−1, the concentration of SiO4 increase due to the increasing of Si–O stretching. Band around 800–1200 cm−1 was associated to the vibration of SiO4 and CdO4 tetrahedron and at this absorption band of glass samples was shifted to a higher wavenumber with the increasing Er2O3 content due to the increases of the degree polymerization of the glasses. Band at 1002–1086 cm−1 is associated to Si–O–Si anti-symmetric stretch of bridging oxygen atoms between tetrahedra, Si–O–Cd anti-symmetric stretching of bridging oxygen within the tetrahedral and Cd–O stretch in CdO4 units. From Table 2 it can be observed that the band position shifted to higher wavenumber with the increasing Er2O3 concentration. This shifting led to change the composition of the glass network due to the addition of Er2O3 to glass network.

Fig. 2
figure 2

Infrared spectra of the investigated glasses

Full size image
Table 2 De-convolution parameter of the infrared spectra of studied glasses (C) is the component band center; (A) is the relative area (%) of the component band of the prepared sample
Full size table
Table 3 Attribution of deconvoluted IR absorption peaks of studied glasses
Full size table
Fig. 3
figure 3

Curve-fitting of IR spectra of the glass sample G 1

Full size image
Fig. 4
figure 4

Curve-fitting of IR spectra of the glass sample G3

Full size image
Fig. 5
figure 5

Curve-fitting of IR spectra of the glass sample G5

Full size image

3.2 Various physical parameters

3.2.1 The erbium ion concentration (Er3+)

The ion concentration of Er can be calculated according to the following equation:

$$E_{r} = \left( {\frac{{6.023 \times 10^{ \wedge } 23x\,{\text{mol fraction of cation}} \times {\text{valency of cation}}}}{{V_{m} }}} \right)$$
(1)

The ion concentration of Er values according to Table 4 increased with increase the concentration of erbium. This increase is related to the decrease in the molar volume.

Table 4 Various physical parameters of the studied glasses
Full size table

3.2.2 Inter ionic distance (Ri)

The inter ionic distance can be calculated according to the following equation:

$$R_{i} = \left( \frac{1}{Er} \right)^{\frac{1}{3}}$$
(2)

The inter ionic distance between two ions is used to give knowledge about the bond length. The values of Ri according to Table 4 decrease as the content of erbium increases. This decrease is connected to the molar volume.

The molar refractivity (Rm), molar polarizability (αm) and Reflection loss (RL) of the samples can be calculated using these relations:

$$R_{m} = V_{m} \left( {1 - \sqrt {E_{g} /20} } \right)$$
(3)
$$\propto_{m} = \left( {\frac{3}{4\pi N}} \right)R_{m}$$
(4)
$$R_{L} = \left( {\frac{{R_{m} }}{{V_{m} }}} \right)$$
(5)

The molar refractivity (Rm) depends on the molar polarizability (αm) of the material. It was found that from (Table 4) the values of (Rm), (αm) and (RL) are decreased with increasing the erbium content. The decrease in these values is related to molar volume, formation of bridging oxygen BO, and the decreasing number of free electrons.

The metallization criterion can be estimated by:

$$M = 1 - \frac{{R_{m} }}{{V_{m} }}$$
(6)

The metallization of the prepared samples is shown in Table 4. It was found that metallization decreases with increasing the erbium concentration, which related to a decrease in the Reflection loss (RL).

The optical electronegativity (χ) of the prepared samples can be calculated from the following relation:

$$\chi = 0.2688E_{g}$$
(7)

where Eg is the optical band gab. So, the electronegativity (χ) increase with increasing of erbium concentration.

Electronic polarizability and optical basicity of the prepared samples are estimated from the following relations:

$$\propto^\circ = - 0.9 \chi + 3.5$$
(8)
$$\wedge = - 0.5\chi + 1.7$$
(9)

Electronic polarizability and optical basicity have the opposite trend value of electronegativity (χ); so, the electronic polarizability and optical basicity values are decreasing with increasing the concentration value of erbium. The decrease in optical basicity value of these glasses is due to that the basicity value of CdO (1.1) is higher than the basicity of erbium (0.929) [46,47,48,49,50].

3.3 Optical characterization

The absorption spectrum in the range of 200–2700 nm of prepared glass has been measured by the UV Jasco 670 and present in Fig. 6. It is observed that, several peaks in the range of 300–1600 nm, due to effect of f → f orbital from the Er ions transition. Figure 7 shows the relation between the absorbance coefficient of the prepared samples versus the wavelength. The optical energy gap of the present glass has been estimated by Tauc's formula [49, 50].

$$\alpha .h\nu = C(h\nu - E_{g} )^{k}$$
(10)
Fig. 6
figure 6

Absorbance of glass system a versus wavelength range of 250–620 nm, b from 600 to 1650 nm

Full size image
Fig. 7
figure 7

Optical absorption coefficient of glass system

Full size image

where Eg is the optical band gap, C is an energy independent constant, and the exponent k takes different values (k = 2 for non-direct transitions). The intercept of \(\sqrt{\alpha h\nu }\) versus hν at \(\sqrt{\alpha h\nu }=0\) denoted the value of Egas shown in Fig. 8. The most obvious finding to emerge from the analysis is that the energy band gap increases with increase the erbium content and tabulated in Table 4. The increasing of energy gap associated to the increase of localized states and formation of bridge oxygen. The increase of bridging oxygen causes a decrease in the number of donor center leads to increase of the optical band gap [51,52,53,54,55,56].

Fig. 8
figure 8

Plot of (α hv)1/2 against photon energy (hv) to calculate the optical band gap from the intercept of the curves

Full size image
Fig. 9
figure 9

Plot of ln(α) versus the photon energy (to estimate the Urbach energy from the slope of the liner range of the curves)

Full size image

The values of Urbach energy have been estimated from the slope of the graph between ln(α) versus the photon energy as shown in Fig. 9 and the values in Table 4. It is observed that decreasing of Eu by increasing the erbium ions content in the samples. Figure 10 shows the relation between Eg and Eu versus the Er content in the samples. It clear that from the figure Eg have direct proportional with the Er content and Eu have inverse proportional with Er content. The increasing values of Eg by increasing the Er2O3 content can be understood in terms of the structural changes that are taking place in the prepared glasses caused by the addition of Er2O3. This consequence suggests that Er2O3 enters into the glass system and it modifies the glass network in such a way that more number of BOs created thus leads to increasing band gap values. Therefore, as discussed previously, increasing the Er2O3 content decreases the bond length of the structural units, which in turn is in direct proportionality to the molar volume, and also creates more BOs. These factors, besides the density of Er2O3 (8640 kg m−3) is higher than the density of CdO (8150 kg m−3) and bond dissociation energies of Er–O (611 kJ mol−1) is higher than the bond dissociation energies of Cd–O (142 kJ mol−1), are responsible for the increase of Eg values. Urbach energy Eu value decreased with increasing Er2O3 content. This may indicate that the addition of Er2O3 decreases the disorder of glass systems. Also the oxygen packing density of the prepared glasses gives a good information on their structure. Otherwise the value of oxygen packing density increases with increasing Er3+ concentration. This indicates that the glass matrix gets more compact. The presence of erbium ion increases the formation of bridging oxygen ions which result the decreasing number of free electrons in the glass system. This will result in the increasing value of optical band gap as the concentration of erbium increases [57,58,59,60,61] (Table 4).

Fig. 10
figure 10

Optical band gap and Urbach energy versus concentration of Er

Full size image

The molar refractivity and molar polarizability are decreased with the increase of Er content in the glass as well as the Reflection loss (RL) and Electron Polarizability (α°) are decreased. On the other hand, metallization criterion (M), Electronegativity (χ) and Optical basicity (˄) are increased by increasing Er content as shown in Table 4. The emission spectrum as a result of excitation with a 355 nm CW laser is shown in Fig. 11 where several emission transitions are observed i.e., 423 nm, 458 nm, 523 nm, 533 nm, 547 nm, 558 nm and 732 nm. The maximum two transitions are at wavelength of 547 nm and 558 nm. The emission spectrum is used to calculate the chromaticity coordinates according to the Commission international de l'clairage (CIE 1931) as shown in Fig. 12 [62]. Er3+ doped 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO has x chromaticity coordinate of 0.29 and y chromaticity coordinate of 0.51. That means, the emission of the proposed compound lays in the green emission region.

Fig. 11
figure 11

Emission spectrum of Er3+ doped 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO

Full size image
Fig. 12
figure 12

Chromaticity coordinates calculated from the emission spectrum of Er3+ doped 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO

Full size image

3.4 Judd–Ofelt analysis

Judd–Ofelt theory [8, 9] has been used to analyze the spectra arising from 4f n-4f n transitions of erbium ions doped 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO. In the present work, the optical parameters such as radiative rates, intensity parameters and line strengths for transitions from ground state to excited states of Er3+ hosted by 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO, have been calculated. Most of f–f transitions are electronic dipole (ED) transitions and the minority are magnetic dipole (MD) transitions. To calculate line strengths and radiative rates, the reduced matrix operator U(t) applied to the wave functions of upper and lower states, which available for the 4fn states. The electronic dipole line strength can be calculated form:

$$S_{ED} \left( {J,J^{\prime}} \right) = \mathop \sum \limits_{t = 2,4,6} \Omega_{t} \left| {f^{n} \left[ {LS} \right]JU^{\left( t \right)} f^{n} \left[ {L^{\prime}S^{\prime}} \right]J^{\prime}} \right|^{2}$$
(11)

The intensity parameters Ωt=2,4,6 can be determined experimentally from the absorption spectra. New values reduced matrix elements, U(t), of Er3+ are listed in Table 5. The experimental line strength Sm is determined from absorption cross-section over the wavelength range of number of transitions by:

Table 5 Reduced matrix elements
Full size table
$$S_{m} = \frac{{3ch\left( {2J + 1} \right)}}{{8\pi^{3} e^{2} \overline{\lambda }}}n\left( {\frac{3}{{n^{2} + 2}}} \right)^{2} \int {\sigma \left( \lambda \right)d\lambda }$$
(12)

where J is the total angular momentum of the lower level, \(J=L\pm S\), \(\stackrel{-}{\lambda }\) is the mean wavelength of the peak, and the integral of absorption cross-section over wavelength \(\int \sigma \left(\lambda \right)d\lambda\) is the integration of cross-section as a function of wavelength.

Figure 6a, b depcits UV–Vis-NIR spectra of the investigated glasses in the wavelength region 250–1800 nm. The band positions have been identified at wavelengths of 357, 365, 378, 451, 488, 521, 544, 650, 800, 978, and 1537 nm. These bands are corresponding to transitions in Er3+ ion from the ground state 4I15/2 to excited levels have the atomic terms (2S+1LJ) 2G7/2, 4G9/2, 4G11/2, 4F3/2, 4F7/2, 2H11/2,4S3/2, 4F9/2, 4I9/2, 4I11/2 and 4I13/2, respectively.

J–O calculations of experimental and theoretical line strengths of ground-excited transitions of 2G7/2, 4G9/2, 4G11/2, 4F3/2, 4F7/2, 2H11/2,4S3/2, 4F9/2, 4I9/2, 4I11/2 and 4I13/2 glasses doped with different concentrations of Er2O3 are listed in Table 6. It is observed that the strong intensities are recorded at 4G11/2 and 2H11/2 transitions with wavelength of 378, 521 nm, respectively, which obviously clear in Fig. 6, as well. These transitions have recorded line strengths values of 1.74–8.33 (dimensionless) for 4G11/2 and 1.59–9.4 for 2H11/2.

Table 6 Measured and calculated line strengths (S-values) of Er3+ doped glasses at different concentrations
Full size table

In Table 6, for the most measured and calculated values of line strengths there is no certain trend followed. The reasonable agreement between experimental (Sm) and theoretical line strengths (Sth) can be assisted from the root mean square deviations (RMS). RMS values are lower in the present work which in the same order for those recorded in other literature [63, 64]. It is obvious that the values of Sm and Sth show good agreement for most transitions such as 4G11/2, 4F7/2, 2H11/2 and 4F9/2. However, in the cases of weak transitions, a large deviation between Sm and Sth has been observed for such as 2G7/2 and 4I13/2. These big differences may be due to the sensitivity of the line strengths for the choice of the wave functions.

The least squares fit method has been applied over a set of reduced matrix elements and experimental values of spectral intensities to calculate the optical intensity parameters, Ωt=2,4,6. Calculated values of Ω2, Ω4, and Ω6 have been listed in Table 7. As it clear in Table 3, the J-O intensity parameters of the Er3+ doped glass decrease with the increasing of Er2O3 concentration in the prepared compositions; this might be due to the quenching processes within the compound [63, 64].

Table 7 Intensity parameters
Full size table

The radiative rates (lifetimes and transition probabilities) of Er3+ doped 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO are shown in Figs. 13 and 14. Lifetime values of 4I9/2,11/2,13/2 as a function of Er2O3 content are shown in Fig. 13. It is obviously clear that the lifetime values of the selected levels in Er3+ decreased with the increasing of Er2O3 content. This trend may be attributed to the quenching processes which dominate the internal processes inside the present composition. As well as, the variation of theoretical spectrum over a wavelength range of about 350–1200 nm is shown in Fig. 14. The largest values of transition probabilities appear at low wavelength rang up to 650 nm. This is because the transition probability depends on the band energy (\(\Delta E\)) which decreases by increasing of wavelength.

Fig. 13
figure 13

Lifetime of selected levels in Er ions as a function of RE content

Full size image
Fig. 14
figure 14

Theoretical spectrum of Er3+ doped 50SiO2 -30Li2O- 1Gd2O3- (19 − x) CdO

Full size image

4 Conclusion

The addition of erbium to the cadmium lithium silicate glasses leads to the modification of the glass network resulting higher optical band gap. The FTIR spectra of the present glass system have been deconvoluted and contribution from different glasses modifier have been identified. Moreover, the density increases with the concentration of erbium content and the molar volume decrease, while the molar refractivity, molar polarizability, reflection loss and optical basicity decreased. Judd–Ofelt method has been used to calculate the optical parameters of the prepared glasses doped Er3+. The present calculations of line strengths, optical intensity parameters (Ωt), and radiative lifetimes show that there is no specific trend in the line strengths with the concentration of rare earths while the intensity parameters and lifetimes decrease with the increasing of Er2O3 concentration. This trend is justified to the quenching processes that dominate the internal processes inside the composition. The prepared glasses are excellent candidates for laser applications.