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Abstract
The kinetics of the electronic transitions within the f-shell of Dy3+ ions were studied with monitoring near- and mid-IR luminescence decay under pulsed laser excitation at 1.3 µm. The luminescence decay curves were found to be profoundly non-exponential in all bands in the range between 1.3-5.5 µm. Such behavior is attributed to cross-relaxation and up-conversion processes dominating in relaxation of Dy3+ ions from the laser-excited multiplet 6H9/2+6F11/2. We suggest that strong collective phenomena occurring under relatively low concentrations are due to anomalous clustering of Dy3+ ions. The cross-relaxation enables an efficient population of 6H13/2 and 6H11/2 multiplets, offering this material as an active medium for a 3-µm and 4.3-µm lasers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Bright light sources in the mid-infrared spectral region 3–6 µm are demanded for medical diagnostics, gas sensing in the environmental protecting and chemical industry. The high selectivity and sensitivity of such sensing is provided by the unique vibrational absorption spectra of different molecules. There has been a significant progress in the recent years has been achieved with fiber lasers operating in the 2.7–4 µm wavelength range, based on fluoride glasses, doped with Er3+, Ho3+ and Dy3+ ions. These fiber lasers demonstrate high output power [1–3], broadband gain for mode-locking [4], and tuning capability [5–7]. The longest lasing wavelength of 3.92 µm has been demonstrated at the ${}_{}^5{I_5} \to {}_{}^5{I_6}\; $ transition of the Но3+ ion [8]. The ${}_{}^4{F_{9/2}} \to {}_{}^4{I_{9/2}}$ transition of Er3+ and the ${}_{}^6{H_{13/2}} \to {}_{}^6{H_{15/2}}$ transition of Dy3+ provide tuning ranges from 3.35 µm to 3.8 µm and from 2.8 µm to 3.4 µm respectively, covering a significant part of the absorption lines for gases of interest [7]. We should mention however, that Dy3+-doped fibers have an advantage of being pumped at one wavelength, while Er3+ ions require two-wavelength pumping to operate on the above transition. Being doped to the chloride crystal the Dy3+ ion can also be used for generation in the 5.5 µm and 4.3 µm regions using the ${}_{}^6{H_{9/2}},{}_{}^6{F_{11/2}} \to {}_{}^6{H_{11/2}}$ and ${}_{}^6{H_{11/2}} \to {}_{}^6{H_{13/2}}\; $transitions correspondingly [9,10]. Unfortunately, these radiative transitions are quenched by phonons in the fluoride host glasses at room temperature.
In this work, we study Dy3+-doped crystalline silver halides AgCl0.5Br0.5. This host possess extremely narrow phonon spectra not exceeding 160 cm-1 [11] and are therefore prospective for obtaining laser action on transitions up to 5.5 µm wavelength [12]. Moreover, this host is suitable for fiber technology by hot extrusion method, but opposite to fluoride fiber is moister resistant. In comparison with previous study of AgCl0.5Br0.5:Dy [12], we were able to find collective phenomena in relaxations processes of excited states of Dy3+ ions by detailed studying of luminescence kinetics and spectral shapes for three near- and mid-IR bands with high time resolution in crystals with different dopant concentrations. This finding allowed us to conclude that AgCl0.5Br0.5:Dy crystal is perspective for generation of oscillations in mid-IR, because an Dy3+ ion excited to at ${}_{}^6{H_{9/2}},{}_{}^6{F_{11/2}}$ multiplet under 1.3-µm pumping gives higher than one ion at the ${}_{}^6{H_{13/2}}$ multiplet enabling emission at 3 µm, and following up-conversion efficiently populates ${}_{}^6{H_{11/2}}$ multiplet enabling emission at 4.3 µm.
2. Growth of silver halide single crystals AgCl0.5Br0.5:Dy
The single crystals have been grown using the Bridgeman-Stockbarger technique in the sealed fused-silica ampoules. For the charge preparation, we have first chemically synthesized single halide AgCl and AgBr in the powder form. These powders have then been purified by zone recrystallization in the sealed fused-silica ampoules for 15-20 times at the scanning speed of 30 mm/hour, producing purified salts in the form of transparent cylinders. After addition of dry dysprosium halides DyCl3 by Aldrich to the mixture of AgCl and AgBr with molar ratio 1:1 the multicomponent powder was loaded into cylindrical fused-silica ampoule, which was then evacuated and sealed. The Dy concentration in the charge varied from 0.05 to 0.3 wt.%. The growth took place at 0.8–1 mm/hour speed with temperature gradient at crystallization front about 20 K/cm (the melting point is at 412 °C). The grown crystals were cooled for 5 days together with the oven. All operations with silver halides have been performed under red light, to avoid building of silver clusters.
The doped boules have the form of 30–50 mm long cylinders with 8–10 mm diameter and conical ends. They are transparent in the head and scatter light in the tail part. This is obviously due to the low solubility of dysprosium in silver halides, causing its accumulation in the melt during growth and multiphase crystallization in the tail part.
Dy concentration in the boules has been measured by inductively coupled plasma mass spectrometry (ICM-MS), giving concentration distribution along the boule and along the cross-section radius. The Dy concentration increases from the center to the surface of the boule. The highest gradient is observed near the side surface at about 1 mm depth. The concentration variation in the inner part of the boule did not exceed 30%. All spectroscopic measurements, described below, have been performed with the inner part of the boule, where Dy distribution is homogeneous and the concentration is well defined.
Figure 1 shows the dysprosium concentration dependence on DyCl3 content in the charge. The concentration NDy has been measured in the head or middle part of the boule, far from the crystal surface. Being measured in these boule parts the dysprosium concentration NDy correlates with the DyCl3 content in the charge, while in the boule tail the concentration significantly varied towards higher or lower levels. Table 1 summarizes the samples used for spectroscopic measurements. The samples were cut from a head or middle part of boules, and the concentration was determined by the ICP-MS method.
Table 1. Dysprosium concentrations in the studied samples.
3. Experimental technique
Absorption and luminescence spectra were investigated with FTIR spectrometer Bruker IFS 125 HR with resolution of 2 cm-1 at the temperatures 5K–300 K. The near-IR absorption spectra have been also recorded using the double-channel Perkin-Elmer-λ9 spectrophotometer at T=300 K. To excite the luminescence spectra, we used either a laser diode operating at 1.312 µm with 4 nm linewidth, or tunable femtosecond optical parametric amplifier (Orpheus, Light Conversion) with 40 nm linewidth and 10 kHz rep rate, or a home-made pulsed Nd:YAG laser operating at 1.319 µm and 5 Hz rep rate. The latter had 50 µs pulse duration in the free-running mode, and 30 ns in the Q-switched mode. Wavelength selection between 1319 nm and 1338 nm of the Nd:YAG laser was done with an intracavity Lyot filter. In order to apply the lock-in amplifier for luminescence detection, the laser diode pump current was modulated at 33 Hz with 15 ms pulses, which is longer, than average IR luminescence lifetime of Dy3+ ions, so that the excitation regime for all emitting transition was equivalent to continuous-wave (CW). The luminescence spectra and kinetics have been recorded with the grating spectrometer ИКС-31 (LOMO) using InGaAsP and InAs (Hamamatsu P7163) photodiodes in the 1–3 µm region (rise time is 0.1 µs), and the photoconductive MCT detector (InfraRed FTIR-16-1.0) in the 3–6 µm region, both with liquid nitrogen cooling. A germanium plate with thickness of 4 mm was used to reject high order diffraction when luminescence in the 4–5 µm region was detected, and an interference filter with cut-off wavelength of 5 µm was used for detecting luminescence in the 5-6 µm region. No filters were used when detecting luminescence in the 1.2-3 µm region.
4. Results
4.1. Absorption
Figure 2(a) shows an overall room temperature and helium absorption spectra of the sample #4, which has the highest Dy concentration. At T=300 K samples with lower Dy concentration have analogous spectral positions of bands, but with slightly different peak height ratios. Overall, the absorption bands in the near- and mid-IR can be unambiguously assigned to the $f - f$ transitions in Dy3+ [9,12,13] (Fig. 3). The absorption band corresponding to transition from ground state to 6F3/2 multiplet has two lines at 13219 cm-1 and at 13241 cm-1 at T=5 K [Fig. 2(b)]. Number of the observed lines coincides with highest possible number of transitions from the lowest Stark sub-level of the ground state. Thus, we conclude that there is predominantly one type of Dy3+ centers in the crystal with maybe moderate number of other centers, indicated by the small tail on the high energy side of the most intense line. Positions of all Starks sublevels of the dominating centers were derived from the low temperature absorption and luminescence spectra of the sample #4 and are shown in Table 2.
Fig. 2. (a) The overall absorption spectra of the sample #4 at T=300 K (red line) and T=5 K (blue line). Terminal multiplets for absorption transitions are shown in the graph. (b) Absorption band of the sample #4 for transition from the ground state to the 6F3/2 multiplet at T=5 K.
Fig. 3. Energy level scheme of Dy3+ ions in AgCl0.5Br0.5 crystal. Energies of the lowest Stark sublevels are shown under each multiplet. Black arrows denote registered luminescence transitions. Solid red and blue arrows denote cross-relaxations {1} and {2}, and the green arrows denote up-conversion {3}. The dashed black arrow denotes an un-registered transition in luminescence.
The 1.3 µm band dominates in the absorption spectra of all samples. The structure and form of this band depends on the dopant concentration (Fig. 4.). The spectra of cross-section have been calculated as $\sigma (\lambda )= \alpha (\lambda )/{N_{\textrm{Dy}}}$ where $\alpha (\lambda )$ is the absorption coefficient and the dysprosium concentration ${N_{\textrm{Dy}}}$ has been determined by ICP-MS for each sample separately. One can see reduction of the bandwidth with the concentration increase. The central peak, hardly visible at low concentration, dominates in stronger doped samples. While the absorption band is almost unstructured at the lowest concentration, one can observe appearance of narrow feature at 1324 nm and more structured short-wavelength side at increasing concentrations. The intensities of other absorption bands also depend on the doping level. Figure 5 summarizes the influence of Dy concentration on the integrated absorption cross-section of the bands (indexed by $k$) ${\mathrm{\Xi }_k}$, calculated from absorption spectra by the formula [13]:
Fig. 4. (a) Absorption cross-section spectra for the 1.3 µm band. (b) The same normalized absorption spectra. Dysprosium concentrations ${N_{\textrm{Dy}}}$ in a crystal are coded in the legend and applied to both plots.
Fig. 5. (a) Integrated absorption cross-sections Ξk for bands centered at 908 nm (blue), 1113 nm (red), 1295 nm (black), 1668 nm (green) as function of the dysprosium concentration ${N_{\textrm{Dy}}}$ in a crystal. (b) Plot of the crystal field parameters calculated by Judd-Ofelt analysis against the dysprosium concentration in a crystal.
Table 2. Energies of Stark’s sub-levels of the Dy3+ ion in the AgCl0.5Br0.5:Dy single crystals determined from the temperature dependences of the luminescence and absorption spectra.
4.2. Luminescence spectra
Under quasi-CW excitation with the 1.3 µm laser diode we observe three intense emission bands for all samples: around 1.8 µm, 2.9 µm and 4.4 µm (Fig. 6). These bands unambiguously match those observed in KPb2Cl5:Dy [13], RbPb2Cl5:Dy [9] and AgClxBr1-x:Dy [12], and are identified as electronic f – f transitions ${}_{}^6{H_{11/2}} \to {}_{}^6{H_{15/2}}$ (“2”$\; \to $”0”), ${}_{}^6{H_{13/2}} \to {}_{}^6{H_{15/2}}$ (“1”$\; \to $”0”), and ${}_{}^6{H_{11/2}} \to {}_{}^6{H_{13/2}}$ (“2”$\; \to $”1”), respectively. The gap near 4.3 µm in the middle of the 4.4 µm band is caused by the CO2 absorption in the atmosphere. The strong narrow 2.6 µm line is the laser diode line in the second order of the diffraction grating. The luminescence bands near 1.3 µm, 2.4 µm, and 5.5 µm, corresponding to the ${}_{}^6{F_{11/2}},{}^6{H_{9/2}} \to {}_{}^6{H_{15/2}}$ (“3”$\; \to $“0”), ${}_{}^6{F_{11/2}},{}^6{H_{9/2}} \to {}_{}^6{H_{13/2}}$ (“3”$\; \to $“1”), and ${}_{}^6{F_{11/2}},{}^6{H_{9/2}} \to {}_{}^6{H_{11/2}}$ (“3”$\; \to $“2”) transitions, were too weak to be observed under quasi-CW excitation.
Fig. 6. Luminescence spectra of crystals with different dysprosium concentrations under quasi-CW excitation at 1312 nm recorded with InAs detector (a, c) and MCT detector (b). (c) Luminescence spectra of the crystal 4 under tunable excitation into the 1.3 µm band. The excitation wavelengths are shown in the plot.
The spectral form of each luminescence band does not depend on dysprosium concentration, but their relative intensities do [Figs. 6(a), 6(b)]. The spectra in Fig. 6(a) are normalized to keep the maximum at 1.8 µm the same for all samples. One can clearly see the increase of the relative strength of the 2.9 µm band with growing concentration.
Figure 6(c) shows luminescence spectra for the 2.9 µm band of the heavily doped sample #4 when it is excited at different wavelengths across the 1.3 µm absorption band by the tunable OPA source. The spectra slightly differ in the region of the dip at 2.9 µm, which becomes less deep when excited in the center of the 1.3 µm absorption band, and this change is beyond the recording noise. This is a sign of a certain degree of inhomogeneous broadening of the absorption spectra.
Using the pulsed excitation by the Nd:YAG laser at 1.319 µm, we were able to observe five luminescence bands in all samples. Namely, three bands described above and two additional bands in the 1.3 and 5.5 µm regions. Intensities of the latter bands are much smaller in comparison to others for all samples, especially for #4, and it increases at smaller Dy concentrations. Spectrum of the 5.5 µm luminescence band is detected with good signal/noise ratio only for the sample #1 (Fig. 7). This band belongs to the “3”$\; \to $“2” transition [9,12,13].
Luminescence corresponding to “3”$\; \to $“1” transition, which according to the level separation scheme in Fig. 3 should be centered around 2.4 µm, could not be observed in our samples under any excitation to the 1.3 µm band.
4.3. Luminescence kinetics
The luminescence decays of 1.3 µm, 1.79 µm, 3 µm and 4.4 µm bands were selectively detected through a grating monochromator under excitation at 1.319 µm by Q-switch pulses. All decay curves are profoundly non-exponential (Fig. 8). The decay curves for samples with varying concentrations do not differ significantly. At 3 µm, the luminescence decays with a time constant of 0.42 ms at the initial stage, and 25 ms at the decay tail. At 1.79 µm and 4.4 µm, the luminescence first grows up to 2.3 ms, and then decays with the time constant of nearly 10 ms.
Fig. 8. Normalized luminescence kinetics for the sample #4 under excitation at 1.319 µm by the Q-switch laser pulse. The luminescence was recorded at 1.295 µm (violet), 3.00 µm (green), and 1.79 µm (blue). The red lines are theoretical fittings. In the inset the vertical solid line t = 0.0213 ms shows coincidence of peaks in the 3.00 µm and 1.79 µm kinetics.
Figure 9 shows the luminescence kinetics for crystals with different dysprosium concentrations. Luminescence decay for the 1.3 µm band was detected through monochromator at 1.295 µm. Luminescence decays for all crystals was found to be strongly non-exponential with slight difference in time constants at the initial stage. For example, at times shorter than 0.1 ms the decay time of the sample #1 is about 73 µs, and of the sample #2 it is about 60 µs. At the longer times, the time constant is about 1.3 ms for both crystals.
Fig. 9. Luminescence kinetics detected at 1.295 µm (a) and in overall 5.5 µm band (b) under 30 ns excitation at 1.319 µm. The green curves: sample #1, the blue curves: sample #2, the magenta curve: sample #4. The red dashed line shows the extrapolated exponential decay with 60 µs time constant in the initial kinetics stage for the sample #2. The detector time constant is ∼2 µs.
The signal of 5.5 µm luminescence was collected in the broad spectral range using a low-pass filter with a cut-off at 5 µm [Fig. 9(b)]. At the initial stage, the luminescence decays is about 60 µs for sample #1, and 50 µs for samples #2 and #3. At longer times, the decay time is about 1.3–2 ms.
5. Judd-Ofelt analysis
We have performed Judd-Ofelt analysis of the absorption spectra for three samples. The starting data were the integrated absorption cross-sections, calculated for the absorption bands at 0.9, 1.1, 1.3 and 1.7 µm using the formula (1) [Fig. 5(a)]. The 2.8 µm band has been excluded from consideration, as it may overlap with the absorption of the impurity OH group. According to the theory, the integral absorption cross-section Ξk is connected with the crystal field parameters ${\mathrm{\Omega }_2},{\; }{\mathrm{\Omega }_4},{\; }{\mathrm{\Omega }_6}$ and reduced-matrix elements of the $f - f$ electric dipole transitions ${U_2},{U_4},{U_6}$ by the formula [13]:
Table 3. Radiative lifetimes of the Dy3+ multiplets calculated by Judd-Ofelt analysis for different dysprosium concentrations in AgCl0.5Br0.5:Dy3+.
6. Discussions and theory of relaxation kinetics
The observed absorption and luminescence spectra fit well to the energy level scheme as shown in Fig. 3, where the horizontal solid lines correspond to the lowest Stark sublevels of a multiplet and dashed lines correspond to the highest Starks sublevels. Analysis of the helium absorption spectra, made in the Section 4.1, allowed us to conclude that there is predominantly one type of Dy3+ centers in the AgCl0.5Br0.5:Dy crystal.
Decrease of the 1.3 µm bandwidth and increase of the integrated absorption cross-section ${\mathrm{\Xi }_k}$ with dysprosium concentration indicate changes in the local crystal field that take place under increase of dysprosium doping (Figs. 4, 5). These changes also presume strong mutual interaction of Dy3+ ions that is obviously should affect relaxation of the excited states.
The electron paramagnetic resonance analysis of the AgCl:Dy crystal (${N_{Dy}} \sim {10^{18}}$ cm-3) suggests, that the charge compensation of the Dy3+ ion occurs locally by two Ag+ vacancies in the nearest coordination sphere, and that the angle between the directions from Dy3+ ion to the two vacancies is 90° [15]. Thus, Dy3+ ion forms an associate ${V^{\prime}_{Ag}} - \textrm{D}{\textrm{y}^{ {\bullet}{\bullet} }} - {V^{\prime}_{Ag}}$, that possess a nonzero dipole moment. Since the AgCl0.5Br0,5 single crystal has the same space group and very close lattice parameter to AgCl, we may assume, that the charge compensation follows the same pattern. At significantly higher dysprosium concentrations, as in our case, such associates may cluster due to dipole attraction that will change the local field symmetry. The non-monotonic change of the spectral form [Figs. 6(a),6(b)] and integral cross-section (Fig. 5) may reflect change of the preferred cluster size or structure. Small change of the 2.9 µm band shape [Fig. 6(c)] under excitation into the different parts of the absorption band at 1.3 µm may reflects variation of the crystal field around Dy3+ ions due to cluster size change (including un-clustered ions).
Since only one type of Dy3+ centers dominates in the crystal, the strongly non-exponential luminescence decay, which we observed for all samples and all bands, cannot be explained by a luminescence decay time difference between Dy3+ ions. Thus, we conclude that it is due to collective relaxation processes with strong dependence of relaxation probability on distance between the interacting centers. Increase of the relative luminescence intensity in the 2.9 µm band with increasing of dysprosium concentration ${N_{\textrm{Dy}}}$ [Fig. 6(a)] indicates a significant role of the cross-relaxational interaction of the excited (donor) and ground-state (acceptor) Dy3+ ions according to the scheme ${}_{}^6{H_{15/2}},\; {}_{}^6{F_{11/2}} + {}_{}^6{H_{9/2}} \to 2{}_{}^6{H_{13/2}}$ ({1} in Fig. 3), because probability of such interaction is proportional to the acceptor concentration, i.e. to ${N_{\textrm{Dy}}}$. Assumption of the cross-relaxation path dominance at initial stages of the level “3“ decay is supported by rapid growth of strong luminescence signal at 3 µm with the simultaneous decay at 1.3 µm. In order to explain this strong cross-relaxation under relatively low concentration of Dy3+ ions, we should suggest that the ${V^{\prime}_{Ag}} - \textrm{D}{\textrm{y}^{ {\bullet}{\bullet} }} - {V^{\prime}_{Ag}}$ associates tend to assemble to clusters due to the dipole interaction that is mentioned above. Moreover, peaks at 0.0213 ms on the decay curves for 3 µm and 1.8 µm luminescence bands indicate contribution of the second cross-relaxation on the scheme ${}_{}^6{H_{9/2}}+{}_{}^6{F_{11/2}}, {}_{}^6{H_{13/2}} \to 2{}_{}^6{H_{11/2}}$ ({2} in Fig. 3). Further growth of the level “2” population up to the maximum at 2.3 ms would be due to the $2\;{}_{}^6{H_{13/2}} \to {}_{}^6{H_{11/2}}, {}_{}^6{H_{15/2}}$ up-conversion, analogously to the up-conversion population of the ${}_{}^3{H_5}$ level in Tm3+ ions, which have a similar energy level scheme [16].
Summarizing, we accept the following model for explanation of the observed luminescence decay. We suggest that Dy3+ ions enter AgCl0.5Br0.5 crystal lattice in two different ways. First, they form clustered centers, where two or more Dy3+ ions or associates are located in the nearest lattice positions. Their interaction causes fast cross-relaxation {1} (${}_{}^6{H_{15/2}},\; {}_{}^6{H_{9/2}} + {}_{}^6{F_{11/2}} \to 2{}_{}^6{H_{13/2}}\; $) leading to rapid depopulation of the level “3” and population of the level “1”, and then to cross-relaxation {2} (${}_{}^6{H_{9/2}}+\; {}_{}^6{F_{11/2}}, {}_{}^6{H_{13/2}} \to 2{}_{}^6{H_{11/2}}$) partially populating level “2” (Fig. 3). Further population of level “2” goes through up-conversion {3}. Second, they stochastically enter the lattice far from each other. Interaction with them is weaker than for the clustered ions and occurs according to the Förster scheme [16]. For the sake of simplicity, we include only the clearly visible Förster-type cross-relaxation {1} into the model. The cross relaxation {2} and up-conversion {3} processes are neglected for the stand-alone ions, because their probabilities turn out to be much lower than that of the process {1} even for the clustered ions (Table 4). Thus, in our model the level “2” is populated only for the clustered ions. In the following, we will denote parameters of the clustered and stand-alone ions as prime and double-prime, respectively. For populations, ${n_i} = {n^{\prime}_i} + {n^{\prime\prime}_i}$, where ${n_i}$ is the total population of the level #i, as shown by red numbers in parentheses in Fig. 3.
Population decay of the level “3” for clustered ions obey the rate equation:
Next, we observe that cross-relaxation of stand-alone ions after the time $t \approx 0.05$ ms obeys the Förster decay [17]:
Populations at levels “2” and “1” obey the following rate equations:
The first term in Eq. (7) and the second term in Eq. (9) are responsible for the up-conversion path {3}. We see that the up-conversion prevails in relaxation of the level “1”. There are two reasons: 1) 1.8 µm luminescence growth, controlled by the up-conversion, is much faster than 3 µm luminescence decrease at the tail, which is controlled by radiative decay of level “1” (third terms in Eqs. (9) and (10); 2) cross-relaxation {2} has small contribution, because the corresponding peak at 0.0213 ms in the 1.8 µm luminescence signal is very small in comparison with the main maximum at 2.3 ms, which is due to the up-conversion {3} (Fig. 8). Thus, the up-conversion is a main relaxation channel followed immediately after cross-relaxation {1}. Since the cross-relaxation {1} always gives two paired excited ions at level “2”, the up-conversion term is linear with respect to population ${n^{\prime}_1}$. In the Eq. (10) two terms in brackets are responsible for population of the level “1” of the stand-alone ions through cross-relaxation according to an equation analogous Eq.(3). Substituting Eq. (4) into Eqs. (7) and (9), then Eq. (5) into Eqs. (8) and (10) we get rate equations:
Large difference in time scales allows fitting the decay for levels “1” and “2” separately from level “3” and further simplifying the model. During the first 0.45 ms, the level “3” population decreases tenfold, so for $t > 0.45$ ms kinetics of the levels “1“ and “2” can be considered independently from that of level “3”, starting from initial excitation of levels “1” and “2” by cross-relaxations {1} and {2} respectively (Fig. 3). Now level “2” of the stand-alone ions is not populated, because we excluded from consideration the radiative relaxation from level “3”to level “2” due to weakness of the 5.5 μm luminescence, and it is assumed that the up-conversion does not work for the stand-alone ions. Thus Eq. (12) can be omitted, and Eq. (13), Eq. (14), and Eq. (11) are respectively transformed to the rate equations:
Judd-Ofelt analysis gives from two to three times lower values for the radiative lifetimes (Table 3) than values obtained from kinetics analysis. We explain this difference by a difference of radiative probabilities for the clustered and stand-alone ions. The clustered ions have higher absorption cross-section, and they dominate in absorption spectra, so that Judd-Ofelt analysis provides radiative lifetimes that are closer to those of the clustered ions (Table 3). The stand-alone ions dominate in the kinetics curve tails, providing the values for radiative lifetimes. In the Table 4 both values are shown. In Ref. [12] the radiative lifetimes obtained by Judd-Ofelt analysis are several times higher than in our work, while dysprosium concentration was nearly the same. This discrepancy could be due to lower clustering in samples investigated in [12] due to difference in the crystal growth regime.
Fig. 10. Spectra of absorption (black) and emission (red) cross-sections, calculated by the reciprocity method for the sample #4.
Since ${\tau _{3c}} < < {\tau ^{\prime}_3},{\tau ^{\prime\prime}_3}$, almost all excited ions relax from the level “3” to levels “1” and “2” during the first 0.45 ms. The obtained relaxation parameters allow calculating kinetics of populations of the levels “1” and “2” relative to the initial population of the level “3”. We found that the peak population at level “1” reaches 77% of the initial population at level “3” (at t=0.45 ms), and the peak population at level “2” reaches 31% (at t=2.3 ms). It is important to note, that under CW excitation the relative population of the level “2” should be even higher, especially for samples with lower Dy3+ concentration, because relative intensity of the 1.8 μm band is higher for samples with lower Dy3+ concentration (Fig. 6(a)). This can be explained by the relative increase of the level “3” population for stand-alone ions, due to their longer lifetime. As a result, additional radiative channel “3” $\to $ “2” for population of level “2” comes into play under CW excitation.
Emission cross-section for the 3 µm emission band for sample #4 was calculated from the absorption spectrum by reciprocity method in the high temperature limit (Fig. 10) [18]. By the reason stated above this emission cross section spectrum is mostly related to the clustered ions, and these ions will be predominantly excited by pumping to 1.3 μm absorption band. Maximum emission cross section for stand-alone ions is obtained with Füchtbauer–Ladenburg formula using ${\tau ^{\prime\prime}_{1r}}$ and luminescence spectra [Fig. 6(a)], it was found as much as $5 \cdot {10^{ - 21}}c{m^2}$ at 3.0 μm, which is expectedly three times lower than that for the clustered ions. However, this value is very similar to the value obtained in Ref. [12], again indicating that the results of Ref. [12] refer to stand-alone ions.
Summarizing, these results make AgCl0.5Br0.5:Dy crystal promising for laser applications at 3 μm and 4.3 μm bands under 1.3 µm pumping.
7. Conclusion
AgCl0.5Br0,5:Dy crystals with Dy concentrations in the $({2 - 8} )\; \cdot {10^{18}}$ cm-3 range demonstrate strong interionic interactions during the decay of excited multiplets with emission in the near- and mid-infrared spectral regions. The dominant relaxation process under excitation to the most strong 1.3 µm absorption band is the cross-relaxation according to the scheme ${}_{}^6{H_{15/2}},\; {}_{}^6{H_{9/2}} + {}_{}^6{F_{11/2}} \to 2{}_{}^6{H_{13/2}}$, resulting in efficient population of the ${}_{}^6{H_{13/2}}$ multiplet. The ${}_{}^6{H_{11/2}}\; $multiplet is efficiently populated through cross-relaxation ${}_{}^6{H_{9/2}} + {}_{}^6{F_{11/2}}, {}_{}^6{H_{13/2}},\; \to 2{}_{}^6{H_{11/2}}$ and up-conversion $2{}_{}^6{H_{13/2}} \to {}_{}^6{H_{11/2}} + {}_{}^6{H_{15/2}}$. These processes make the AgCl0.5Br0,5:Dy crystal a perspective active medium for oscillation in the regions of 3 µm and 4.3 µm under pumping at 1.3 µm. Further on, polycrystalline silver halides fibers are manufactured by the hot extrusion. Thus, a mid-IR fiber laser based on these water-stable crystals and pumped by commercially available 1.3 µm diode lasers is feasible.
Funding
Russian Science Foundation (grant #19-12-00134).
Disclosures
The authors declare no conflicts of interest.
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