ARTICLE IN PRESS Journal of Luminescence 130 (2010) 1021–1025
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Spectroscopic investigations of 1.06 mm emission in Nd3 + -doped alkali niobium zinc tellurite glasses S. Surendra Babu a,1, R. Rajeswari b, Kiwan Jang a,n, Cho Eun Jin a, Kyoung Hyuk Jang c, Hyo Jin Seo c, C.K. Jayasankar b a
Department of Physics, Changwon National University, Changwon 641-773, Republic of Korea Department of Physics, Sri Venkateswara University, Tirupati 517-502, India c Department of Physics, Pukyong National University, Pusan 608-737, Republic of Korea b
a r t i c l e in fo
Article history: Received 1 September 2009 Received in revised form 10 January 2010 Accepted 15 January 2010 Available online 21 January 2010
Thermal, structural and optical properties of Nd3 + ions in tellurite glass (TeO2–ZnO–Na2O–Li2O–Nb2O5) have been investigated. Differential thermal analysis revealed reasonably good forming tendency of the glass composition. FTIR spectra were used to analyze the functional groups present in the glass. Judd–Ofelt intensity parameters were derived from the absorption spectrum and used to calculate the radiative lifetime, branching ratio and stimulated emission cross-section of the 4F3/2-4I9/2, 11/2, 13/2 transitions. The quantum efﬁciency of the 4F3/2 level is comparable as well as higher than the typical value of the other tellurite based glasses. The decay from the 4F3/2 level is found to be single exponential for different concentrations of Nd3 + ions with a shortening of lifetime with increasing concentration. The experimental values of branching ratio and saturation intensity of 4F3/2-4I11/2 transition indicate the favourable lasing action with low threshold power. & 2010 Elsevier B.V. All rights reserved.
Keywords: Luminescence properties Nd3 + -doped glasses Tellurite glasses Emission cross-section Saturation intensity
1. Introduction With the rapid development of diode-pumped solid-state laser technology, research on more efﬁcient new laser materials has gained most importance. In this direction, trivalent neodymium (Nd3 + ) is widely studied ion in a variety of glasses and crystals under 808 and 885 nm laser diode excitation to develop high peak-power solid state lasers in the near infra-red (NIR) region at 1.06 mm [1–4]. Since the maximum phonon energy of host plays an important role in Nd3 + ion emission, an appropriate selection of host material for Nd3 + ions is inevitable to minimize the multiphonon relaxation rate to enhance quantum efﬁciency of emission levels . Among the oxide glasses, tellurium dioxide (TeO2) based glasses possess large rare earth (RE) ion solubility, wide transmission window ( 0.4–5 mm), high linear and non-linear refractive indices and moderate phonon energy (750 cm 1), which is lower than germinate, silicate and phosphate glasses . A combination of relatively high refractive index and low phonon energy increase the quantum efﬁciency of the excited states of Nd3 + ions in these glasses and provides the possibility of developing more efﬁcient lasers, non-linear optical devices, and so on.
Corresponding author. Fax: + 82 55 267 0264. E-mail address: [email protected]
(K. Jang). 1 Present address: Laser Instrumentation Design Centre, Instruments Research and Development Establishment, Raipur Road, Dehradun 248 008, India. 0022-2313/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2010.01.017
The present work reports the systematic investigation of thermal, structural and optical properties of Nd3 + -doped alkali-niobium zinc-tellurite (TZNLN) glasses. The Nd3 + -doped TZNLN glass is found to be thermally stable and the maximum phonon energy is higher than the other zinc-tellurite glasses. Branching ratios and emission cross-section calculations reveal the possibility of using the Nd3 + -doped TZNLN glass for lasing action at 1.06 mm. It is interesting to note that the measured decay curves of the 4F3/2 level remain nearly single exponential even for higher Nd3 + ion concentration but with shortening of lifetime.
2. Experimental Nd3 + -doped alkali-niobium zinc-tellurite glasses of molar compositions; (60-x) TeO2–20ZnO–7.5Na2O–7.5Li2O–5Nb2O5– xNd2O3 (x =0.1, 1.0 and 2.0) (referred as TZNLN glass) were prepared by the conventional melting procedure as explained in our earlier works [6–8]. Reagent grade of TeO2, ZnO, Na2CO3, Li2CO3, Nb2O5 and Nd2O3 raw chemicals were used as starting materials. The amorphous nature of the as quenched glasses was conﬁrmed by X-ray powder diffraction pattern using the Cu Ka radiation (X’pert MPD, Philips). The glass sample in powdered form of about 50 mg was heated in a platinum pan at a heating rate of 10 1C/min in the 30–1200 1C temperature range to record the DTA spectrum. FTIR spectrum was recorded using a
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Perkin-Elmer 2000 FTIR spectrophotometer. The absorption spectrum was measured using a Hitachi U-3400 spectrophotometer. The second harmonic generated Nd:YAG laser (Spectron Laser Sys. SL802G) was used as an excitation source for the photoluminescence and decay measurements. The ﬂuorescence was dispersed by a 75 cm monochromator (Acton Research Corp. Pro-750), and observed with a photomultiplier tube (PMT; Hamamatsu R 928). The signal from the PMT was fed to a digital oscilloscope (Le Croy 9310) and then the data were stored in a personal computer. Decay curves were obtained using a digital storage oscilloscope interfaced to a personnel computer that recorded and averaged the signal. The refractive index was measured by Brewster angle method using He–Ne laser as the source. The density was measured by the Archimede’s method using water as an immersion liquid. All the measurements were carried out at room temperature (RT) only. Fig. 2. DTA curves of the 1.0 mol% Nd3 + -doped TZNLN glass.
3. Results and discussion
Fig. 1 shows the XRD pattern of the Nd3 + -doped TZNLN glass. As can be seen from the ﬁgure, the XRD pattern exhibits a broad scattering at lower angles suggesting a structural disorder which conﬁrms the amorphous nature of the TZNLN glass. Thermal stability of the Nd3 + -doped TZNLN glass has been examined by measuring the differential thermal analysis (DTA), which is shown in Fig. 2. As shown in the ﬁgure, the DTA scan exhibits a small endothermic peak corresponding to the glass transition temperature, Tg. The onset crystallization process is marked by a single exothermic peak, Tx and the melting is identiﬁed by the endothermic peak, Tm. The difference between the onset crystallization temperature and glass transition temperature, (Tx–Tg), has been frequently used as a measure of thermal stability of the host glass. It is desirable for a host glass to have a large value of (Tx–Tg) and a low temperature interval (Tm–Tx) to be a best candidate for rod fabrication. The thermal stability, which is of prime importance for processing glassy materials, was assessed by using the Hruby criterion  expressed as HR =(Tx Tg)/(Tm Tx). For Nd3 + doped TZNLN glass, Tg =277 1C, Tx =401 1C and Tm =670 1C. Hence, the values of (Tx–Tg) and HR are found to be 124 and 0.46, respectively. The (Tx–Tg) value is found to be higher than boro-tellurite  and Er3 + -doped TeO2–BaO (Li2O, Na2O)–La2O3  glasses and slightly
Fig. 1. XRD pattern of 1.0 mol% Nd3 + -doped TZNLN glass.
Transimitance (arb. units)
3.1. Glass stability and FTIR analysis
1,090 cm-1 879 cm-1 cm-1
425 462 cm-1 780 cm-1 700 500
700 800 900 Wavenumber (cm-1)
Fig. 3. FTIR spectrum of 1.0 mol% Nd3 + -doped TZNLN glass.
lower than Er3 + -doped 10ZnO–10Na2O–80TeO2 (Tx–Tg =130 and HR =0.72) glass . The quantitative value of (Tx–Tg) and HR of Nd3 + -doped TZNLN glass indicates the reasonably good glass forming tendency and the stability of the system. The FTIR spectrum of the 1.0 mol% Nd3 + -doped TZNLN glass is shown in Fig. 3. In general the tellurite glasses follow the pattern of crystalline a-TeO2, which are formed by [TeO4] groups as trigonal bipyramids (tbp). The introduction of modiﬁer ions destroy the three dimensional network, creating non-bridging oxygen (NBO) species and gradually transforming the TeO4 units into TeO3 + 1 and TeO3 [13,14]. The presence of the modiﬁer ion such as Zn2 + leads to the creation of TeO3 and additional TeO3 + 1 polyhedra, which are responsible for the band at 750 cm 1 in the tellurite glass . The addition of alkali metals to the zinctellurite glass has no signiﬁcant effect on this bond. On the other hand, the addition of Nb2O5 causes signiﬁcant change. This peak becomes broader from 640 to 780 cm 1 with an additional peak at around 879 cm 1. This value is considerably higher than that of other tellurite glasses [13–15]. The later peak is due to the existence of [NbO6] octahedral groups which are also observed in binary and ternary tellurite glasses containing Nb2O5 . The observed peaks in the range of 425–462 cm 1 have been attributed to the Te–O–Te symmetric stretching mode at corner sharing sites. This indicates that the vibrations of the Te–O–Te
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linkage in these glasses are due to the transformation of TeO4 group into TeO3 groups. The ﬁrst over tone of these peaks are observed at around 1090 cm 1. Due to experimental conditions, our analysis is limited upto 400 cm 1 only.
3.2. Optical spectra and radiative properties Fig. 4 shows the RT optical absorption spectra of the 1.0 mol% Nd3 + -doped TZNLN glass along with the band assignments. The inhomogeneously broadened absorption bands correspond to the transitions from the ground 4I9/2 state to various excited states within the 4f shell of Nd3 + ions in the TZNLN glass. The location and assignments of the absorption bands have been made as carried out as in the earlier studies on Nd3 + -doped glasses [6–8] and the band positions of these transitions are collected in Table 1. Fig. 5 shows the NIR emission spectra of Nd3 + :TZNLN glass corresponding to 4F3/2-4IJ (J=9/2, 11/2 and 13/2) transitions. The absorption and emission spectra are inhomogeneously broadened due to site-to-site variations in the local ligand ﬁeld. From the absorption spectrum, experimental oscillator strengths (fexp) of the f-f transitions were obtained and are used in the frame work of Judd–Ofelt (JO) theory [17,18]. The three Judd–Ofelt parameters (Ol, l = 2, 4 and 6), were calculated by ﬁtting the electric-dipole contributions of the experimental
Fig. 4. Optical absorption spectrum of 1.0 mol% Nd2O3-doped TZNLN glass. Table 1 Absorption level positions (l, nm), experimental (fexp, 10 6) and calculated (fcal, 10 6) oscillator strengths for 1.0 mol% Nd2O3-doped TZNLN glass and experimental oscillator strengths for other reported Nd3 + :glasses. Transition 4I9/2-
F3/2 F5/2, 2H9/2 F7/2, 4S3/2 4 F9/2 2 H11/2 4 G5/2, 2G7/2 4 G7/2, 4G9/2 2 G9/2,2D23/2,K15/2 2 P1/2 4 D1/2, 3/2, 5/2, 2I11/2, 2L15/2 s (N)a 4 4
879 810 749 684 628 587 521 471 431 –
TZN  fcal
2.94 2.61 7.41 8.08 8.95 8.48 0.73 0.65 0.12 0.17 17.46 17.48 5.84 5.42 1.93 1.02 0.44 0.66 – – 7 0.39 (9)
2.00 6.90 7.62 0.60 0.15 21.22 7.20 1.73 0.43 10.04 70.59 (10)
2.80 10.06 8.75 0.55 0.27 25.33 8.28 1.74 0.96 – 7 0.69 (9)
a s refers rms deviation between experimental and calculated values and N refers the number of levels used in the ﬁt.
Fig. 5. NIR emission spectrum of 1.0 mol% Nd2O3-doped TZNLN glass.
oscillator strengths to the calculated ones (fcal) by following the same procedure as reported in earlier work [5–8]. Table 1 collects the experimental and theoretical oscillator strengths of the Nd3 + -doped TZNLN glasses along with the ZnO based TeO2– ZnO–Nd2O3 (TZN)  and B2O3–ZnO–Nd2O3 (BZN)  glasses. The JO parameters obtained for the TZNLN glass were collected in Table 2 along with those of the similar other glass compositions [3,8,19–26]. As seen in Table 2, it is interesting to note that the trends of magnitude Ol parameters for Nd3 + -doped TeO2 based glasses in general are found to be O4 4 O6 4 O2. The O2 parameter exhibits the dependence of the covalency between Nd3 + ions and ligand anions, because O2 is connected to the asymmetry of the local environment around the Nd3 + sites . The lesser the value of O2, the more centrosymmetrical the ion site and the more ionic its chemical bond with the ligands . As seen in Table 2, the value of O2 of TZNLN glass is found to be less than other glasses by 30–40% [6,19–26], which may be due to smaller value of the oscillator strength of the hypersensitive 4I9/2-4G5/2 transition than in the other glasses. The lesser value of O2 in TZNLN glass indicates that the hosts exhibit weaker covalence and lower symmetry for Nd–O bond when compared with other glass hosts that are shown in Table 2. Due to the zero value of certain reduced matrix elements, ðlÞ 2 :U : , the emission intensity from the 4F3/2 level of Nd3 + ions can be uniquely characterized by the ratio of intensity parameters O4 and O6, which is known as spectroscopic quality factor, w. If w is smaller than unity, the intensity of the 4F3/2-4I11/2 transition is stronger than that of the 4F3/2-4I9/2 transition in that host. The w value for TZNLN glass is found to be 0.88 which is comparable to other oxide glasses including commercial laser glasses [23,24,26,28]. From the w values listed in Table 2, it can be predicted that the intensity of 4F3/2-4I11/2 transition in the TZNLN glass will be larger than that of the 4F3/2-4I9/2 transition which is similar to the TeO2–Na2O glass . Further it is interesting to note that the w value of other tellurite glasses is higher than unity indicating the possibility of obtaining lasing action at 1.33 mm (4F3/2-4I9/2 transition). The radiative emission probabilities (AR) from the most important 4F3/2 states of the Nd3 + ions, their branching ratios (bR) and the radiative lifetimes (tR) were estimated on the basis of the calculated JO intensity parameters, using the procedure described in Refs. [5–8]. The total radiative transition probability
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Table 2 Judd–Ofelt parameters (Ol, 10 20 cm2), spectroscopic quality factor (w), radiative and ﬂuorescence lifetimes (ms) and quantum efﬁciency of 4F3/2 level of Nd3 + in TZNLN glass for some of the reported Nd3 + :glasses. Glass
TZNLN (present glass) TeO2 WO3 Nd2O3  TZN  BZN  TeO2 TiO2 Nb2O5 Nd2O3  68TeO2 31ZnO 1Nd2O3  79TeO2–20Li2O 1Nd2O3  79TeO2–20Na2O-1Nd2O3  90TeO2–10Na2O  TeO2 Nb2O5 Al2O3 Nd2O3  45SiO2–25Al2O3–5CaO–10NaF–15CaF2  40SiO2–30Na2CO3–20PbO–10ZnO  PbO–Bi2O3–Ga2O3–BaO 
2.13 4.71 3.80 5.2 3.62 3.62 3.64 4.06 5.24 3.12 2.36 3.66 3.2
3.29 4.06 4.94 3.6 4.21 4.63 4.88 4.79 3.22 4.84 3.69 5.53 2.7
3.83 3.89 4.54 5.0 2.95 4.26 4.55 4.62 4.47 3.28 3.93 2.73 3.1
0.86 1.04 1.09 0.72 1.43 1.07 1.07 1.04 0.72 1.48 0.94 2.03 0.87
154 149 153 311 158 163 154 154 – 1.59 513 290 134
136 105 104 – 146 181 170 177 – – – 313 113
0.88 0.70 0.68 – 0.92 0.90 0.90 0.87 – – – 0.92 0.85
Table 3 Emission band positions (lP, nm), effective linewidths (Dleff, nm), stimulated emission cross-section (s(lp), 10 20 cm2) and saturation intensity (Is, 108 W/m2) from 4F3/2 level of Nd3 + ion in TZNLN glass along with various other Nd3 + :glasses. Glass
TZNLN (present work) 4 F3/2-4I9/2 4 F3/2-4I11/2 4 F3/2-4I13/2
905 1061 1335
42.11 28.35 50.11
1.24 4.27 1.21
13.03 3.22 9.78
TeO2 WO3 Nd2O3  4 F3/2-4I11/2
68TeO2–31ZnO 1Nd2O3  4 F3/2-4I11/2
79TeO2–20Li2O 1Nd2O3  4 F3/2-4I11/2
79TeO2–20Na2O 1Nd2O3  4 F3/2-4I11/2 PbO–Bi2O3–Ga2O3–BaO  LHG–80  LG–770  Q-88 
1062 1069 1054 1053 1054
– – 23.9 25.4 21.9
4.9 2.6 4.2 3.9 4.0
2.48 6.50 1.33 1.38 1.44
TZN  4 F3/2-4I11/2 TeO2 TiO2 Nb2O5 Nd2O3  4
Fig. 6. Luminescence decay from the 4F3/2 level of Nd3 + ions (0.1, 1.0 and 2.0 mol %) in TZNLN glasses.
The observed values of lp, Dleff and s(lp) were collected in Table 3 and were compared with other reported glass systems. As seen in Table 3, all these parameters were well within the ranges commonly reported for Nd3 + -doped laser glasses [6–8,19–26]. 3.3. Decay time measurements
(SAR) is found to be 6494 s 1 and the tR (1/SAR) is 154 ms. The calculated bR values of the 4F3/2-4IJ (J =15/2, 13/2, 11/2 and 9/2) is found to be 0.01, 0.1, 0.49, 0.40, respectively, which shows a considerable deviation from the experimental values of 0.1, 0.77, 0.12 for 4F3/2-4IJ (J= 15/2, 13/2, 11/2 and 9/2), respectively, obtained from the luminescence spectra. The experimental branching ratio for the 4F3/2-4I11/2 level is found to be relatively maximum indicating an intense transition in the titled glasses. From the experimental luminescence spectra, the stimulated emission cross-sections, s(lp), of the laser transitions were evaluated using the following equation:
sðlp Þ ¼
l4p AR 8pcn2 leff
where n is the refractive index, lp is the emission peak wavelength and Dleff is the emission effective linewidth of the transition given by Z 1 Dleff ¼ ð2Þ IðlÞdl Ip
The decay proﬁle of the luminescence from 4F3/2 level of Nd3 + ion in TZNLN glass has been measured by monitoring the 4 F3/2-4I11/2 transition and is shown in Fig. 6 for three concentrations of Nd3 + ions. It is interesting to note that the decay curves are almost single exponential even for higher Nd3 + ion concentrations. The near single exponential nature of these decay curves is due to either fast decay of excited Nd3 + ions or the effect of ligands is considerably small on Nd3 + ions. From the decay curves, ﬂuorescence lifetime (tf) of the 4F3/2 level has been determined by ﬁnding the ﬁrst e-folding times of the decay intensity. The tf value of 1.0 mol% Nd3 + -doped glass is found to be 136 ms which gives quantum efﬁciency, the ratio of tf to tR, equal to 88%. The tf of the 1.0 mol% Nd3 + -doped glasses under investigation is found to be lower than the tR obtained from Judd–Ofelt analysis which indicates the existence of non-radiative de-excitation channels from 4F3/2 level. The non-radiative 1 transition rate (WNR) is given by WNR ¼ t1 f tR and is found to be 859 s 1. The considerable value of the WNR also indicates the existence of non-radiative channels. The non-radiative channel
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may be multiphonon relaxation, cross-relaxation between a pair of Nd3 + ions and energy transfer to the impurities. According to Miyakawa–Dexter , the non-radiative decay rate due to multiphonon relaxation process between two states can be described using an energy-gap law ð3Þ WMR ¼ W0 expðaDEÞ where a ¼ ð_wÞ1 ln pg 1 , p DE=_w. DE is the energy gap between the levels of interest, _w is the phonon energy, p is the effective phonon number, g is the electron–phonon coupling strength, W0 and a are the positive constants which depend on the properties of the host material. For a tellurite glass DE =5490 cm-1, W0 =6.3 1010 s 1 and hence, the number of phonons necessary to bridge the 4F3/2 4I15/2 energy gap is about six [7,29]. Using these parameters, the multiphonon relaxation rate, WMR was estimated to be about 65 s 1 for TZNLN glasses. Therefore, the multiphonon relaxation process is also found to be negligible factor for the shortening of the lifetime of the 4F3/2 level in the glasses under investigation. Hence, the decrease in lifetime with increase in Nd3 + ions concentration may be due to the onset of fast Nd3 + –Nd3 + diffusion processes . 3.4. Saturation intensity The pump input power to reach threshold for cw laser operation is directly proportional to the saturation intensity which depends on the material properties such as emission crosssection and ﬂuorescence lifetime. The saturation intensity is given by Is ¼ hc=lsðlp Þtf . From the expression, it is clear that material with a large product of stimulated emission cross-section and ﬂuorescence lifetime (s(lp)tf) in turn low value of the Is will have a low laser threshold. The Is value for the Nd3 + doped TZNLN glass is found to be 3.2 108 W/m2, which is one order higher than that of Nd:YAG (2.9 107 W/m2) indicating a higher threshold in the titled glass than in Nd:YAG . Table 3 collects the Is of various Nd3 + -doped glasses along with the Nd3 + -doped TZNLN glass. It is interesting to note that the Is value of the present glass is higher than binary tellurite and commercial glasses [21,28] and is considerably lower than the other reported glasses [3,6,20,25,26]. This observation along with the high value of bR for 4F3/2-4I11/2 transition indicate the possibility of using the Nd3 + -doped TZNLN glass for lasing action at 1.06 mm with relatively lower threshold power than the other glasses.
4. Conclusion Nd3 + -doped alkali niobium zinc tellurite glasses were prepared and their thermal, structural and optical properties were evaluated. The alkali niobium zinc tellurite glass was found to be thermally stable for rare earth ion doping and maximum phonon energy is found to be higher than the zinc tellurite glasses because of the presence of the niobium oxide. Absorption, ﬂuorescence spectra, and ﬂuorescence lifetimes of neodymium doped alkali niobium zinc tellurite glasses were measured and analyzed. The quantum efﬁciency of the ﬂuorescent 4F3/2 level is found to be 88% favouring lasing action at 1.06 mm. Multiphonon relaxation rate
from the 4F3/2 level is found to be negligible and the shortening of lifetime with increasing Nd3 + ion concentration is attributed to the Nd3 + Nd3 + diffusion process. The study of the saturation intensity indicates lower laser threshold power for the studied glass system than most of the other glasses.
Acknowledgements This work has been carried out under a Major Research Project supported by DAE-BRNS (no. 2007/34/25-BRNS/2415, dt. 18-01-2008) and UGC (F.32-28/2006(SR) dt. 19-03-2007), Government of India. References  Antonio Agnesi, Paolo Dallocchio, Federico Pirzio, Giancarlo Reali, Opt. Commun. 282 (2009) 2070.  I. Iparraguirre, J. Azkargorta, J.M. Fernandez-Navarro, M. Al-Saleh, J. Fernandez, R. Balda, J. Non-Cryst. Solids 353 (2007) 990.  Hamit Kalaycioglu, Huseyin Cankaya, Gonul Ozen, Lutfu Ovecoglu, Alphan Sennaroglu, Opt. Commun. 281 (2008) 6056.  V. Lupei, N. Pavel, T. Taira, Appl. Phys. Lett. 80 (2002) 4309.  R. Reisfeld, C.K. Jorgensen, in: Handbook of Physics and Chemistry of Rare Earths, Excited State Phenomena in Vitreous Materials, Ch. 58, Elsevier Science, Publishers B.V., Amsterdam, 1987 and references there in.  S. Surendra Babu, P. Babu, C.K. Jayasankar, A.S. Joshi, A. Speghini, M. Bettinelli, J. Phys. Condens. Matter 18 (2006) 3975.  K. Upendra Kumar, P. Babu, Kyoung Hyuk Jang, Hyo Jin Seo, C.K. Jayasankar, A.S. Joshi, J. Alloys Compd. 458 (2008) 509.  K. Upendra Kumar, V.A. Prathysha, P. Babu, C.K. Jayasankar, A.S. Joshi, A. Speghini, M. Bettinelli, Spectrochim. Acta A 67 (2007) 702.  A. Hruby, Czech. J. Phys. B 22 (1972) 1187.  S. Hocde, S. Jiang, X. Peng, N. Peyghambarian, T. Luo, M. Morrell, Opt. Mater. 25 (2004) 149.  H. Chen, Y.H. Liu, Y.F. Zhou, Z.H. Jiang, J. Alloys Compd. 397 (2005) 286.  G. Nunzi Conti, V.K. Tikhomirov, M. Bettinelli, S. Berneschi, M. Brenci, B. Chen, S. Pelli, A. Speghini, A.B. Seddon, G.C. Righini, Opt. Eng. 42 (2003) 2805.  H. Burger, K. Kneipp, H. Hobert, W. Vogel, V. Kozhukharov, S. Neov, J. NonCryst. Solids 151 (1992) 134.  T. Sekiya, N. Mochida, A. Ohtsuka, J. Non-Cryst. Solids 168 (1994) 106.  L. Fortes, L.F. Santos, M. Clara Goncalves, R.M. Almeida, J. Non-Cryst. Solids 352 (2006) 690.  M.A. Villegas, J.M. Fernandez Navarro, J. Eur. Ceram. Soc. 27 (2007) 2715.  B.R. Judd, Phys. Rev. 127 (1962) 750.  G.S. Ofelt, J. Chem. Phys. 37 (1962) 511.  Giorgio Pozza, David Ajo, Marco Bettinelli, Adolfo Speghini, Maurizio Casarin, Solid State Commun. 97 (1996) 521.  R. Balda, J. Fernandez, M.A. Arriandiag, J.M. Fernandez-Navarro, J. Phys.: Condens. Matter 19 (2007) 086223.  M.J. Weber, J.D. Myers, D.H. Blackburn, J. Appl. Phys. 52 (1981) 2944.  Hong Li, S. Kamakshi Sundaram, P. A. Blanc-Pattison, Liyu Li, J. Am. Ceram. Soc.. (2002) 1377.  Marta Zambelli, Adolfo Speghini, Gianluigi Ingletto, Clinio Locatelli, Marco Bettinelli, Fiorenzo Vetrone, J. Christopher Boyer, John A. Capobianco, Opt. Mater. 25 (2004) 215.  Yuansheng Daqin Chen, Yunlong Wang, En Yu, Feng Ma, Liu, J. Phys. Chem. Solids 68 (2007) 193.  E.O. Serqueira, N.O. Dantas, A.F.G. Monte, M.J.V. Bell, J. Non-Cryst. Solids 352 (2006) 3628.  L.R.P. Kassab, N.D.R. Junior, S.L. Oliveira, J. Non-Cryst. Solids 352 (2006) 3224.  C.K. Jorgensen, R. Reisfeld, J. Less Common Met. 93 (1983) 107.  J.H. Campbell, T.I. Suratwala, J. Non-Cryst. Solids 263&264 (2000) 318.  T. Miyakawa, D.L. Dexter, Phys. Rev. B. 1 (1970) 2961.  J. Azkargorta, I. Iparraguirre, R. Balda, J. Fernandez, E. Denoue, J.L. Adam, J. IEEE, Quant. Electron. 30 (1994) 1862.  N. Hodgson, H. Weber, in: Laser Resonator and Beam Propagation, Springer Series in Optical Sciences, London, 2005.