The spectra of Er:Lu2O3 have been studied between 7 K and room temperature, particularly for transitions between the 4I13/2 and 4I15/2 manifolds. This includes the determination of energy levels for Er in the C2 site and some levels for the C3i site, as well as absorption and stimulated emission cross sections and radiative lifetimes. At cryogenic temperatures, the emission lines at 1576 and 1601 nm are promising for laser operation, and the unusual breadth of the 1535-nm zero line makes it attractive for diode laser pumping, thus providing the potential for very small quantum defect lasing.
© 2013 Optical Society of America
In recent years there has been growing interest in cubic sesquioxides doped with rare-earth laser ions. These host materials have chemical formula M2O3, with M including Sc, Y and Lu, and are of interest due particularly to their superior thermal properties [1–3]. Although the thermal conductivity of Lu2O3 is somewhat lower than that of Sc2O3 and Y2O3, it is higher than that of YAG (yttrium aluminum garnet), and the close similarity of Lu3+ to trivalent rare earths in mass and ionic radius results in its thermal conductivity remaining more nearly constant with increasing dopant concentration than that of these other materials. Among the rare earth dopants in these hosts with promise for lasers, Er3+ has proven interesting because the energy spacing between its 4I15/2 and 4I13/2 manifolds facilitates lasing at relatively eyesafe wavelengths around 1.6 microns and diode pumping with very small quantum defect [4–6].
Recent years have also seen increased interest in cryogenic solid-state lasers [7–9]. The thermal conductivity, thermo-optic coefficient and coefficient of thermal expansion in crystals all tend to be considerably better around 100 K than at room temperature. These combine to enable dramatic reduction in thermal beam distortion, which is particularly important for high power laser operation. In addition, the peak absorption and stimulated emission cross sections of spectral lines in trivalent rare earth laser ions become larger due to line narrowing as the temperature is reduced, and the ground-state absorption at most practical laser wavelengths becomes smaller.
For this combination of reasons, we have studied the laser-related properties of Er:Y2O3 and Er:Sc2O3, including spectroscopy and laser performance, with emphasis on cryogenic properties [5,6]. In this paper, we report our extension of that study to the spectroscopy of Er:Lu2O3. We present basic parameters such as cross sections at some of the most likely laser wavelengths and in the spectral region of the zero-line, where the absorption is best suited to laser- or diode-pumping of a laser with minimal quantum defect .
2. Experimental details
Absorption spectra were taken using a Cary 6000i UV-vis-nIR spectrophotometer, typically with a spectral bandpass of 0.1 nm. Fluorescence was excited by a Spectra-Physics Tsunami Ti:sapphire laser operated in continuous wave (CW) mode, and analyzed using a Horiba Fluorolog-3 system with an iHR-320 monochromator and a grating blazed at 1500 nm. The signal was detected by a liquid nitrogen-cooled Teledyne Judson InGaAs detector with a nominal long-wavelength cut-off of 2600 nm. Fluorescence lifetime data were taken with a different system, with the Er 4I13/2 manifold excited directly by a Continuum Panther optical parametric oscillator that was pumped by a Q-switched, frequency-tripled Quanta-Ray PRO-230 Nd:YAG laser or with the 4I11/2 manifold excited at about 984 nm by a diode laser with 2-ms pulse duration. The resulting fluorescence was detected by the same or similar InGaAs, and analyzed by a Tektronix TDS 7104 digitizing oscilloscope coupled to the detector by selectable resistors to optimize the system’s response time and sensitivity. Resulting time constants were approximately 30 µs.
Spectra and lifetime data were taken over a range of temperatures from about 7 K to 300 K. This was done using a Janis CCS-350 cryogenic refrigerator and resistance heater.
Both ceramic and single crystalline samples of Er:Lu2O3 were used in this study, the single crystal having been grown by some of us by a floating zone method. The as-grown crystal is transparent with a pink color and homogeneous appearance. The crystal and ceramic spectra prove to be nearly identical, so that the choice of sample for a given experiment was based on sample size and Er concentration. A sample from the crystal was analyzed by Galbraith Laboratories, Knoxville, TN, yielding a concentration of 0.24% atomic (6.85 × 1019 Er/cm3). Concentrations of other samples were inferred by comparing 4I13/2 absorption strengths with this sample. The samples currently available to us are not of sufficient quality for laser experiments, but are quite sufficient for spectroscopy.
3. Experimental data
The room temperature absorption spectrum of 0.22% atomic Er:Lu2O3 is shown in Fig. 1, after subtraction of slow baseline variations. The Lu2O3 band gap is sufficiently wide that transitions to manifolds as high as 4D5/2 and 4D7/2 can be measured with confidence. Conversion of these absorption coefficient data to cross sections requires knowledge of the Er concentration of the absorbing centers, which is complicated by the existence of two types of cation site into which the dopant can substitute in cubic sesquioxides. Three-quarters of these sites have C2 symmetry and the other one-quarter have C3i symmetry . Since Er3+ and Lu3+ are of similar ionic size , it is reasonable to assume that this dopant enters the inversion-symmetric C3i sites without causing much distortion, in contrast to Er:Sc2O3 [12,13]. Thus, admixture of opposite-parity wave functions is likely to be small for ions in the nominally C3i sites, so that electric dipole transitions are much weaker for rare earth dopants in the nominal C3i sites than in the nominal C2 sites. Since magnetic dipole and higher-order multipole transitions are usually weaker than electric dipole, it is also reasonable to assume that the spectrum in Fig. 1 is due largely to the transitions of Er3+ in the C2 sites. In the similar case of Er:Y2O3, the 4I15/2 → 4I13/2 spectrum of Er in the C3i site, though substantial, is considerably weaker than that due to C2 . If we further assume that the dopant ions enter the C2 and C3i sites randomly, we can obtain approximate cross section spectra by using three-quarters of the total Er concentration in the usual expression, α = σN, where α is the absorption coefficient, σ is the absorption cross section and N is the concentration of Er ions contributing to the spectrum. For absorption to the 4I13/2 manifold, the resulting cross section spectra for two temperatures are given in Fig. 2.
Close inspection of absorption and fluorescence between these two manifolds, particularly at the lowest temperatures available to us, (~7-10 K,) yield the 4I15/2 and 4I13/2 energies shown in Table 1.They correspond well to the energy levels reported by Peters, but with refinements of up to four cm−1 . These assignments account for most of the lines of significant strength observed in absorption and fluorescence between these two manifolds, with the exceptions of the peaks listed as non-C2 in the table. Of particular interest are the peaks at 1543.7, 1545.0 and 1548.5 nm, which are of significant strength in the fluorescence spectra. The positions and strengths of the 1543.7 and 1548.5-nm absorption lines at 7-20 K mean that, if they were due to Er in the C2 site, the principal of reciprocity would predict impossibly large stimulated emission cross sections for them, confirming that they must be associated with one or more different sites with different energy level spacings. Comparison with Er:Y2O3 lines attributed to Er in the C3i site suggests that most of these non-C2 Er:Lu2O3 peaks can be attributed to Er in the C3i site, and are labeled as such in Table 1 . Also shown there are the several C3i-site Er3+ energy levels that can be identified from the transition energies. The remaining lines may be due to perturbed sites. All the non-C2 lines must be interpreted with caution in analysis of stimulated emission spectra, since they do not arise from the center whose population provides the basis for calculating cross sections.
Stimulated emission spectra may be inferred from the absorption and fluorescence spectra by combining the familiar reciprocity and Füchtbauer-Ladenburg (F-L) methods [14,15]. These are susceptible to complementary sources of error, primarily the concentration in reciprocity and the radiative lifetime and reabsorption in F-L. By scaling the F-L result to be consistent with reciprocity where F-L is minimally affected by reabsorption but the reciprocity result is sufficiently clear, the error sources in F-L are eliminated. The results in the wavelength region of interest for laser emission are shown for two temperatures in Fig. 3, again assuming that three-quarters of all Er ions reside in C2 sites. At room temperature, only for wavelengths longer than about 1600 nm are there emission lines sufficiently stronger than the absorption to be promising laser lines, whereas at liquid nitrogen temperature, peaks at wavelengths as short as 1576 nm – and perhaps 1556 nm – can be useful.
Once the full 4I13/2 → 4I15/2 spectrum has been obtained, the radiative lifetime, τrad, can be calculated by rearranging and integrating the standard F-L equation, giving the following.Eq. (1) the integral over each non-C2 line noted above, taking the wavelength limits to be the minima on either side of each such peak. This subtraction has a significant effect on the resulting radiative lifetime values, which would be about 4.6 ms at room temperature and 5.6 ms at 77K if these peaks were assumed to be part of the C2-site spectrum, versus 5.4 ms and 7.8 ms, respectively, with these peaks removed. In Fig. 4, the resulting radiative lifetimes at several temperatures are shown as violet x’s and line, compared with the green stars and line that are obtained if the non-C2 lines are not removed.
Also shown are the observed fluorescence lifetimes for several cases. Relatively broad-band diode excitation was used to obtain decay waveforms from a 0.1-cm thick sample with 0.22% atomic Er, and from a 1% Er sample of about the same thickness. The resulting waveforms exhibited a tail that deviated slightly from a single exponential, but too slightly to give reliable fitting to a more complex function. Thus, only the best-fit single exponential is reported in the figure. Narrower-line OPO pulses were used to achieve a degree of selective excitation of C2 and non-C2 absorption lines in the 0.22% sample at a few temperatures, shown as dark brown triangles and light brown diamonds, respectively, with cleaner exponential tails that suggest different lifetimes for different sites. In some cases faster initial decays, on the order of 2-4 ms, were also observed. The significance of the black pluses and the difference between calculated and observed lifetimes will be discussed in the next section.
The overall form of the Er:Lu2O3 4I13/2 → 4I15/2 emission spectrum in Fig. 3 is, not surprisingly, similar to those of other Er-doped sesquioxides [6,16]. Peak absorption and stimulated emission cross sections are presented in Table 2 for three temperatures. The 100-K data are included to indicate how these quantities change just above liquid nitrogen temperature, since the most practical operating schemes for cryogenic lasers are nitrogen-cooled but it can be assumed that any such laser generates enough heat to operate somewhat above the cryogen’s temperature.
There are stimulated emission peaks at sufficiently long wavelengths to have very little absorption even at room temperature, in particular those at 1648-9 and 1670 nm, but their cross sections are about one-third as large as those of lines in a similar wavelength range in Er:YAG . Thus, although it certainly should be possible to lase a sufficiently low-loss sample of Er:Lu2O3 in that wavelength range at room temperature, its lower gain relative to Er:YAG may make the laser threshold high enough to offset its advantage in thermal conductivity.
The laser potential of Er:Lu2O3 is more interesting at and near liquid nitrogen temperature, particularly if shorter-wavelength laser operation is desired (as for example to minimize the laser quantum defect.) The energy splitting of the 4I15/2 manifold in Er:YAG gives a gap in the low-temperature fluorescence spectrum that precludes such short-wavelength operation [17,18]. In contrast, there are Er:Lu2O3 peaks at 1576 and 1601 nm, short enough wavelengths to give much smaller quantum defects than the long-wavelength Er:YAG lines if similar pump wavelengths are used for both, yet long enough to have usefully weak absorption at 77-100 K, and peak cross sections competitive with those of Er:YAG. Indeed, an even shorter potential wavelength may be considered at nitrogen temperature, that at 1556 nm. Its peak stimulated emission cross section is about twice that of the 1576-nm line, but its absorption cross section is about 20% as large as the stimulated emission – very probably resulting in a high laser threshold. This is approximately the same ratio of absorption to stimulated emission cross sections of the analogous 1546-nm line in Er:YAG, which proved infeasible to lase . When an extremely small quantum defect is desired from an Er3+ laser at or near nitrogen temperature, Er:Sc2O3 is a better choice, as its 1558-nm line has just enough larger quantum defect for its absorption cross section to be only about 15% of the stimulated emission value. We have observed this to be sufficiently small to enable efficient laser operation at 1558 nm at and even above liquid nitrogen temperature [6,18].
One other specific spectral feature is worthy of note for potential laser operation: the peak at about 1535 nm. This is the wavelength of the 4I13/2 ↔ 4I15/2 zero line, and is the longest wavelength at which strong absorption is available for diode pumping. The energy levels given in the previous section indicate that a second line (that between the third levels of the same two manifolds) has almost exactly the same wavelength. Its transition strength must be greater than that between the two lowest states of those manifolds, as the peak cross section grows with temperature from 7 K up through about 77 K, despite thermal broadening. For higher temperatures, the peak cross section falls again, due primarily to further thermal broadening. Thus, the absorption at that wavelength is at its strongest, with a cross section of about 1.8 × 10−19 cm−2, at or near liquid nitrogen temperature. Since laser diodes often have very substantial linewidths, the full width at half maximum of this absorption peak is of interest. Its temperature dependence is shown in Fig. 5.Due to the 0.1-nm spectrophotometer resolution used for these measurements, the widths up through 40 K are instrument-limited. By 77 K instrumental broadening is a modest fraction of the observed width, so that the 0.25-nm width at that temperature and 0.38-nm width at 100 K are approximately correct. These values are much greater than the widths of the analogous 1532-nm line in Er:YAG, which are 0.023 and 0.037 nm, respectively . Thus, diode pumping of Er:Lu2O3 at low temperature would require far less aggressive line narrowing of the diodes to achieve efficient absorption than is the case for Er:YAG. At higher temperatures, the growth of nearby absorption lines affects the shape and width of the 1535-nm line. For that reason, no attempt has been made to fit the temperature dependence of the linewidth to the functional forms for standard broadening processes.
Figure 4 shows that the radiative lifetime gets shorter with increasing temperature similarly to the trend in the observed lifetimes. Thus, the observed temperature dependence is probably due to changes in thermal population of strongly-emitting levels, rather than to quenching. However, even after correction for non-C2 lines, the calculated radiative lifetime is shorter than the observed lifetime over the full range of temperatures studied. Often, the observation of fluorescence lifetimes longer than radiative indicates substantial radiative reabsorption. However, in the present case there are reasons to doubt that interpretation. Measurements on samples of approximately the same thickness whose concentrations differ by a factor of four give similar lifetimes over most of the temperature range, but differ from the predicted radiative values over that entire range.
One can estimate the effect of reabsorption on the observed lifetime by means of a simple model. Let the typical excited ion be treated as at the center of a sphere of doped material, with so few ions excited that the unexcited concentration can be taken as equal to the total concentration. Then the probability of an emitted photon being reabsorbed before escaping the doped region is 1 – exp(-σeffNtR), where σeff is the effective absorption cross section in the fluorescence spectral region, Nt is the total dopant concentration and R is the radius of the doped volume. If σeffNtR << 1, the observed lifetime, τobs, differs from the individual ion’s lifetime, τtrue, as follows.
Since the samples for our lifetime measurements were approximately 0.1 cm thick and the excitation and detection directions were orthogonal to each other and about 45° from the sample plane, R should be on the order of 0.07 cm. The total Er concentration for the 0.22% sample is 4.71 × 1019 cm−3, and the resulting fraction absorbed, σeffNtR, for that sample and radius varies from 0.020 at 295 K to 0.062 at 77 K. The resulting lifetime is shown in Fig. 4 as the black symbols and line. Clearly, it affects the lifetime only subtly, consistent with the observed similarity of the lifetimes for the two Er concentrations, and not at all consistent with the difference between observed and calculated lifetimes. To get reasonable agreement with experiment, we must assume the product of concentration and radius to be an order of magnitude larger than the values estimated above. Even for the higher concentration sample the model radius required for a fit is unrealistic – more than twice the sample thickness. Thus, it appears unlikely that reabsorption can explain the observed lifetimes.
The predicted radiative lifetime must therefore be reconsidered. It can be checked for realism by comparison with Judd-Ofelt analysis of the room temperature absorption data. We have analyzed the data of Fig. 1 in the standard way [19,20], using the Er3+ reduced matrix elements tabulated by Kaminskii . Again assuming that three-quarters of the Er ions reside in the C2 sites, the measured and best fit theoretical line strengths, the best fit Judd-Ofelt parameters and the resulting predicted 4I13/2 radiative lifetime are given in Table 3.The RMS deviation of the line strength is only 9% of the average line strength, indicative of a good fit. Note that these calculations were performed without removing non-C2 lines, as we have not identified all such lines in absorption data, particularly for the higher-energy manifolds. Since such lines may well be due to ions in the C3i sites allowed by the magnetic dipole interaction, and since that interaction tends to be more prominent in longer wavelength spectra rather than shorter, their inclusion in the calculation may affect the results somewhat less than it affected the F-L calculation reported above. The predicted room temperature radiative lifetime of 4.70 ms is close to that calculated by F-L with the non-C2 lines included (4.6 ms.) Given the well-known approximations in the Judd-Ofelt theory, this agreement is more than satisfactory, suggesting that our radiative lifetime calculations are sound.
Other possible causes for the difference between predicted radiative and observed lifetimes may be noted. We have not been able to identify enough non-C2 lines in the 4I15/2 ↔ 4I13/2 spectra to account for all the expected C3i energy levels, and indeed perturbed sites may exist that would give rise to still more non-C2 lines. Thus, the integral over the stimulated emission spectrum in Eq. (1) may still contain extraneous (non-C2) features that make the calculated radiative lifetime too short. It may also be noted that all the cross section (and hence radiative lifetime) values derived here depend on the concentration of Er3+ in the C2 site, and thus on the assumption that three-quarters of all Er3+ ions reside in that type of site. However, there are reports in the literature of rare-earth-doped cubic sesquioxides in which the C2 sites are populated preferentially [22,23]. Calculating from the observed absorption data, a larger C2 population would lead to reduced cross sections. However, the fact that non-C2 lines comprise a significant fraction of the integrated 4I13/2 absorption, 0.12 at 295 K and 0.19 at 77 K, indicates that the C2 concentration must be significantly less than 100% of the total Er3+ concentration. It is thus unlikely that the C2 concentration could be enough larger to account for the full lifetime disagreement. The complications observed in the lifetime data suggest yet another potential cause for the disagreement. There are at least two sites with different lifetimes, and the faster initial decay seen in some cases suggests a third. To determine the lifetime to be compared with the radiative value, a more extended study would be required to extract the C2 lifetime and the possible effects of energy transfer from this complex decay pattern.
The spectroscopic properties of Er:Lu2O3, particularly those relevant to potential 4I13/2 → 4I15/2 laser action, have been studied over the temperature range 7-300 K. Its features are similar to those of other Er-doped sesquioxides, and are quite different from those of Er:YAG. The latter material has superior cross sections for laser operation at room temperature, due to its strong emission peaks at wavelengths longer than 1600 nm. However, for liquid nitrogen temperature operation, the lines at 1576 and 1601 nm in Er:Lu2O3 offer stimulated emission cross sections very competitive with that of any viable line in Er:YAG, sufficiently low absorption, and smaller quantum defects. For diode pumping of the zero line and transitions overlapping it, Er:Lu2O3 offers an order of magnitude greater width than does Er:YAG, a value very similar to that in Er:Sc2O3 and somewhat greater than in Er:Y2O3 . This greater width is due in part to the overlap of different transitions, but other processes such as differences in electron-phonon coupling are probably involved.
The differences between observed fluorescence lifetimes and those inferred from the transition strengths and spectra are greater than can be explained by reabsorption. The experiments required to detect nonuniform site occupation, and the intensive decay kinetics study needed to be sure of the true C2 site Er3+ lifetime, are beyond the scope of the present study. The possibility of preferential occupation of one type of cation site introduces a degree of uncertainty into the determination of cross sections, and given the similarity in structure and cation size, a similar uncertainty may well exist for Er:Y2O3. However, in neither of these materials are uncertainties about site occupation likely to rival the complications in Er:Sc2O3, where the much larger difference between dopant and host cation sizes appears to cause major distortion, including interstitial locations of dopant ions . Indeed, the combination of pump line width equal to that of Er:Sc2O3 with the probability that the crystal structure remains simpler may make Er:Lu2O3 more attractive than Er:Sc2O3 for some laser applications.
The authors thank Akio Ikesue for providing the ceramic samples. H. Z., H. Y., and J. W. gratefully acknowledge the support of the National Science Foundation of China, projects 51032004 and 51102156.
References and links
1. P. H. Klein and W. J. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77°-300°K,” J. Appl. Phys. 38(4), 1603–1607 (1967). [CrossRef]
2. V. Peters, E. Mix, L. Fornasiero, K. Petermann, G. Huber, and S. A. Basun, “Efficient Laser Operation of Yb3+:Sc2O3 and spectroscopic characterization of Pr3+ in cubic sesquioxides,” Laser Phys. 10, 417–421 (2000).
4. C. Brandt, N. A. Tolstik, N. V. Kuleshov, K. Petermann, and G. Huber, “Inband pumped Er:Lu2O3 and Er,Yb:YVO4 Lasers near 1.6 µm for CO2 LIDAR,” in Advanced Solid-State Photonics, Technical Digest (CD) (Optical Society of America, 2010), paper AMB15.
6. N. Ter-Gabrielyan, V. Fromzel, and M. Dubinskii, “Performance analysis of the ultra-low quantum defect Er3+:Sc2O3 [Invited],” Opt. Mater. Express 1(3), 503–513 (2011). [CrossRef]
7. D. C. Brown, “The Promise of Cryogenic Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 11(3), 587–599 (2005). [CrossRef]
8. T. Y. Fan, D. J. Ripin, R. L. Aggarwal, J. R. Ochoa, B. Chann, M. Tilleman, and J. Spitzberg, “Cryogenic Yb3+-Doped Solid-State Lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 448–459 (2007). [CrossRef]
9. I. B. Mukhin, O. V. Palashov, E. A. Khazanov, A. G. Vyatkin, and E. A. Perevezentsev, “Laser and thermal characteristics of Yb:YAG crystals in the 80-300 K temperature range,” Quantum Electron. 41(11), 1045–1050 (2011). [CrossRef]
10. J. B. Gruber, K. L. Nash, D. K. Sardar, U. V. Valiev, N. Ter-Gabrielyan, and L. D. Merkle, “Modeling optical transitions of Er3+(4f11) in C2 and C3i sites in polycrystalline Y2O3,” J. Appl. Phys. 104, 023101 (2008). [CrossRef]
11. R. D. Shannon, “Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides,” Acta Crystallogr. A 32(5), 751–767 (1976). [CrossRef]
12. Volker Peters, “Growth and Spectroscopy of Ytterbium-Doped Sesquioxides,” dissertation, U. Hamburg (2001), http://www.physik.uni-hamburg.de/services /fachinfo/___Volltexte/Volker___Peters/Volker___Peters.pdf.
13. K. Anduleit and G. Materlik, “A Holographic approach to point defect structure determination in inorganic crystals: Er-doped Sc2O3.,” Acta Crystallogr. A 59(Pt 2), 138–142 (2003). [CrossRef] [PubMed]
14. B. F. Aull and H. P. Jenssen, “Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections,” IEEE J. Quantum Electron. 18(5), 925–930 (1982). [CrossRef]
15. S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared Cross-Section Measurements for Crystals Doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992). [CrossRef]
16. N. Ter-Gabrielyan, L. D. Merkle, G. A. Newburgh, and M. Dubinskii, “Resonantly-Pumped Er3+:Y2O3 Ceramic Laser for Remote CO2 Monitoring,” Laser Phys. 19(4), 867–869 (2009). [CrossRef]
17. S. D. Setzler, M. P. Francis, Y. E. Young, J. R. Konves, and E. P. Chicklis, “Resonantly Pumped Eyesafe Erbium Lasers,” IEEE J. Sel. Top. Quantum Electron. 11(3), 645–657 (2005). [CrossRef]
18. L. D. Merkle, N. Ter-Gabrielyan, and V. Fromzel, “Cryogenic laser properties of Er:YAG and Er:Sc2O3 – A comparison,” in Advanced Solid-State Photonics, Technical Digest (CD) (Optical Society of America, 2011), paper AWA02.
19. D. K. Sardar, W. M. Bradley, J. J. Perez, J. B. Gruber, B. Zandi, J. A. Hutchinson, C. W. Trussell, and M. R. Kokta, “Judd-Ofelt analysis of the Er3+ (4f11) absorption intensities in Er3+ – doped garnets,” J. Appl. Phys. 93(5), 2602–2607 (2003). [CrossRef]
20. M. Brian, Walsh, “Judd-Ofelt Theory: Principles and practices,” in Advances in Spectroscopy for Lasers and Sensing, B. di Bartolo and O. Forte, eds. (Springer, 2006), pp. 403–433.
21. A. A. Kaminskii, Crystalline Lasers: Physical Processes and Operating Schemes (CRC Press, 1996), pp. 274–294.
22. M. Mitric, B. Antic, M. Balanda, D. Rodic, and M. Lj. Napijalo, “An x-ray diffraction and magnetic susceptibility study of YbxY2-xO3,” J. Phys. Condens. Matter 9(20), 4103–4111 (1997). [CrossRef]
23. G. Concas, G. Spano, E. Zych, and J. Trojan-Piegza, “ Nano- and microcrystalline Lu 2 O 3 :Eu phosphors: variations in occupancy of C 2 and S 6 sites by Eu 3+ ions, ” J. Phys. Condens. Matter 17(17), 2597–2604 (2005). [CrossRef]
24. L. D. Merkle and N. Ter-Gabrielyan, “Er3+ in Sc2O3 and Y2O3: Spectroscopy to elucidate laser behavior,” J. Lumin. 133, 254–256 (2013), doi: [CrossRef] ; L. D. Merkle, N. Ter-Gabrielyan and K. J. Cote, International Conference on Luminescence 2011, paper ThII1.