Radiation trapping in selected Er<sup>3&#x002B;</sup> doped chalcogenide glasses and the extraction of the nonradiative lifetime

Cyril Koughia; Chris Craig; Daniel W. Hewak; Safa Kasap

doi:10.1364/OME.9.002368

1. Introduction

Radiation trapping (RT) is a phenomenon wherein photons are emitted, absorbed and re-emitted many times before they leave the volume of the material. RT has been observed and reported in a variety of materials where there is a strong overlap of the emission and absorption bands. Historically, its discovery dates back to the mid-1920s [1,2]. Indeed, Lucy Hayner's paper in 1925 included a term “radiation imprisonment” to describe the delay involved in the passage of luminescence radiation through an Hg vapor [1]. Over the last two decades it has been widely observed in materials doped with multivalent rare earth ions [3–13]. Among various rare earths ions, the trivalent Er³⁺ offers a unique opportunity for RT because there is a whole set of perfectly overlapping emission and absorption bands [14]. Usually, RT is regarded a ‘nuisance’ that leads to the distortion of PL spectra and radiative lifetimes [3,11]. Researchers try to eliminate RT by experimenting on fine powders [7,11] or by using excitation and detection through spatially separated pinholes [15–17] or by using a confocal setup [18].

In the present work, we use RT as a means of separating the direct relaxation of ⁴I_11/2 state to ground ⁴I_15/2 state and relaxation via intermediate ⁴I_13/2 state. Based on our previous findings [19], we build a simple model of RT. We apply this model to ⁴I_13/2−⁴I_15/2 and ⁴I_11/2−⁴I_15/2 bands of Er³⁺ embedded in several chalcogenide glasses with different compositions and offer a way to separate direct radiative transition and non-radiative relaxation of the ⁴I_11/2 state.

2. Experimental procedure

Er³⁺ doped glasses were prepared by melt quenching of raw materials mixed in the proportions shown in Table 1. The lanthanum sulphide-oxide glasses (rows 1 and 2 in Table 1) were prepared at the University of Southampton. The detailed description of their preparation technique may be found elsewhere [19]. The germanium gallium sulphide (3) and germanium gallium selenide (4) glasses were synthesized at the University of Saskatchewan. The synthesis details have been described in Refs. [20,21].

Table 1. Glass compositions; E_g - optical gap; τ₁₀(0) and τ₂₀(0) PL decay times in fine powders for ⁴I_13/2−⁴I_15/2 and ⁴I_11/2−⁴I_15/2 bands, respectively; a - slope of the straight lines in Fig. 3; τ₂₀ and τ₂₁ relaxation times of ⁴I_11/2−⁴I_15/2 and ⁴I_11/2−⁴I_13/2, respectively (deduced in the present paper). Optical gap (E_g) is accepted to be equal to the photon energy at which absorption coefficient is equal to 10³ cm⁻¹.

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The effects of photon trapping depend on the sample geometry. Following a geometrically wise approach, we have used three types of samples (as an illustration, see inset of Fig. 2).

(1) Fine powders with an average particle diameter around 30 µm were prepared by crushing bulk materials and passing them through a sequence of sieves with appropriate meshes. The powders were collected on a sticky scotch tape. A control experiment confirmed the absence of a PL response from the virgin scotch tape.
(2) The optical plates were cut off from a glass rod (diameter around 2 mm) and had typical thickness around 1 mm. They were polished on both sides for optical transmittance and PL measurements.
(3) Cylinders were cut off from the same glass rod and polished on both sides. The length of cylinders varied from 10 to 44 mm. As a result of polishing, the cylinders had all shiny surfaces favoring an effective “imprisonment” of light due to internal reflection. For some of the experiments, the samples were submerged in glycol, a liquid with high refractive index. More details on sample preparation and experiments involving glycol submersion may be found in Ref. [19].

PL corresponding to ⁴I_13/2−⁴I_15/2 and ⁴I_11/2−⁴I_15/2 transitions in Er³⁺ ions was dispersed by Cornerstone monochromator and detected using Peltier cooled InGaAs detector. The excitation corresponding to the ⁴I_15/2−⁴I_9/2 transition in Er³⁺ ions was performed by laser diode operating at 808 nm. A ORIEL mechanical chopper was used for transient PL measurements and the signal from the InGaAs detector built-in-amplifier was directly coupled to PicoScope oscilloscope for registration and further analysis.

It should be mentioned that GaLaS(O) glasses used in this work have negligible OH⁻ content as reported previously and confirmed by the absorption spectra around 3 µm [22]. In the case of GeGaS and GeGaSe glasses, the addition of Ga leads to a large increase in the solutibility of Er³⁺ in this glass system, especially if stoichiometric compositions of constituent compounds are alloyed as in this work [21]. Further, the Er³⁺ concentration used in this work is much less than that needed for concentration quenching [7] and the results and conclusions are not affected by the latter phenomenon.

3. Experimental results

Figure 1 compares the PL decays from the steady-state after cessation of excitation at 808 nm in samples of Er³⁺ doped gallium lanthanum sulphide-oxide glasses with two different compositions marked as samples 1 and 2 in Table 1. The measurements were performed for two different emission bands ⁴I_13/2−⁴I_15/2 and ⁴I_11/2−⁴I_15/2. The fastest PL decays were observed in powdered materials with particle size L ≈ 30 µm. As the geometrical size of samples becomes bigger, the PL decays become slower. This effect was observed in all investigated glasses in this work and for both emission bands.

Fig. 1. The influence of geometrical size on PL decays from steady-state after switching-off the excitation in two samples with compositions shown in Table 1 and for two emission bands. The meaning of sample size (L) is explained in the caption of Fig. 2. Solid lines are the best single exponential fits to experimental data. All experiments are performed in air. Excitation is by a laser diode at 808 nm.

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Figure 2 depicts the dependence of PL decay times on the geometrical size of samples. This figure illustrates that the rate of increase depends on the glass composition and the emission band. Thus, changes of PL decay time are less pronounced for glass 1 than glass 2 in particular for ⁴I_11/2−⁴I_15/2 emission band. Figure 2 shows also the acceleration of PL decay (reduction of decay time) when the sample is submersed in glycol.

Fig. 2. The PL decay times vs. geometrical size of samples for ⁴I_11/2−⁴I_15/2 (upper pane (a)) and ⁴I_13/2−⁴I_15/2 (lower pane (b)) emission bands. Numbers 1 and 2 stand for two different glass compositions as shown in Table 1. Open symbols are results collected in air. Full symbols show the results for samples submersed in glycol. Powders in air and in glycol give coinciding results. The inset to figure (b) illustrates the geometry of samples (glass #1) used in the present research. The samples of fine powders with particle size (L≈ 0.03 mm) were collected on scotch tape. Round optical plates had a diameter close to 2 mm and thickness (L ≈ 1 mm (shown in the inset)). Cylinders with both polished ends had a diameter close to 2 mm and varying heights (L = 10, 26 and 44 mm. Cylinders with L = 10 and 26 mm are shown in the inset). Solid lines are guides to the eye.

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Here and after we will refer to ⁴I_15/2 manifold as the ground or 0^th level, to ⁴I_13/2 as 1^st level and to ⁴I_11/2 as 2^nd level. Accordingly, the measured PL decay times for ⁴I_13/2−⁴I_15/2 transitions in fine powders and bulk materials will be referred to as τ₁(0) and τ₁(L), respectively. Similar notations τ₂(0) and τ₂(L) will be used for PL decay times for ⁴I_11/2−⁴I_15/2 transitions in fine powders and bulk materials, respectively. Figure 3 compares the ratios of PL decay times for ⁴I_11/2−⁴I_15/2 and ⁴I_11/2−⁴I_15/2 emission bands for different glasses. It shows linear dependence in a form

(1)$$\frac{{{\tau _2}(0)}}{{{\tau _2}(L)}} = a\frac{{{\tau _1}(0)}}{{{\tau _1}(L)}} + (1 - a)$$

where a is a slope with values listed in Table 1. The meaning of the graphs and the importance of linearity are explained and discussed in detail in the next section.

Fig. 3. Ratio of PL decay times τ₂(L)/τ₂(0) versus ratio τ₁(L)/τ₁(0). Here τ₂(L) is the PL decay time for Er³⁺ ⁴I_11/2−⁴I_15/2 emission band in bulk samples; τ₂(0) is the PL decay time for the same band in fine powders; τ₁(L) is the PL decay time for Er³⁺ ⁴I_13/2−⁴I_15/2 emission band in bulk samples and τ₁(0) is the PL decay time for the same band in fine powders. Numbers from 1 to 4 correspond to different glass compositions as listed in Table 1. Open symbols are results collected in air. Full symbols are for samples submersed in glycol. Solid lines are least square fits to experimental data using Eq. (1) with slopes a listed in Table 1.

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4. Model and discussion

In this section, a simplistic model of radiation trapping is developed. Let N_i be the total number of excited ions in the whole sample. Suppose excited ions may relax through two independent processes with characteristic times τ₁ and τ₂. In this case, the decay of N_i after switching-off the excitation may be described by a simple rate equation

(2)$$\frac{{d{N_i}}}{{dt}} = - \frac{{{N_i}}}{{{\tau _1}}} - \frac{{{N_i}}}{{{\tau _2}}}$$

The solution of Eq. (2) will obviously be a single exponential decay with a characteristic time

(3)$$\tau (0) = \frac{{{\tau _1}{\tau _2}}}{{{\tau _1} + {\tau _2}}}$$

For the future let us assume that the first process (with characteristic time τ₁) is a radiative transition. Experimentally, τ(0) may be observed in fine powders where the influence of RT has been proven to be negligible, as, for example, in Refs. [7,11]. However in the presence of RT some modifications of Eq. (2) are required. First of all, we note that the radiative transition becomes “less efficient” because part of emitted PL photons is reabsorbed by Er³⁺ ions. Therefore, Eq. (2) should be corrected as

(4)$$\frac{{d{N_i}}}{{dt}} = - \frac{{{N_i}}}{{{\tau _1}}}{p_{\textrm{esc}}}(L) - \frac{{{N_i}}}{{{\tau _2}}}$$

here p_esc(L) is the probability of photon to escape the sample with the size L without being reabsorbed. Obviously, the parameter p_esc depends on the sample size. Thus, in fine powders, p_esc(L)→1 due to the small size of powder particles and the inefficiency of reabsorption. On the other hand, in large samples p_esc(L)→ 0, meaning that nearly all photons are being reabsorbed within a huge volume of the sample. The solution of Eq. (4) gives again a single exponential decay but with a different characteristic time

(5)$$\tau (L) = \frac{{{\tau _1}{\tau _2}}}{{{\tau _1} + {\tau _2}{p_{\textrm{esc}}}(L)}}$$

which is observed in bulk samples with effective geometrical size L as PL decay time. Dividing Eq. (3) by (5) we find the ratio of two characteristic PL decay times in powdered and bulk materials as

(6)$$\frac{{\tau (0)}}{{\tau (L)}} = \frac{{{\tau _1}}}{{{\tau _1} + {\tau _2}}} + \frac{{{\tau _2}}}{{{\tau _1} + {\tau _2}}}{p_{\textrm{esc}}}(L)$$

Equation (6) is a general relation that can be applied to some particular cases. Let us start with the ⁴I_13/2−⁴I_15/2 relaxation of Er³⁺ ions. Usually, the relaxation from ⁴I_13/2 level (it is referred to as level 1 in this paper) to ground level ⁴I_15/2 (level 0) occurs by radiative emission which is known to be the dominant relaxation process in many glasses [7,23]. In other words, there is only one relaxation mechanism and hence Eq. (6) may be reduced to

(7)$$\frac{{{\tau _1}(0)}}{{{\tau _1}(L)}} = p_{\textrm{esc}}^{(1)}(L)$$

here the index (1) shows that Eq. (7) refers to the first emission/absorption band, i.e. ⁴I_13/2− ⁴I₁₅_/2.

Er³⁺ in second exited state ⁴I_11/2 may relax either directly to the ⁴I_15/2 ground state or through an intermediate excited ⁴I_13/2 state. The first ⁴I_11/2−⁴I_15/2 relaxation is purely radiative and may be strongly affected by RT due to the presence of the matching ⁴I_15/2−⁴I_11/2 absorption band. The presence of RT is supported by Fig. 1 and reported earlier for some other glasses [3–7,14]. Let us assume that ⁴I_11/2−⁴I_15/2 radiative lifetime is τ₂₀.

The relaxation from ⁴I_11/2 to ⁴I_13/2 state may be radiative or non-radiative. Obviously, for non-radiative relaxation there is no RT. However, for ⁴I_11/2−⁴I_13/2 radiative relaxation the RT influence is also negligible because detectable ⁴I_13/2−⁴I_11/2 excitation stimulated absorption appears only at very high pumping levels far exceeding those used in present paper. Assuming that the radiative lifetime is $\tau _{21}^{(\text{R})}$ and non-radiative relaxation time is $\tau _{21}^\text{NR})$we get an effective time of relaxation from ⁴I_11/2 to ⁴I_13/2 as τ₂₁ = (1/$\tau _{21}^{(\text{R})}$+1/$\tau _{21}^{(\text{NR})}$)⁻¹ and in the case of relaxation of ⁴I_11/2 level, Eq. (6) may be presented as

(8)$$\frac{{{\tau _2}(0)}}{{{\tau _2}(L)}} = \frac{{{\tau _{20}}}}{{{\tau _{20}} + {\tau _{21}}}} + \frac{{{\tau _{21}}}}{{{\tau _{20}} + {\tau _{21}}}}p_{\textrm{esc}}^{(2)}(L)$$

By combining experimental results presented by Eq. (1) with Eqs. (7) and (8), it is easy to derive the relation between $p_{\textrm{esc}}^{(1)}(L)$and $p_{\textrm{esc}}^{(2)}(L)$as

(9)$$\frac{{{\tau _{20}}}}{{{\tau _{20}} + {\tau _{21}}}} + \frac{{{\tau _{21}}}}{{{\tau _{20}} + {\tau _{21}}}}p_{\textrm{esc}}^{(2)}(L) = (1 - a) + ap_{\textrm{esc}}^{(1)}(L)$$

In very big samples (L→∞), as we already mentioned earlier, the escape becomes improbable, i.e. p_esc→0 for both bands giving us a simple relation between τ₂₀ , τ₂₁ and the experimental value of a

(10)$$\frac{{{\tau _{20}}}}{{{\tau _{20}} + {\tau _{21}}}} = (1 - a)\quad \quad \textrm{or}\quad \quad a = \frac{{{\tau _{21}}}}{{{\tau _{21}} + {\tau _{20}}}}$$

Equation (10) is the final result of our simple model and it shows that the slope of the linear dependence (a) in Eq. (1) may be used to evaluate τ₂₀ and τ₂₁ as

(11)$${\tau _{20}} = \frac{{{\tau _2}(0)}}{a}\quad \quad \textrm{and}\quad \quad {\tau _{21}} = \frac{{{\tau _2}(0)}}{{1 - a}}$$

The results of these calculations for four different glasses doped with Er³⁺ ions are summarized and presented in Table 1. The validity of these conclusions is presented in Table 2 which compares the predicted values of τ₂₀ with calculations using Judd-Ofelt model. In overall, Table 2 shows quite good agreement of ⁴I_13/2−⁴I_15/2 radiative recombination times $\tau _{10}^{\textrm{JO}}$ with experimental values of PL decay times in fine powders τ₁₀(0), confirming the applicability of the JO model to our case. Table 2 also shows a reasonable agreement of values of ⁴I_13/2−⁴I_15/2 radiative recombination times $\tau _{20}^{\textrm{JO}}$ and τ₂₀ which are calculated in the present paper.

Table 2. Glass compositions; Judd-Ofelt parameters (Ω₂, Ω₄ and Ω₆) ; β - branching ratio for level ⁴I_11/2 ; $R_{10}^{\textrm{ed}}$- electric dipole ⁴I_13/2−⁴I_15/2 transition rate; $R_{10}^{\textrm{md}}$- magnetic dipole ⁴I_13/2 −⁴I_15/2 transition rate; $\tau _{10}^{\textrm{JO}}$- calculated ⁴I_13/2 −⁴I_15/2 transition radiative lifetime; $R_{20}^{\textrm{ed}}$- electric dipole ⁴I_11/2 −⁴I_15/2 transition rate; $\tau _{20}^{\textrm{JO}}$- calculated ⁴I_11/2 −⁴I_15/2 transition radiative lifetime. The values of τ₁₀(0) and τ₂₀ are reproduced from Table 1 to facilitate comparison with $\tau _{10}^{\textrm{JO}}$ and $\tau _{20}^{\textrm{JO}}$, respectively. The values for Judd-Ofelt parameters for glasses 3 and 4 were published previously in [24] and [7], respectively.

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5. Conclusions

We investigated radiation trapping in four different classes of Er³⁺ doped chalcogenide glasses. Radiation trapping appears in materials in which there is a strong overlap of emission and absorption spectra. From this point of view, Er³⁺ ions are ideal the manifestation of radiation trapping as they possess many overlapping absorption and emission bands including ⁴I_13/2−⁴I_15/2 and ⁴I_11/2−⁴I_15/2. We have developed a simple model for radiation trapping that incorporates the sample size effect into the observed PL decay time, and applied this model to the above mentioned bands in Er³⁺ ions in four different chalcogenide glass hosts. By comparing model conclusions with experimental data for different sample sizes, we were able to separate the direct relaxation of ⁴I_11/2 state to ground ⁴I_15/2 state and relaxation via the intermediate ⁴I_13/2 state. This procedure was shown to be effective for four different glasses with very different compositions.

Funding

Natural Sciences and Engineering Research Council of Canada (NSERC) (Discovery Grants); Engineering and Physical Sciences Research Council (EPSRC) (EP/M015130/1).

Acknowledgments

Saskatchewan acknowledges NSERC Discovery Grants for financial support. Southampton acknowledged the support of the Engineering and Physical Sciences Research Council, United Kingdom, through a grant EP/M015130/1, Manufacturing and Application of Next Generation Chalcogenides.

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	Glass compositions	E_g, eV	τ₁₀(0), ms	τ₂₀(0), ms	a	τ₂₀ , ms	τ₂₁ , ms
1	73 Ga₂S₃ + 27 La₂O₃ + 0.5 Er₂O₃	3.05	3.35	0.89	0.22	3.98	1.15
2	66 Ga₂S₃ + 32 La₂S₃ + 3 La₂O₃ + 0.5 Er₂O₃	2.79	2.73	1.40	0.53	2.62	2.98
3	90 GeS₂ + 10 Ga₂S₃ + 0.5 Er₂S₃	3.00	2.71	1.58	0.40	3.96	2.63
4	90 GeSe₂ + 10 Ga₂Se₃ + 0.5 Er₂S₃	2.31	1.91	0.94	0.59	1.60	2.29

	Glass	Ω₂	Ω₄	Ω₆	β	$R_{10}^{ed}$	$R_{10}^{md}$	$τ_{10}^{JO}$	τ₁₀(0)	$R_{20}^{ed}$	$τ_{20}^{JO}$	τ₂₀
	compositions	(10⁻²⁰cm²)	(10⁻²⁰cm²)	(10⁻²⁰cm²)	(%)	(s⁻¹)	(s⁻¹)	(ms)	(ms)	(s⁻¹)	(ms)	(ms)
1	73 Ga₂S₃ + 27 La₂O₃ + 0.5 Er₂O₃	6.78	1.17	0.49	14	186	112	3.36	3.35	267	3.75	3.98
2	66 Ga₂S₃ + 32 La₂S₃ + 3 La₂O₃ + 0.5 Er₂O₃	6.22	1.92	0.49	14	236	127	2.75	2.73	402	2.49	2.62
3	90 GeS₂ + 10 Ga₂S₃ + 0.5 Er₂S₃	11	2.9	1.6	11	314	70	2.60	2.71	349	2.87	3.96
4	90 GeSe₂ + 10 Ga₂Se₃ + 0.5 Er₂S₃	8.6	2.1	1.1	12	417	117	1.87	1.91	699	1.43	1.6

	Glass compositions	E_g, eV	τ₁₀(0), ms	τ₂₀(0), ms	a	τ₂₀ , ms	τ₂₁ , ms
1	73 Ga₂S₃ + 27 La₂O₃ + 0.5 Er₂O₃	3.05	3.35	0.89	0.22	3.98	1.15
2	66 Ga₂S₃ + 32 La₂S₃ + 3 La₂O₃ + 0.5 Er₂O₃	2.79	2.73	1.40	0.53	2.62	2.98
3	90 GeS₂ + 10 Ga₂S₃ + 0.5 Er₂S₃	3.00	2.71	1.58	0.40	3.96	2.63
4	90 GeSe₂ + 10 Ga₂Se₃ + 0.5 Er₂S₃	2.31	1.91	0.94	0.59	1.60	2.29

	Glass	Ω₂	Ω₄	Ω₆	β	$R_{10}^{ed}$	$R_{10}^{md}$	$τ_{10}^{JO}$	τ₁₀(0)	$R_{20}^{ed}$	$τ_{20}^{JO}$	τ₂₀
	compositions	(10⁻²⁰cm²)	(10⁻²⁰cm²)	(10⁻²⁰cm²)	(%)	(s⁻¹)	(s⁻¹)	(ms)	(ms)	(s⁻¹)	(ms)	(ms)
1	73 Ga₂S₃ + 27 La₂O₃ + 0.5 Er₂O₃	6.78	1.17	0.49	14	186	112	3.36	3.35	267	3.75	3.98
2	66 Ga₂S₃ + 32 La₂S₃ + 3 La₂O₃ + 0.5 Er₂O₃	6.22	1.92	0.49	14	236	127	2.75	2.73	402	2.49	2.62
3	90 GeS₂ + 10 Ga₂S₃ + 0.5 Er₂S₃	11	2.9	1.6	11	314	70	2.60	2.71	349	2.87	3.96
4	90 GeSe₂ + 10 Ga₂Se₃ + 0.5 Er₂S₃	8.6	2.1	1.1	12	417	117	1.87	1.91	699	1.43	1.6

Radiation trapping in selected Er³⁺ doped chalcogenide glasses and the extraction of the nonradiative lifetime

Abstract

1. Introduction

2. Experimental procedure

3. Experimental results

4. Model and discussion

5. Conclusions

Funding

Acknowledgments

References

Cited By

Figures (3)

Tables (2)

Equations (11)

Optical Materials Express