Manifestation of up-conversion in Yb³⁺/Tm³⁺ doped Li₂O–Y₂O₃–SiO₂ glass system

Abstract

In this study, we have investigated the principal role of Y₂O₃ on the emission features of Tm³⁺ ion and up-conversion phenomenon in Tm³⁺ and Yb³⁺ co-doped Li₂O–Y₂O₃–SiO₂ glass system. The concentration of Y₂O₃ is varied from 0 to 5 mol% while that of Yb³⁺ and Tm³⁺ is fixed. When the glasses are doped with Tm³⁺ ions, the intense blue and red emissions were observed, whereas Yb³⁺ doped glasses exhibited NIR emission at about 980 nm. When the glasses are co-doped with Tm³⁺ and Yb³⁺ ions and excited at 900 nm, the blue and red emission lines were observed to be reinforced and strengthened with increase in the concentration of Y₂O₃. The IR emission band detected at about 1.8 μm due to ³F₄ → ³H₆ transition of Tm³⁺ ions is also observed to be strengthened due to co-doping. The reasons for enhancement in the intensity of various emission bands due to co-doping have been identified and discussed with the help of rate equations for various emission transitions.

1 Introduction

The short wavelength solid-state lasers are being used for a variety of applications such as color displays, high density optical data storage and reading, biomedical diagnostics, infrared laser viewers and indicators, biomedicine, etc.

One of the effective ways of producing short wavelength lasers is the frequency up-conversion process using rare earth ion-doped glass materials; this process is based on conversion of near-infrared photons into visible photons via multiphoton [1]. The pioneering work of Auzel [2] on energy transfer demonstrated the advantages of an activator–sensitizer combination in laser hosts for improving the quantum yield of photons at the lasing wavelength. The rare earth host materials with low phonon energy can reduce non-radiative losses due to the multi-phonon relaxation and thus offer suitable environment for up-conversion process [3–5]. Further, it is well-known that the rare earth doped oxide glasses are of particular interest for the photoinduced nonlinear optics. In fact, rigorous studies along these lines on several glass systems were reported earlier by Kassab et al. [6, 7].

Among different rare earth ion-doped glasses, the Tm³⁺ ion-activated glasses have gained much attention because of the fact that Tm³⁺ ion possesses two meta-stable excited levels viz., ¹D₂ and ¹G₄, in its energy level structure for displaying blue emission either from its normal emission or by up-conversion luminescence process [8, 9].

Further, among different rare earth ions, Yb³⁺ ion is considered as a promising sensitizer for Tm³⁺ ions in glass matrices due to its significantly high absorption cross-section in the NIR region and favourable energy level structure. The ground state of trivalent ytterbium ion (Yb³⁺) is ²F_7/2. The doublet splitting of this state is approximately 10,000 cm⁻¹ with the ²F_5/2 component lying above the ground state, ²F_7/2, with the average radiative lifetime ~0.28 ms. Yb³⁺ ion is reported to act as a donor or alternately as an energy transfer bridging ion between a donor and an acceptor ion in several glass systems [10]. In fact, efficient energy transfer processes from Yb³⁺ to Tm³⁺ ions [11] when excited at the wavelength corresponding to ²F_7/2 → ²F_5/2 transition of Yb³⁺ ion, intense R, G and B emissions were reported in different kinds of glass matrices [12–17].

For lasing ions, it is well-known that the combination of the energy gaps between the excited level and the one just below it and the maximum phonon energy (MPE) plays an important role in the non-radiative relaxation rate that influences luminescence efficiency significantly. For Tm³⁺ ions, different host materials show a great difference in the MPE value. Two most common host materials used for Tm³⁺ ions are silica and fluoride glass. Their MPE differs about several times, being 1,100 cm⁻¹ (silicate) and 550 cm⁻¹ (fluorides), respectively [18]. Large MPE of the silicate glasses limits its infrared transparency range less than 2.2 μm and improves its multi-phonon relaxation rates.

The thermo-physical, chemical and mechanical stability of the lithium silicate glasses can be improved by adding sesquioxides like Y₂O₃. In fact, the addition of Y₂O₃ to this type of glass systems is reported to enhance refractive index and to lower the phonon energy considerably. For these reasons, the glasses mixed with Y₂O₃ were proved to be high efficient luminescence materials [19, 20] and are being considered as good candidates for integrated optics, photonic and biomedical applications [21]. Further, solid-state laser materials consisting of Y₂O₃, were proved to have the efficient operation both in continuous wave operation and in pulsed regimes [22].

The principal goal of the present work is to study the fluorescent features of Tm³⁺ and Yb³⁺ ions and the up-conversion phenomenon involved in the Li₂O–Y₂O₃–SiO₂ glass system co-doped with Tm³⁺ and Yb³⁺ ions as a function of Y₂O₃ concentration. The variation of Y₂O₃ content in the glass network is expected to inculcate the structural modifications and local field variations around Ln³⁺ ion embedded in the glass network which influence luminescence transition probabilities.

2 Experimental

The following composition contents were chosen for the present study:

(49−x) Li₂O–xY₂O₃–50SiO₂: 1.0Tm₂O₃, (49−x) Li₂O–xY₂O₃–50SiO₂: 1.0Yb₂O₃ and (49−x) Li₂O–xY₂O₃–50SiO₂: 0.5Tm₂O₃ + 0.5Yb₂O₃ with x = 1.0–5.0 mol%.

The details of the composition are presented in Table 1.

Table 1 The details of the composition of glasses (in mol%)

Appropriate amounts of analytical grade reagents of Li₂CO₃, SiO₂, Y₂O₃, Tm₂O₃ and Yb₂O₃ powders (Metall, China), all in mol%, were thoroughly mixed in an agate mortar and melted in a platinum crucible in the temperature range of 1,400–1,450 °C in an automatic temperature-controlled furnace for about 1 h. The resultant bubble-free melt was then poured in a brass mould and subsequently annealed at 400 °C. The samples prepared were ground and optical polished to the dimensions of about 1 cm × 1 cm × 0.2 cm. The density d of the bulk samples was determined (to an accuracy of ±0.0001) by the standard principle of Archimedes’ using o-xylene (99.99 % pure) as the buoyant liquid. The mass of the samples was measured to an accuracy of 0.1 mg using Ohaus digital balance, Model AR2140 to evaluate the densities. The refractive index (n _d) of the samples was measured (at λ = 589.3 nm) using Abbe refractometer with mono bromo naphthalene as the contact layer between the glass and the refractometer prism. There is a provision in this apparatus to measure the refractive index up to an accuracy of ±0.0001. The methods adopted for recording optical absorption, photoluminescence were similar to those reported in our earlier papers [23, 24]. The fluorescence decay curves were recorded using spectrofluorometer Fluorolog-3 (HORIBA Jobin Yvon) fitted with pulsed xenon lamp of 450 W.

3 Results

From the measured values of the density and average molecular weight M of the samples, various other physical parameters such as rare earth ion concentration N _i, mean rare earth ion separation R _i and polaron radius for all the glass samples were evaluated and presented in Table 2. The dependence of density d on the concentration of Y₂O₃ for all the titled glasses shows slight enhancement with increasing Y₂O₃ content. The increasing density can be understood due to the replacement of Li₂O (molecular weight 29.88) by Y₂O₃ (molecular weight 225.81).

Table 2 Physical parameters of Li₂O–Y₂O₃–SiO₂ glasses doped with different concentrations of Tm₂O₃

The optical absorption spectra (Figs. 1, 2) of Tm³⁺ doped Li₂O–Y₂O₃–SiO₂ glasses mixed with different concentrations of Y₂O₃ recorded at room temperature in the wavelength range 400–1,800 nm, have exhibited the following absorption bands: ³H₆ → ¹G₄, ³F₂, ³F₃, ³H₄, ³H₅ and ³F₄. Among these, ³H₆ → ³H₅, ³F₄ transitions are found to be in the near-infrared region, ³H₆ → ¹G₄ in the blue region, whereas ³H₆ → ³F₂, ³F₃, ³H₄ transitions are in orange and red spectral regions. As shown in the Fig. 1, due to strong absorption of the host glass in the ultraviolet range, the absorption bands at wavelength shorter than 400 nm (viz., transitions to the multiplets above ¹G₄) could not be observed. Further, the NIR band corresponding to ³H₆ → ³H₅ transition is found to be relatively sharper in the spectra of all the glasses. The influence of Y₂O₃ content on the strength of absorption on each band could clearly be seen from these spectra.

Fig. 1

Absorption spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃ glasses mixed with different concentrations of Y₂O₃ (all the transitions are from the ground state ³H₆) in the visible region

Fig. 2

Absorption spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃ glasses mixed with different concentrations of Y₂O₃ (all the transitions are from the ground state ³H₆) in the NIR region

Experimental oscillator strengths (OS) of the absorption transitions are estimated from the absorption spectra in terms of the area under an absorption peak. The theoretical OS have been evaluated using the modified Judd–Ofelt theory as proposed in reference [25]. The OS of the electric dipole transition between two states have been calculated using the J–O theory, with the conventional equation [26, 27]. The $\left\| {U^{{{\uplambda}}} } \right\|$ reduced matrix elements used for evaluating OS have been re-calculated, using recent literature data on Tm³⁺ ions. Hamiltonian parameters were taken from Ref. [28]. The procedure of fitting of the calculated OS to those evaluated from the experimental spectra is described in [29]. A set of matrix equations (which includes the U², U⁴, and U⁶ matrices, the matrices of the experimental OS and the energies of the corresponding transitions) have been solved to minimize the difference between the calculated $f_{\text{calc}}$ and observed $f_{\exp }$ OS. The quality of fitting determined by the root mean squared deviation is presented in Table 3. The values of Ω_λ are found to be in the following order: Ω₂ > Ω₄ > Ω₆. The comparison of the data on Ω_λ parameters of Tm³⁺ ions in various other glass matrices [30–35] indicated the similar trend. The detailed values of Ω_λ for the Tm³⁺ doped glasses mixed with different concentrations of Y₂O₃ are presented in Table 4. The Ω₂ parameter is observed to decrease considerably with the concentration of Y₂O₃.

Table 3 The absorption band energies (cm⁻¹), the experimental (f _exp) and calculated (f _cal) oscillator strengths (×10⁻⁶) for the absorption transitions of Tm³⁺ doped Li₂O–Y₂O₃–SiO₂ glasses

Table 4 The summary of J–O parameters Ω_λ (×10⁻²⁰ cm²)

Figure 3 represents the optical absorption spectra of Yb³⁺ doped Li₂O–Y₂O₃–SiO₂ glasses recorded at room temperature in the wavelength region 800–1,200 nm. The spectra have exhibited an absorption band with a degeneracy corresponding to localized ²F_7/2 → ²F_5/2 transition of Yb³⁺ ion spreading over a spectral range covering 900–1,000 nm [36]. In the absorption spectra of co-doped glasses (Fig. 4), the bands due to transitions of both the ions are present. However, with the increase in the concentration of Y₂O₃ a significant increase in the intensity of all absorption bands is observed.

Fig. 3

Absorption spectra of Li₂O–Y₂O₃–SiO₂: Yb₂O₃ glasses mixed with different concentrations of Y₂O₃

Fig. 4

Absorption spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃/Yb₂O₃ glasses mixed with different concentrations of Y₂O₃

The luminescence spectra of all the studied glasses recorded at room temperature in the visible and NIR regions are shown in (Figs. 5, 6), respectively. The spectra exhibited the following prominent emission bands:

Fig. 5

Photoluminescence spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃ glasses mixed with different concentrations of Y₂O₃ in the visible region (λ _exc = 400 nm)

Fig. 6

Photoluminescence spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃ glasses mixed with different concentrations of Y₂O₃ in the NIR region (λ _exc = 400 nm)

$$\begin{array}{*{20}c} {{\text{Tm}}^{{3 + }} \left( {\lambda _{{{\text{exc}}}} = {\text{ }}400{\text{ nm}}} \right):\;^{1} {\text{D}}_{2} \to \,^{3} {\text{F}}_{4} ,\,^{3} {\text{H}}_{{4,5}} ,\,^{1} {\text{G}}_{4} \to \,^{3} {\text{H}}_{{5,6}} ,\,^{3} {\text{F}}_{4} \left( {{\text{vis}}{\text{. region}}} \right).} \\ {^{3} {\text{H}}_{5} \to \,^{3} {\text{H}}_{6} ,\,^{3} {\text{H}}_{4} \to \,^{3} {\text{F}}_{4} ,\,^{3} {\text{F}}_{4} \to \,^{3} {\text{H}}_{6} \left( {{\text{NIR region}}} \right)} \\ \end{array}$$

The luminescence spectra of Yb³⁺ solely doped Li₂O–Y₂O₃–SiO₂ glasses excited at 900 nm exhibited a broad luminescence band corresponding to standard ²F_5/2 → ²F_7/2 transition of Yb³⁺ ions (Fig. 7). As the concentration of Y₂O₃ is increased, the spectral intensity of this band is found to increase.

Fig. 7

Photoluminescence spectra of Li₂O–Y₂O₃–SiO₂: Yb₂O₃ glasses mixed with different concentrations of Y₂O₃ in the NIR region (λ _exc = 900 nm)

Figure 8 represents the luminescence spectra of Tm³⁺ and Yb³⁺ co-doped Li₂O–Y₂O₃–SiO₂ glasses excited at 400 nm. The spectra exhibited all emission bands due to both the ions including ²F_5/2 → ²F_7/2 transition of Yb³⁺ ions.

Fig. 8

Photoluminescence spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃/Yb₂O₃ glasses doped with different concentrations of Y₂O₃ (λ _exc = 400 nm)

In Fig. 9, the luminescence spectrum for one of the co-doped Li₂O–Y₂O₃–SiO₂ glasses (viz., TmYbY₅) excited at 900 nm is presented. The spectrum exhibited following intense R, B, G and NIR emission bands due to up-conversion phenomenon.

Fig. 9

Photoluminescence spectra of Li₂O–Y₂O₃–SiO₂: Tm₂O₃/Yb₂O₃ glasses mixed 5.0 mol% of Y₂O₃ in the visible and NIR region (λ _exc = 900 nm)

$$ {^{1}{\text{G}}_{4}} \to \,{^{3}{\text{H}}_{6}} \left( {\text{B}} \right),\,{^{1}{\text{G}}_{4}} \to \,{^{3}{\text{F}}_{4}} \left( {\text{G}} \right),\,{^{1} {\text{G}}_{4}} \to \,{^{3} {\text{H}}_{5}} \left( {\text{R}} \right){\text{ and }} {^{3} {\text{H}}_{4}} \to \, {^{3} {\text{H}}_{6}} \left( {\text{R}} \right)\, {^{3} {\text{H}}_{4}} \to \, {^{3} {\text{F}}_{4}} \left( {\text{NIR}} \right). $$

As the concentration of Y₂O₃ is increased the intensity of these three bands is observed to increase. In addition, the band due to ²F_5/2 → ²F_7/2 transition of Yb³⁺ ions is also observed in the spectra of all the glasses.

Figure 10 represents the energy level diagram containing the up-conversion transitions for one of the co-doped glasses (viz., TmYbY₅) excited at 900 nm. Using these spectra and Ω_λ parameters, the radiative transition probability, radiative life time $\tau$ of upper level and the branching ratio $\beta_{{{\text{JJ}}'}}$ for each transition are evaluated and presented in Table 5. Following the shapes of spectral lines, we have estimated approximately scattering losses and found that these are less than 4 % as such do not disturb the principal peaks.

Fig. 10

Principal energy level diagram showing energy transfer from Tm³⁺ to Yb³⁺ ions in co-doped Li₂O–Y₂O₃–SiO₂ glasses

Table 5 Radiative properties of Li₂O–Y₂O₃–SiO₂: Tm₂O₃ glasses for the two principal transitions

4 Discussion

Among various constituents of Li₂O–Y₂O₃–SiO₂ glass composition, SiO₂ is a well-known glass former and participates in the glass network with tetrahedral [SiO_4/2]⁰ units and all the four oxygens in SiO₄ tetrahedral are shared. On addition of modifiers like Li₂O, the Si–O–Si linkage is broken and form Si–O⁻ termination. Thus, the structure is depolymerised and there will be formation of meta, pyro and ortho-silicates viz., [SiO_4/2]⁰, [SiO_3/2O]⁻, [SiO_2/2O₂]²⁻, [SiO_1/2O₃]³⁻ and [SiO₄]⁴⁻ as per the following equilibrium [37]:

$$ \begin{gathered} 2\left[ {{\text{SiO}}_{4/2} } \right]^{0} + {\text{ Li}}_{2} {\text{O}} \to \,2\left[ {{\text{SiO}}_{3/2} {\text{O}}} \right]^{ - }\,+\,2{\text{Li}}^{ + } \hfill \\ 2\left[ {{\text{SiO}}_{2/2} {\text{O}}_{2} } \right]^{2 - } + {\text{ Li}}_{2} {\text{O }} \to \, 2\left[ {{\text{SiO}}_{1/2} {\text{O}}_{3} } \right]^{3 - }\,+\,2{\text{Li}}^{ + } \hfill \\ \end{gathered} $$

In general, Y₂O₃ participates in the glass network with tetrahedral (YO₄) and octahedral (YO₆) occupancy. The YO₄ tetrahedra alternate with SiO₄ groups, whereas octahedral yttrium ions occupy interstitial positions [38] and induce bonding defects in the glass network.

The concentration of tetrahedral and octahedral positions of yttrium ions depends upon the content of Y₂O₃ in the glass network [39, 40]. The ytterbium ion is expected to be coordinated by three SiO₄/YO₄ tetrahedral ligands. The evidence for six-fold coordination of Yb³⁺ in different glasses was derived from the application of crystal field theory on the basis of optical absorption and emission spectra by Robinson et al. [41]. The YbO₆ spheres can be assumed to be surrounded by yttrium ions of different cationic field strengths and polarizabilities. Although such specific coordination number cannot be assigned to Tm³⁺ ions, the variation in the concentration of yttrium ions also causes variations in the crystal field strength around Tm³⁺ ions. Such variations in the concentration of different structural units of Y₂O₃ and silicate groups around Ln³⁺ ions might be responsible for the observed differences of the luminescence intensity of various transitions of these samples.

Out of the three J–O parameters, the values of Ω₄ and Ω₆ are expected to be influenced strongly by the vibrational levels associated with the central rare earth ions bound to the ligand atoms, whereas Ω₂ depends on the covalence and distortion related to structural changes in the neighbourhood of rare earth ions (short-range effect).

The observed decreasing trend of Ω₂ parameter with the increase in the content of Y₂O₃ indicates decreasing interaction of rare earth ions with the ions of the host materials due to increasing distortion or structural change in the vicinity of rare earth ions. As the concentration of Y₂O₃ is increased, there may be an increasing concentration of YO₆ structural units that induce bonding defects. Hence, the larger the concentration of modifying ions, the larger will be the average distance between silicates, inter lithium silicates and Si–Y chains. This ultimately leads to the increase of average bond length of Tm–O causing weaker field around Tm³⁺ ion. This leads to the decreasing value of Ω₂ with increase in the concentration of Y₂O₃.

For Tm³⁺ doped glasses (TmY₅), the value of β (branching ratio) of the blue emission (¹D₂ → ³F₄ and ¹G₄ → ³H₆) is found to be ~50 %, whereas for the red emission (¹G₄ → ³H₅) it is ~39 %; a slight variation in these values could be observed with Y₂O₃ concentration.

The fluorescence decay curve of the blue emission corresponding to ¹G₄ → ³H₆ transition of Tm³⁺ doped glass (TmY₅) is shown in (Fig. 11); the curve viewed to be single exponential. The decay curves recorded for other glasses have also exhibited similar behavior. The radiative life time τ, evaluated from these curves for the transition ¹G₄ → ³H₆ is presented in Table 6.

Fig. 11

Fluorescence decay curves of the blue emission for Tm³⁺ and co-doped glasses mixed with 5 mol% of Y₂O₃ corresponding to the emission line ¹G₄ → ³H₆ at 400 nm

Table 6 Radiative life times for ¹G₄ level of Tm³⁺ ion in Li₂–Y₂O₃–SiO₂ glasses

The radiative decay rate for the given upper level is defined as $\frac{1}{{\tau_{\text{m}} }} = A_{\text{rad}}$. In addition, energy transform multi-phonon decays (harmonic and anharmonic) may also contribute to the above term. Overall, for the studied samples the radiative life time is observed to increase with the increase in concentration of Y₂O₃ indicating decreasing trend of vibrational losses with increase in the concentration of Y₂O₃. Thus, the measurements on radiative life times also support the viewpoint that there is a decreasing tendency of interaction between the rare earth ions and glass network with increase in the concentration of Y₂O₃.

Up-conversion mechanism involved Yb³⁺ and Tm³⁺ co-doped glasses can be understood as follows: With 900 nm excitation of the co-doped glasses, the Yb³⁺ ion goes to ²F_5/2 excitation level and de-excites to the ²F_7/2 level. The resulting emitted photon excites the Tm³⁺ ions from ³H₆ to ³H₅, ³F₄ to ³F₃ and ³H₄ to ¹G₄. The ¹G₄ level is further populated by non-radiative decays and internal excitations viz., three-photon absorption processes shown as a, b and c in Fig. 10. Subsequent transitions from ¹G₄ to ³H₅, ³F₄ and ³H₆ give rise to blue, green and red emissions, respectively.

The corresponding rate equations for the Tm³⁺ ion under co-doping conditions can be written as:

For Tm³⁺ ions:

$$ \frac{{{\text{d}}n_{1} }}{{{\text{d}}t}} = W_{51} n_{5} + W_{1'1} n_{1'} + \varphi \sigma_{12} n_{1} + W_{31} n_{3} - (C_{1} + \tau_{1}^{ - 1} )n_{1} $$

(1)

$$ \frac{{{\text{d}}n_{2} }}{{{\text{d}}t}} = W_{52} n_{5} + \varphi V_{02} n_{0} + W_{42} n_{4} - (C_{2} + \tau_{2}^{ - 1} )n_{2} $$

(2)

$$ \frac{{{\text{d}}n_{3} }}{{{\text{d}}t}} = W_{{1^{\prime}3}} n_{{1^{\prime}}} + \varphi \sigma_{43} n_{4} - (C_{3} + \tau_{3}^{ - 1} )n_{3} $$

(3)

$$ \frac{{{\text{d}}n_{4} }}{{{\text{d}}t}} = W_{54} n_{5} + \varphi V_{14} n_{1} - (C_{4} + \tau_{4}^{ - 1} )n_{4} $$

(4)

$$ \frac{{{\text{d}}n_{5} }}{{{\text{d}}t}} = \varphi V{}_{35}n_{3} - (C_{5} + \tau_{5}^{ - 1} )n_{5} $$

(5)

For Yb³⁺ ions:

$$ \frac{{{\text{d}}n_{{1^{'} }} }}{{{\text{d}}t}} = \varphi V_{{0^{'} 1^{'} }} n_{{0^{'} }} - \varphi_{{1^{'} 0}} n_{{1^{'} }} - \varphi_{{1^{'} 1}} n_{{1^{'} }} - \varphi_{{1^{'} 3}} n_{{1^{'} }} - (C_{{1^{'} }} + \tau_{{1^{'} }}^{ - 1} )n_{{1^{'} }} $$

(6)

Solving Eqs. (1–6) as per the procedure reported in our earlier papers [23] the population of the energy level 5 (¹G₄) is estimated as

$$ n_{5} = \frac{{\varphi^{2} V{}_{35}\,V_{{0^{\prime}1^{\prime}}} \,W_{{1^{\prime}3}} \,n_{{0^{\prime}}} }}{{(\varphi_{{1^{\prime}0}} + \varphi_{{1^{\prime}1}} + \varphi_{{1^{\prime}3}} + \,(C_{{1^{\prime}}} + \tau_{{1^{\prime}}}^{ - 1} ))\,(C_{5} + \tau_{5}^{ - 1} )\,(C_{3} + \tau_{3}^{ - 1} )}} + \frac{{\varphi^{2} V{}_{35}\,\sigma_{43} \,(W_{54} \,n_{5} + \varphi V_{14} \,n_{1} )}}{{(C_{5} + \tau_{5}^{ - 1} )\,(C_{3} + \tau_{3}^{ - 1} )\,(C_{4} + \tau_{4}^{ - 1} )}} $$

(7)

In the above equations n ₀ and n _i represent the populations of the ground state and the excited level i, respectively, W _ij represents transitions between levels i and j of the rare earth ion, τ _i indicates the life time of level i of rare earth ion and C _i represents the energy quenching rates. The absorption cross-section for each transition is denoted by V _ij , whereas the incident pumping flux is indicated by φ.

The total population of ¹G₄ level represented by Eq. (7) depends on up-conversion from ground state of Yb³⁺ ions and also from its own levels due to step wise up-conversion mechanism as explained in the text. The energy transfer efficiency parameter (η _eff) from Yb³⁺ to Tm³⁺ can be written as:

$$ \eta_{\text{eff}} = 1 - \frac{{\tau_{\text{Tm\,+\,Yb}} }}{{\tau_{\text{Tm}} }} $$

(8)

The value of η _eff for the emission from ¹G₄ level for the glass, TmYbY₅, is found to be 38 %. The variation of η _eff indicated an increasing trend with increasing the concentration of Y₂O₃ (Table 7).

Table 7 Measured radiative life times for ¹G₄ level of Tm³⁺/Yb³⁺ co-doped Li₂–Y₂O₃–SiO₂ glasses and energy transfer parameter

5 Conclusions

We have established principal role of Y₂O₃ on the features of the photoluminescence spectra of Tm³⁺, Yb³⁺ ions in Li₂O–Y₂O₃–SiO₂ glass system. With increase in the concentration of Y₂O₃ a slight red shift in the peak positions with considerable increase in the intensity of various emission bands could clearly be seen. When Tm³⁺ and Yb³⁺ are present together in the glass, the incident radiation ²F_5/2 → ²F_7/2 (900 nm) excites both the ions. For Tm³⁺ ion, the excitation takes place from ³H₆ to ¹G₄ level by absorbing three photons and transitions takes place to ³H₆, ³H₄ and ³F₄ levels giving rise to blue, green and red emission.

The observed decreasing trend of Ω₂ parameter with the increase in the content of Y₂O₃ indicates decreasing interaction of rare earth ions with the ions of the host materials. This is due to the increasing distortion or structural change in the vicinity of rare earth ions due to the growing presence of octahedral yttrium ions that act as glass modifiers.

The ³H₄ level of Tm³⁺ ions is populated due to the non-radiative relaxation from ³F₂ or ³F₃ levels and de-excited to ³F₄ level. In view of these, more intense ³H₄ → ³F₄ (~1.5 μm) NIR emission in the co-doped samples is observed in the glasses mixed with higher concentration of Y₂O₃.