1. Introduction

In today’s technological age, there is a constant demand for new optical materials taking advantage of a variety of their properties. LiLa₉(SiO₄)₆O₂ (LLS) belongs to the nesosilicate family that can be easily synthetized in the form of small hexagonal transparent rods with a partially disordered lattice analogous to that of apatite [1,2].

Apart from the good optical, thermal and mechanical characteristics exhibited by apatite-structure materials [3], LLS presents the advantage of containing Lanthanum as one of its cationic lattice. This feature represents an additional advantage in comparison to other materials as it enables the incorporation of active trivalent lanthanide ions in large doping levels without the need of charge compensation, preserving the crystal quality and homogeneity needed for technological applications.

The highly efficient energy transfer processes that occur between Er³⁺ and Yb³⁺ ions make them some of the most attractive rare-earths (RE) to activate crystalline and amorphous materials. In fact, this high efficiency in the transfer processes from Yb³⁺ to Er³⁺ has played a fundamental role in the development of Er³⁺/Yb³⁺ co-doped materials with different functionalities such as optical amplifiers and solid state lasers operating at different wavelengths [4–7] and efficient up-converting submicron- and nano-sized phosphors [8–13]. In this wide variety of applications Yb³⁺ acts as sensitizer, providing its high absorption cross section as well as its broad absorption band (900 – 1100 nm) to excite the Er³⁺ luminescence via energy transfer. However, these ion-ion interactions can be useful or unsuitable depending on the concentration range and the final desired application, as they can potentiate or quench a luminescent band depending on the concentration range. Therefore, the knowledge and quantification of these cross-relaxation mechanisms between Er³⁺ and Yb³⁺ ions is an essential tool to optimize and assure the technological application of the co-doped material.

In this work, the energy transfer between Yb³⁺ and Er³⁺ ions in LLS crystals is investigated under selective Er³⁺ excitation. CW experiments, performed under Ti:Sapphire pumping, reveal an efficient energy transfer from Yb³⁺ to Er³⁺ (around ten times larger than the back transfer from Er³⁺ to Yb³⁺). The dynamics of the main emission bands have been also explored, in this case by using the second harmonic of a pulsed Nd:YAG laser. These measurements have allowed the full quantification of the macroscopic transfer and back transfer coefficients as well as the detection, and characterization, of a quenching process that affects the relaxation of the Er³⁺ green emitting levels. The macroscopic parameters have been used to establish a rate-equation model that can be used to describe the dynamics of Er³⁺/Yb³⁺ co-doped LLS crystals.

2. Experimental procedure

Co-doped LiLa₉(SiO₄)₆O₂:Er³⁺/Yb³⁺ single crystals have been grown by the flux technique following the procedure reported elsewhere [14]. The starting melts have a fixed Er³⁺ concentration (1 mol %) and five different Yb³⁺ concentrations (0, 1, 2, 5, 10 mol %). Table 1 summarizes the rare-earth concentration in the different samples (1 mol% = 1.54 × 10²⁰ ions/cm³).

Table 1. Er³⁺ and Yb³⁺ concentrations in the studied samples

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The grown crystals present a prismatic shape with a size up to 0.5 × 1 × 2 mm³ and good optical quality and homogeneity as it can be observed in the optical microscope photograph shown in Fig. 1.

 

Fig. 1 Optical microscope photograph showing the morphology of the LLS grown crystals.

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Spectroscopic measurements were performed by using two different excitation sources, a Millenia pumped Ti:Sapphire laser for exploring the CW-regime and a Nd:YAG laser (Spectra Physics model DCR 2/2A 3378, linked to a harmonic generator) to investigate the temporal dynamics. Independently from the excitation regime, the signal was dispersed through an ARC monochromator model SpectraPro 500-I and then detected by a Thorn Emi photomultiplier (QB9558) or an InGaAs Judson photodiode depending on the spectral region (visible or IR radiation, respectively). Additionally, for lifetime measurements, the signal was synchronously detected and recorded by a TEKTRONIX TDS 420 oscilloscope.

3. Results and discussion

3.1 CW pumping: ratio between the energy transfer coefficients

The 4f¹¹ electronic configuration of Er³⁺ ions splits into a wide energetic distribution of ^{2S + 1}L_J multiplets, when they are embedded in a solid. Such variety of energy levels makes possible the use of several excitation schemes to explore the spectroscopic properties of Er³⁺/Yb³⁺ co-doped samples. In the present work, we have chosen CW excitation at λ = 800 nm for several reasons. First, it minimizes sizeable up-conversion processes at sufficiently low pump powers; second, it provides a convenient way of excitation to Er³⁺ ions that does not interfere with the relevant emissions of interest in near infrared and, finally but not less important, it is adequate from the experimental point of view, considering the availability of suitable excitation sources (Ti:Sapphire laser or semiconductor laser diodes). For all these reasons, 800 nm becomes an excellent pumping wavelength for the present study.

Figure 2(a) shows the emission bands in the 900 – 1700 nm spectral range measured in samples #1 and #2 (singly Er³⁺-doped and Er³⁺/Yb³⁺ co-doped, respectively), under selective excitation at 800 nm (⁴I_15/2 → ⁴I_9/2 Er³⁺ absorption band). As it is sketched in Fig. 2(b), the excitation to the ⁴I_9/2 level efficiently populates the lower lying level, ⁴I_11/2, via non radiative relaxation [15]. In Er³⁺ singly doped samples, as it is the case of sample #1, the decay from this level is basically governed by the non-radiative connection to the ⁴I_13/2 manifold. As a consequence, the most intense band in its IR emission spectrum corresponds to the ⁴I_13/2 → ⁴I_15/2 transition (λ_emi ~1.5 μm) while only a weak luminescence from the ⁴I_11/2 → ⁴I_15/2 transition (λ_emi ~1.0 μm) can be detected (note that in the figure the 1.0 μm band has been enlarged by a factor × 10).

 

Fig. 2 (a) Infrared emission spectra measured in samples #1 and #2 under selective Er³⁺ excitation at 800 nm (blue and red lines respectively). (b) Partial energy level diagram showing the dominant emission bands and energy transfer processes observed after excitation at 800 nm.

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In Er³⁺/Yb³⁺ co-doped samples, the presence of Yb³⁺ ions opens an additional relaxation route for the ⁴I_11/2 Er³⁺ manifold: the energy transfer process ⁴I_11/2 → ⁴I_15/2 (Er³⁺): ²F_7/2 → ²F_5/2 (Yb³⁺) [16–18]. This transfer mechanism excites the Yb³⁺ ions to the ²F_5/2 level, which relaxes to the ground state giving luminescence that partially overlaps with the ⁴I_11/2 → ⁴I_15/2 Er³⁺ transition. Then, in the case of sample #2, the intensity of the luminescence band around 1.0 μm becomes substantially higher than in the Er³⁺ singly doped sample. The energetic coincidence of the ⁴I_11/2 (Er³⁺) and ²F_5/2 (Yb³⁺) excited states makes it possible that the transfer operates not only from Er³⁺ to Yb³⁺ but also in the opposite direction, that is from Yb³⁺ to Er³⁺. Under CW pumping, the populations of the resonant ⁴I_11/2 (Er³⁺) and ²F_5/2(Yb³⁺) levels reach a dynamical equilibrium, and the relative intensities of the emissions at 1.0 μm in Er³⁺- doped and Er³⁺/Yb³⁺ co-doped samples allows the determination of the ratio between transfer (C₂₅) and back transfer (C₅₂) coefficients, as will be shown next.

Figure 2(b) illustrates the most relevant optical processes after selective excitation of Er³⁺ ions (λ_exc = 800 nm) via the ⁴I_15/2 → ⁴I_9/2 absorption band. Excitation power is kept sufficiently low to assure that: i) there is negligible ground state depletion, so that the population of the ground state of Er³⁺ and Yb³⁺ ions remains basically constant and coincident with the corresponding RE concentrations (N_Er and N_Yb), and ii) it is possible to neglect up-conversion processes.

Under these conditions, the population dynamics of the infrared levels can be described by the following rate equations:

Under CW pumping, after reaching steady state conditions (dN_i/dt = 0), from Eqs. (3)–(5):

That is, after reaching the stationary regime, the ratio of populations of the resonant ⁴I_11/2 (Er³⁺) and ²F_5/2(Yb³⁺) manifolds is governed, apart from RE concentrations by the ratio between the transfer and back transfer coefficients that can be experimentally determined. In order to do that, it is usual to define (P_r) as the ratio between the Er³⁺ emission at around 1.0 μm (P₅₃) over the total Er³⁺/Yb³⁺ emission also at 1.0 μm (P₅₃ + P₂₁) [16,18]:

Thus, measuring P_r in samples with fixed Er³⁺ concentration and variable Yb³⁺ concentrations, the quantity (1- P_r)/P_r should give a linear dependence on ytterbium concentration and the slope of such fit (β) links the transfer and back transfer coefficients by the relationship:

Nevertheless, from the experimental point of view, in co-doped samples it is impossible to measure the ⁴I_11/2 → ⁴I_15/2 (Er³⁺) and ²F_5/2 → ²F_7/2 (Yb³⁺) emissions around 1.0 μm independently, see Fig. 2(a). Therefore, the standard procedure [16–18] is to compare the overall Er³⁺/Yb³⁺ emission at 1.0 μm (P₂₁ + P₅₃) with the Er³⁺ emission at 1.5 μm (P₄₃, ⁴I_13/2 → ⁴I_15/2), which ratio with the ⁴I_11/2 → ⁴I_15/2 can be evaluated from Er³⁺ singly doped samples [16].

Then, according to Eq. (11), the experimental P_r values were determined from the emission bands at 1.0 μm and 1.5 μm measured for different doping levels (samples #1 - #5), and the calculated (1- P_r)/P_r values are represented in Fig. 3.

 

Fig. 3 Least squares fit of (1 - P_r)/P_r as function of Yb³⁺ concentration.

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As it can be observed, the experimental data can be conveniently fit by a linear dependence with a slope value β = (1.63 ± 0.05) × 10⁻²⁰ cm³ which together with the known spectroscopic parameters (Table 2), gives the numerical values that link the transfer coefficients C₂₅ and C₅₂ through Eq. (10).

Table 2. Radiative, A_ij, and total, A_im = τ_i,exp⁻¹ = Σ_j A_ij + W_ij^NR , transition probabilities.

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In order to obtain the absolute values of these transfer parameters we shall examine the temporal dynamics under pulsed excitation.

3.2 Pulsed excitation: full quantification of the energy transfer coefficients

The second harmonic of a pulsed Nd:YAG laser (λ_exc = 532 nm) has been used as excitation source to explore the temporal dynamics of the Er³⁺ and Yb³⁺ excited states. The emission spectra in the visible range, measured in samples #1 and #2, are depicted in Fig. 4(a).

 

Fig. 4 (a) Visible emission spectra measured in samples #1 and #2 under selective Er³⁺ excitation at 532 nm (blue and red solid lines respectively). (b) Partial energy level diagram showing the dominant emission bands and energy transfer processes observed after excitation at 532 nm.

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Now the pumping wavelength populates the ²H_11/2:⁴S_3/2 Er³⁺ thermally coupled manifolds through the ⁴I_15/2 → ²H_11/2 absorption band giving rise to the occurrence not only of the previously mentioned IR emission bands (λ_emi ~1.0 μm and λ_emi ~1.5 μm), but also an additional luminescent band in the visible spectral range (λ_emi ~550 nm) associated to the radiative decay from the ²H_11/2:⁴S_3/2 levels to the ground state. Then, as it is sketched in Fig. 4(b), this excitation scheme results adequate to explore the temporal dynamics of ²H_11/2:⁴S_3/2 and ⁴I_13/2 Er³⁺ manifolds as well as that corresponding to the resonant levels, ⁴I_11/2 (Er³⁺):²F_5/2 (Yb³⁺).

The temporal evolution of ²H_11/2:⁴S_3/2 → ⁴I_15/2 transition as function of Yb³⁺ concentration measured under resonant pumping (samples #1 to #5), is presented in Fig. 5(a).

 

Fig. 5 (a) Temporal evolution of the ²H_11/2:⁴S_3/2 → ⁴I_15/2 emission band as function of Yb³⁺ concentration. (b) Estimation of the C_GQ energy transfer coefficient associated to the cross relaxation process ⁴S_3/2 → ⁴I_13/2 (Er³⁺):²F_7/2 → ²F_5/2 (Yb³⁺).

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As it can be observed, after pulsed laser excitation (pulse width ~10 ns), the luminescent signals decay following a single exponential dependence with a lifetime value that decreases as Yb³⁺ concentration increases. Within the Yb³⁺ co-doping levels explored in this work, the ²H_11/2:⁴S_3/2 lifetime is slightly reduced in comparison to the intrinsic lifetime value, τ₀ = 5.0 μs, measured in the Er³⁺ singly doped LLS sample (sample #1). This reduction in the lifetime of the green emitting manifolds has been previously reported in other Er³⁺/Yb³⁺ co-doped materials and it is due to the occurrence of a quenching process involving Yb³⁺ ions [19–21].

The presence of Yb³⁺ ions opens a new de-excitation channel that partially depopulates the ²H_11/2:⁴S_3/2 manifolds transferring the excitation to the ⁴I_13/2 (Er³⁺) and ²F_5/2 (Yb³⁺) excited states, via the non-resonant cross relaxation process ⁴S_3/2 → ⁴I_13/2 (Er³⁺):²F_7/2 → ²F_5/2 (Yb³⁺). This additional mechanism has been also included in Fig. 4(b), and its probability will be quantified by a new transfer coefficient, C_GQ.

In order to model the dynamics of the LLS:Er³⁺/Yb³⁺ system under this pulsed excitation scheme (λ = 532 nm, see Fig. 4(b)), it is necessary to consider a new set of rate-equations including the additional de-excitation paths operative under this pumping, the quenching mechanism and the ⁴F_9/2 Er³⁺ level.

Equation (12) contains now the pumping term that populates the ²H_11/2:⁴S_3/2 manifolds during the laser pulse width and it predicts a single exponential decay when the pulse ends. This equation implies that, for moderate pumping levels (N₁ ≈N_Yb), the experimental lifetime of these coupled manifolds depends on Yb³⁺ concentration as:

Following Eq. (12), the measured lifetime values (τ_exp) have been used to evaluate the quantity (τ_exp⁻¹- A_7m) as function of Yb³⁺ concentration. In fact for a given Yb³⁺ concentration, this value gives the energy transfer probability, W_TR, at this doping level, see for instance [22]. Therefore, Eq. (19b) can be used to quantify the C_GQ transfer coefficient. The least squares fit of the transfer probability values are presented in Fig. 5(b). As it can be seen, in good accordance with Eq. (19b), W_TR increases linearly with ytterbium concentration and the slope of the linear fit gives directly the transfer coefficient that quantifies the energy transfer between ⁴S_3/2(Er³⁺) and ²F_7/2 (Yb³⁺):

Then, it is possible now to use the rate-equation model, Eqs. (12)–(18), to describe the temporal evolution of all Er³⁺ and Yb³⁺ emission bands, after 532 nm pulsed excitation. The spectroscopic parameters indicated in Eqs. (12)–(18) are summarized in Table 2, including the lifetime of LLS:Yb³⁺ measured also in the present work (sample #0).

The set of coupled differential equations were integrated as function of Yb³⁺ concentration by using a fourth order Runge-Kutta algorithm and the transition probabilities and transfer coefficients shown in the Table. The numerical integration allows the calculation of the temporal evolution corresponding to the different luminescent emissions, including their decay times as well as the associated rise-times. The only fitting parameter used is the value of one of the Er³⁺ ↔ Yb³⁺ transfer coefficients, given that the other one remains linked by the relationship Eq. (10) determined from CW experiments.

Figure 6 shows the experimental lifetimes of the resonant ⁴I_11/2 (Er³⁺):²F_5/2 (Yb³⁺) manifolds (dots) as function of Yb³⁺ concentration. As it can be seen, the presence of Yb³⁺ ions induces a lengthening of the lifetime value, from τ = (20 ± 1) μs (intrinsic value of ⁴I_11/2 level) up to τ = (86 ± 5) μs, when Yb³⁺ doping level is 10 times higher than the Er³⁺ content (sample #5).

 

Fig. 6 Experimental (dots) and predicted lifetimes (lines) of the resonant levels, ⁴I_11/2(Er³⁺):²F_5/2(Yb³⁺), as function of Yb³⁺ concentration.

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The experimental data can be fit by using a constant transfer coefficient using a least square criterion; the best fit is obtained for C₂₅ = 9.5 × 10⁻¹⁷ cm³s⁻¹. The back transfer coefficient C₅₂ = 1.4 × 10⁻¹⁷ cm³s⁻¹ is determined by inserting the C₂₅ value in the experimental relationship given by Eq. (10). The calculated lifetime values are quite sensitive to small variations in the transfer coefficients. Estimated dependencies with ± 5% variations are included in the Fig. 6 (dotted lines).

To illustrate this fact some calculated dependencies using slightly different values for the transfer parameter (C₂₅) have been included in the figure.

The obtained transfer parameters indicate that the efficiency of the transfer process (Yb³⁺ → Er³⁺) is significantly higher than that associated to the back transfer (Er³⁺ → Yb³⁺). Then, it can be expected that Yb³⁺ ions were ideal candidates to act as sensitizers of Er³⁺ luminescence in LLS crystals.

In Fig. 7, the temporal evolution of the luminescence bands measured in sample #4 (symbols) are compared with those predicted by the rate-equation model (solid lines) using the calculated transfer coefficients; that is, C_GQ = 6.1 × 10⁻¹⁷ cm³s⁻¹, C₂₅ = 9.5 × 10⁻¹⁷cm³s⁻¹ and C₅₂ = 1.4 × 10⁻¹⁷cm³s⁻¹.

 

Fig. 7 Temporal evolution of the dominant emission bands in sample #4: measured after pulsed excitation at 532 nm (symbols) and calculated by numerical integration (solid lines).

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The numerical integration, lines in Fig. 7, represents the predictions of the rate equations without any further recalculation of the parameters. It can be observed that the predictions are in excellent agreement with the observed experimental dynamics: the decays as well as the rise-times of the IR emission bands are very well reproduced. These rise-times are originated by the time required to activate the decay paths (energy transfer and the radiative and non-radiative connections) that populate the ²F_5/2, ⁴I_11/2 and ⁴I_13/2 manifolds from the upper levels.

As a summary, the dependencies of the lifetimes corresponding to ⁴I_13/2, ⁴I_11/2 (Er³⁺):²F_5/2 (Yb³⁺) and ²H_11/2:⁴S_3/2 manifolds on Yb³⁺ concentration are shown in Fig. 8, where the experimental data (dots) are compared with the predictions of the model (solid lines). As it can be seen, model and experiments indicate that while the three cross relaxation mechanisms modify the temporal dynamics of the green emitting levels and the resonant manifolds, the dynamics of the Er³⁺ metastable level remains unaltered.

 

Fig. 8 Experimental (symbols) and calculated (solid lines) lifetimes, under excitation at 532 nm, for the three main luminescence emissions of LLS:Er³⁺/Yb³⁺ as function of Yb³⁺ concentration.

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Finally it should be noted that, although the transfer coefficients have been quantified and checked under specific excitation schemes, the knowledge of the C_GQ, C₂₅ and C₅₂ values will represent an essential tool to understand other pumping wavelength dependent effects such as the infrared-to-visible energy conversion under Yb³⁺-excitation.

4. Conclusions

The analysis of the infrared luminescence of Er³⁺/Yb³⁺ co-coped LLS samples under CW Er³⁺ excitation indicates that transfer and back transfer coefficients are not independent but are linked by a linear relationship including decay rates of the emitting levels and Er concentration, given by Eq. (10), that can be determined by comparing the IR emissions at 1.0 μm and 1.5 μm.

The absolute values of these coefficients can be calculated examining the temporal dynamics under pulsed excitation. By comparing the experimental data with the predictions of a model based on the rate-equation formalism, the transfer and back transfer coefficients have been determined: C₂₅ = 9.5 × 10⁻¹⁷cm³s⁻¹ and C₅₂ = 1.4 × 10⁻¹⁷ cm³s⁻¹.

Additionally, the experimental results obtained for the green emission reveal that the presence of Yb³⁺ ions opens a quenching mechanism that reduces the lifetime of the ²H_11/2:⁴S_3/2 Er³⁺ manifolds. The macroscopic coefficient associated to this non-resonant cross-relaxation has been also quantified: C_GQ = 6.1 × 10⁻¹⁷cm³s⁻¹.

The three transfer coefficients above mentioned can be used to predict the temporal dynamics of the main emission bands of Er³⁺/Yb³⁺ co-doped LLS.