1. Introduction

Glasses doped with rare-earth (RE) are widely used in erbium-doped fiber amplifiers (EDFA). These amplifiers are still bulky and expensive which limit their use to long-distance applications. In order to produce compact amplifiers, the doping concentration has to be increased to chemical and physical limits. Unfortunately, the greatest risk of heavy doping is the formation of ionic clusters, which may appear as chemical clusters (i.e. chemically or structurally distinct inclusions) or physical clusters (or clusters of interaction) where the excitation effectively migrates from one Er³⁺ ion to another [1]. The energy migration may occur as direct ion-to-ion excitation transfer or as radiation trapping. In the first case, the energy is primarily relayed by dipole-dipole (or more generally multipole-multipole) ion-ion interactions [2,3]. This kind of interaction usually reduces the photoluminescence (PL) decay time (τ_D) and leads to the effect of self-quenching. In the radiation trapping effect, photons that are spontaneously emitted from a metastable level are trapped by reabsorption by ions in the ground state. These emerging excited-state ions then relax by spontaneously emitting more photons, which are then reabsorbed, and the entire process is repeated. As a result, the radiation trapping may substantially increase τ_D. The interplay of radiation trapping and self quenching may lead to a substantial difference between measured PL decay time and the real radiative lifetime. In the present paper, we discuss this problem in terms of the ⁴I_15/2–⁴I_13/2 transitions in Er³⁺ ions embedded in chalcogenide GeGaSe and GeGaS glasses. The details of glass preparation have been described elsewhere [4,5].

2. The importance of radiation trapping in Ge-Ga-S and Ge-Ga-Se glasses

Figure 1(a) offers direct experimental proof of the existence of radiation trapping in the case of ⁴I_15/2–⁴I_13/2 transitions in Er³⁺ ions in GeGaSe and GeGaS glasses. In these experiments, GeGaSe:Er and GeGaS:Er glass samples are positioned on the top or/and inside of the “black box” whose top and bottom are made of Si wafers and walls are non-transparent. The PL corresponding to the ⁴I_13/2–⁴I_15/2 transition (around 1.54 µm) is detected by a Ge photodiode with Si wafers playing the role of filters cutting off the scattered excitation light (808 nm) and unwanted highest PL bands (at around 980, 810, 660 nm etc.). Figure 1(a) clearly shows that the PL decays labeled (1) and (3), corresponding to GeGaS:Er and GeGaSe:Er placed on the top of the box, are nearly exponential with very different characteristic decay times. However, the PL decay (2), corresponding to GeGaS:Er inside and GeGaSe:Er on the top of the box, is clearly non-exponential. Moreover, the decay curve (2) can be presented as a sum of two exponentials (“slow” and “fast”) whose characteristic times are exactly equal to those of decays in (1) and (3). The natural explanation of this experiment is that the PL emitted by GeGaSe:Er is partially absorbed and later re-emitted by GeGaS:Er. In other words, the PL from GeGaSe:Er is used to pump the PL in GeGaS:Er. Figures 1(b) and 1(c) justify the likelihood of this process by showing that emission and absorption bands in GeGaSe:Er and GeGaS:Er are not only practically identical but also strongly overlap. Therefore, the emitted PL quantum may be easily reabsorbed by a previously unexcited Er³⁺ ion. One should keep in mind also that the branching ratio for the ⁴I_13/2–⁴I_15/2 transition is equal to unity and that radiative recombination dominates the relaxation [6]. These conditions are known to be highly favorable for severe radiation trapping [7].

 

Fig. 1. (a). PL decay in GeGaS:Er (1) and GeGaSe:Er (3) glasses after the interruption of excitation, measured in configurations shown in insets (1)–(3) of Fig. (a). In configuration (2), the PL emitted by GeGaSe:Er glass is used to pump the PL in GeGaS:Er. The exact composition of GeGaSe:Er glass is Ge₂₈Ga_6.2Se_64.5S_0.8:Er_0.5. A small amount of S appears from Er₂S₃ which is the dopant used. The composition of GeGaS:Er is Ge₂₈Ga_6.2S_65.3:Er_0.5. The glass thicknesses are 0.7 mm for GeGaSe:Er and 1.78 mm for GeGaS:Er, respectively. The PL has been excited by a laser diode operating at 808 nm. The broken lines present the decomposition of the PL decay (2) as a sum of two “fast” and “slow” exponentials.

(b) and (c). Optical absorption (b) and PL (c) spectra in GeGaS:Er and GeGaSe:Er glasses. The PL has been excited by a laser diode operating at 532 nm.

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3. Size dependence of the PL decay time

The experiments on radiation trapping highlighted in Fig. 1 were done on relatively thick GeGaS:Er (≈1.8 mm). Meanwhile, it is well known that the radiation trapping may be suppressed in powdered materials [8, 9]. Fig. 2(a) and 2(b) show this effect for the present glasses. It is clearly seen that PL decay becomes faster in smaller samples and powders. It is worth noting that the dependence of PL decay time vs. particle size is close to being linear as shown Fig. 2(c). There is well known general theory for radiation trapping developed by Milne [10] for the case of weak absorption αd≪1. In our case, α values do not exceed 6 cm^-1 and therefore αd≪1 in all cases of interest. Therefore, the application of Milne’s theory seems relevant here. This theory predicts a linear dependence for the PL decay time versus particle size behavior as observed approximately in the experimental data shown in Fig. 2(c)

 

Fig. 2. PL decays after cessation of excitation as a function of average particle size (<L>) in bulk and powdered samples of GeGaSe:Er (a) and GeGaS:Er (b) glasses. The glass compositions are the same as in Fig. 1. All experiments are done under an excitation at 808 nm. (c) summarizes the dependence of PL decay times (τ _D) on <L>. The broken lines are least square fits to experimental data 1.80+4.27×10^-4<L> for GeGaSe:Er (blue) and 2.55+6.75×10^-4<L> for GeGaS:Er (red).

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where C _Er is the concentration of Er³⁺ ions, σ is the effective cross-section characterizing the radiative energy transfer form one ion to another and τ ₀ is the decay time limit for infinitely small particles. The values of τ ₀ for GeGaSe:Er and GeGaS:Er are found to be 1.78 and 2.56 ms, respectively, which are nearly perfect matches to Judd-Ofelt estimations of radiative lifetimes of ⁴I_15/2–⁴I_13/2 transitions in these glasses (τ _JO=1.8±0.1 and 2.6±0.2 ms, respectively), which have been published elsewhere and are not discussed here [11].

4. Influence of self-quenching

Having established the correlation between τ ₀ and radiative lifetime τ _JO, we can now examine the effect of self-quenching in which an increase of the active ion concentration leads to a correlative increase of the radiative energy diffusion towards non-radiative sinks [12]. There is a semiempirical relation connecting the emission lifetime with ion concentration

where τ ₀(C _Er) is Er³⁺ concentration dependent decay time measured as the small-size powder limit of decay time τ _D, τ _w is the lifetime at very small concentrations and (C _Er)₀ is the critical concentration for self-quenching [12].

In the present paper we compare the properties of two series (referred to as Ga6 and Ga12) of GeGaSe(S):Er glasses with varying concentrations of Er³⁺. Both series have stoichiometric glass compositions with different concentrations of Ga (C _Ga), namely 6 and 12 at.%. The exact compositions of these glasses are given in Table 1. These values are measured using an electron microprobe analyzer (EMPA) equipped with a wavelength dispersive spectrometer (WDS) and/or calculated using the weights of initial components for glass preparation. Both methods give results within 10%, thus limiting the accuracy of Judd-Ofelt analysis. The refractive index is calculated as n(λ)=2.35+10⁵×λ^-2 which, in our experience, is a reasonable approximation for GeGaSe glasses. The average glass density has been measured to be (4.30±0.04) and (4.40±0.06) g/cm³ for Ga6 and Ga12 series, respectively.

Table 1. Compositions of samples for two series of GeGaSe(S) glasses Ga6 and Ga12. The concentration of Er is presented in at.% and ion number density. The Judd-Ofelt parameters Ω_2,4,6 and corresponding radiative lifetimes τ _JO of ⁴I_13/2→⁴I_15/2 transitions in Er³⁺ ions are calculated using methods described elsewhere [11,13]. The values σ are the effective cross-sections appearing in Eq. (3).

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The importance of high amounts of Ga as well as compositional stoichiometry has been established elsewhere and is not discussed here [4,5]. Fig. 3 shows the experimentally determined dependence of τ ₀ versus C _Er as well as the best least square fits using Eq. (2). The best values for the adjustable parameters τ _w and (C _Er)₀ are listed in Table 2 in comparison with Judd-Ofelt estimations. The values of (C _Er)₀ are surprisingly high which means that the self-quenching effect in GeGaSe and GeGaS may appear only at very high concentrations, which, in turn, means that in all practical cases Er³⁺ ions are very well isolated from each other and behave as such, in full agreement with our previous findings [6,14].

 

Fig. 3. The symbols show the dependence of PL decay rate which is the inverse of τ ₀ (τ ₀ is the limit of τ _D at <L>→0) vs. the squared concentration of Er³⁺ in two series of GeGaSe(S):Er glasses with different concentrations of Ga, 6 and 12 at.%, respectively. The lines present least-square fits of Eq. (2) to experimental values. The values (C _Er)₀ and τ _w are used as adjustable parameters and are listed in Table 2.

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Table 2. Critical concentrations (C _Er)₀ and lifetimes τ _w for the two series of glasses. The radiative lifetimes τ _JO are calculated as the average of Judd-Ofelt lifetimes presented in the Table 1.

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5. Erbium concentration dependence of cross-section

The combination of Eqs. (1) and (2) can be used as a general case when the PL decay time depends simultaneously on the particle size and Er concentration [12]

This dependence may be fitted to experimental data using (C _Er)₀ calculated earlier (Table 2) and σ as the only one adjustable parameter. The results of the fitting procedure are shown in Fig. 4 in comparison with experimental data. The values of σ giving the best fit to the experimental data are listed in Table 1. It is clearly seen that σ remains approximately constant and comparable for both series in the small erbium concentration range while for larger concentrations the values of σ drop rapidly. Fig. 5 shows a plausible origin for such a behavior. One can see a sudden transformation of the optical absorption band at C _Er=2 at.%. This transformation by itself may substantially reduce the overlap of absorption and emission bands and therefore the cross-section σ. Moreover, the inset of Fig. 5 shows the possibility of the appearance of structural non-uniformities and even Er enriched inclusions at high C _Er. These non-uniformities may lead to strong light scattering which may further reduce the cross-section σ.

The last point worth noting is that the erbium concentration that causes the absorption band to collapse is much smaller than the critical concentration (C _Er)₀ “responsible” for self-quenching (Table 1). Therefore, in Er³⁺-doped GeGaSe and GeGaS chalcogenide glasses the formation of chemical clusters seems to precede the effective self-quenching.

 

Fig. 4. PL decay time (τ _D) vs. average size of powder particles for the two series of glasses. The symbols are the experimental data. The lines are the best fits to experimental data using Eq. (3). The values (C _Er)₀∝N _o and σ are summarized in Tables 1 and 2.

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Fig. 5. The “collapse” of optical absorption band with the increase of Er-concentration in Ga6 series. The inset shows the TEM detected microstructure of the sample with C _Er=2 at.%. White inclusions are Er enriched precipitates. The size of the view field is ~240×170 µm.

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6. Conclusions

Using the photoluminescence from GeGaSe:Er to pump GeGaS:Er, we have demonstrated the effect of light trapping in these glasses. By measuring the photoluminescence decay time in samples with decreasing particle size, we were able to exclude the influence of light trapping and to pinpoint the effect of self-quenching. The critical concentrations of Er³⁺ for efficient self-quenching were determined by fitting experimental data to existing models. These concentrations were found to be much larger than the concentrations inducing inhomogeneities in these glasses including the formation of Er-clusters.