Abstract
Radiation trapping (RT) is a phenomenon wherein photons are emitted, absorbed and re-emitted many times before they leave the volume of the material. Trivalent Er3+ ions are particularly prone to RT because there is a whole set of strongly overlapping emission and absorption bands including 4I13/2−4I15/2 and 4I11/2−4I15/2 bands. The effect of RT on the PL decay time was investigated experimentally in this work in a variety of Er3+-doped GeGaS, GeGaSe, GaLaS(O) glasses. Sample geometry (powders, plates, disks, cylinders) and size were varied and the samples were also immersed in glycol, a liquid with high refractive index. PL decay times were measured and compared with the Judd-Ofelt results. A simple model of RT was developed and applied to the above mentioned bands. By comparing model conclusions with experimental data for different sample sizes, we were able to separate the direct relaxation of the 4I11/2 state to ground 4I15/2 state and relaxation via the intermediate 4I13/2 state; and hence obtain an approximate nonradiative lifetime.
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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 4I11/2 state to ground 4I15/2 state and relaxation via intermediate 4I13/2 state. Based on our previous findings [19], we build a simple model of RT. We apply this model to 4I13/2−4I15/2 and 4I11/2−4I15/2 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 4I11/2 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].
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 4I13/2−4I15/2 and 4I11/2−4I15/2 transitions in Er3+ ions was dispersed by Cornerstone monochromator and detected using Peltier cooled InGaAs detector. The excitation corresponding to the 4I15/2−4I9/2 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 4I13/2−4I15/2 and 4I11/2−4I15/2. 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.
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 4I11/2−4I15/2 emission band. Figure 2 shows also the acceleration of PL decay (reduction of decay time) when the sample is submersed in glycol.
Here and after we will refer to 4I15/2 manifold as the ground or 0th level, to 4I13/2 as 1st level and to 4I11/2 as 2nd level. Accordingly, the measured PL decay times for 4I13/2−4I15/2 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 4I11/2−4I15/2 transitions in fine powders and bulk materials, respectively. Figure 3 compares the ratios of PL decay times for 4I11/2−4I15/2 and 4I11/2−4I15/2 emission bands for different glasses. It shows linear dependence in a form
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.4. Model and discussion
In this section, a simplistic model of radiation trapping is developed. Let Ni 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 Ni after switching-off the excitation may be described by a simple rate equation
The solution of Eq. (2) will obviously be a single exponential decay with a characteristic time 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 asEr3+ in second exited state 4I11/2 may relax either directly to the 4I15/2 ground state or through an intermediate excited 4I13/2 state. The first 4I11/2−4I15/2 relaxation is purely radiative and may be strongly affected by RT due to the presence of the matching 4I15/2−4I11/2 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 4I11/2−4I15/2 radiative lifetime is τ20.
The relaxation from 4I11/2 to 4I13/2 state may be radiative or non-radiative. Obviously, for non-radiative relaxation there is no RT. However, for 4I11/2−4I13/2 radiative relaxation the RT influence is also negligible because detectable 4I13/2−4I11/2 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 4I11/2 to 4I13/2 as τ21 = (1/$\tau _{21}^{(\text{R})}$+1/$\tau _{21}^{(\text{NR})}$)−1 and in the case of relaxation of 4I11/2 level, Eq. (6) may be presented as
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 4I13/2−4I15/2 and 4I11/2−4I15/2. 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 4I11/2 state to ground 4I15/2 state and relaxation via the intermediate 4I13/2 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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