Journal of Non-Crystalline Solids 347 (2004) 197–203 www.elsevier.com/locate/jnoncrysol
Eﬀect of Bi2O3 on spectroscopic properties of Er3+-doped lead oxyﬂuorosilicate glasses for broadband optical ampliﬁers Shiqing Xu
, Zhongmin Yang a, Shixun Dai a, Guonian Wang a, Lili Hu a, Zhonghong Jiang a
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, 390 Qinghe Road, Jiading, Shanghai 201800, People’s Republic of China Graduate School of Chinese Academy of Sciences, Beijing 100039, People’s Republic of China Received 6 June 2003; received in revised form 27 February 2004 Available online 12 October 2004
Abstract The spectroscopic properties of Er3+-doped lead oxyﬂuorosilicate glasses were analyzed with Judd–Ofelt and McCumber theories. The obtained data suggest that the ﬂuorescence full width at half maximum (FWHM) is related to the X6 parameter, the larger the X6 parameter, and the broader the FWHM. The results showed that Er3+-doped 45SiO2–5Bi2O3–50PbF2 glass had the broadest FWHM (64 nm) and large stimulated emission cross-section (0.73 · 1020 cm2) in these glass samples. Compared with other glass hosts, the gain bandwidth properties of Er3+-doped 45SiO2–5Bi2O3–50PbF2 glass is close to those of tellurite and bismuth glasses, and has advantage over those of silicate, phosphate and germante glasses. The results suggest that Er3+-doped 45SiO2–5Bi2O3– 50PbF2 glass can be used as potential host material for developing broadband optical ampliﬁers in wavelength-division-multiplexing network system. 2004 Elsevier B.V. All rights reserved. PACS: 78.20.Ci; 42.70.Hj; 42.70.Ce
1. Introduction In recent years, the demand for increased transmission capacity of wavelength-division multiplexed telecommunication systems requires extension of the transmission window from the conventional C band (1530–1565 nm) to the L band (1570–1610 nm). It is of great importance to ﬂatten the gain spectrum and broaden the ampliﬁcation bandwidth of Er3+-doped ﬁber ampliﬁers (EDFAs) because of their key function in the wavelength-division-multiplexing (WDM) network system [1–6]. Although the performance of the present EDFAs can be used in WDM but with fewer *
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(S. Xu). 0022-3093/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2004.08.099
channels, there exists the requirement for larger number of channels, which could be possible by using EDFAs with a wider gain spectrum . Broadening and ﬂattening of the ampliﬁcation bandwidths of EDFAs are now becoming important for meeting these requirements [7– 10]. So far, many researchers have paid much attention to phosphate [11,12], ﬂuorophosphates , ﬂuoride , germanate , tellurite [16,17], and bismuth [1,18] glasses. However, chemical and mechanical stability and ﬁberizability of these glasses as practical materials still remain problems . However, silicate glasses are the most chemically and mechanically stable and also are more easily fabricated into various shapes such as a rod and optical ﬁber . Therefore, the design of a new silicate glass host for Er3+ for wide and ﬂat spectra of the 4I13/2 ! 4I15/2 transition around 1.55 lm bands is a target at present.
S. Xu et al. / Journal of Non-Crystalline Solids 347 (2004) 197–203
In our previous work , spectroscopic properties of Er3+-doped oxyﬂuorosilicate glasses were investigated, and Er3+-doped 50SiO2–50PbF2 glass showed broad ﬂuorescence spectrum of 1.55 lm with a large stimulated emission cross-section and long lifetimes of 4I13/2 level and good thermal stability. In this work, eﬀect of Bi2O3 on spectroscopic properties and thermal stability of Er3+-doped lead oxyﬂuorosilicate glasses were analyzed.
2. Experimental The compositions of the prepared glasses are (50 x) SiO2–xBi2O3–50PbF2 glasses (x = 0, 3, 5, 8, 10, 13, and 15 mol%). The starting materials are reagent grade SiO2, Bi2O3, and PbF2. The Er3+ doping concentration in the glasses was 1.0 mol%, which was introduced as with 99.99% purity. The glass samples are named as described in Table 1 in order to recognize the composition easily. The glass samples were prepared using the conventional melting and quenching method described in . The glass transition temperature (Tg), and crystallization onset temperature (Tx) were determined by diﬀerential thermal analysis (DTA) at a heating rate of 10 C/ min. Densities were measured according to the ArchimedesÕ principle using distilled water as the medium. Refractive indices were measured on prism minimum deviation method. The Er3+ concentrations were calculated from the measurement densities and the initial composition. Table 1 shows the refractive indices, densities and Er3+ concentrations of the glass samples. UV/ VIS/NIR absorption spectra were recorded between 300 and 1700 nm using a spectrophotometer on the glass samples optically polished. Fluorescence spectra were recorded using a laser diode excitation source at 970 nm. The ﬂuorescence lifetimes of 4I13/2 level of Er3+ were measured with light pulses of 970 nm laser diode (LD) and a HP546800B 100-MHz oscilloscope. All the measurements were taken at room temperature.
Table 1 Refractive indices, densities and Er3+ concentrations of Er3+-doped (50 x)SiO2–xBi2O3–50PbF2 (x = 0, 3, 5, 8, 10, 13, and 15 mol%) glasses Glass samples
Er3+ concentration (·1020 ions/cm3)
SBP1 SBP2 SBP3 SBP4 SBP5 SBP6 SBP7
0 3 5 8 10 13 15
5.6122 5.7012 5.7576 5.9032 6.0813 6.1265 6.2220
1.7625 1.8012 1.8156 1.8213 1.8365 1.8516 1.8620
2.20 2.06 1.98 1.89 1.86 1.76 1.71
3. Results 3.1. Absorption spectra and Judd–Ofelt analysis Fig. 1 shows absorption spectra of Er3+-doped SBP1, SBP3, SBP5 and SBP7 glasses. The absorption spectra consist of 10 absorption bands peaks at 1532, 975, 800, 652, 543, 521, 488, 450, 406, and 378 nm, corresponding to the absorptions from the ground state 4 I15/2 to the excited states 4I13/2, 4I11/2, 4I9/2, 4F9/2, 4S3/2, 2 H11/2, 4F7/2, 4F5/2, 2H9/2, 4G11/2 respectively. The peak absorption wavelengths scarcely change with increasing Bi2O3 content, but the cut oﬀ band shifts to a longer wavelength by the band gap absorption of the glass matrix. The Judd–Ofelt theory [23,24] was often used to calculate the spectroscopic parameters such as intensity parameters Xt (t = 2, 4, 6), spontaneous emission probability, ﬂuorescence branching ratios, radiation lifetime and the line strength of electric-dipole transition (Sed) and magnetic dipole transition (Smd) of rare-earth ion doped glasses. The three parameters Xt (t = 2, 4, 6) for the glass samples can be calculated from the measured absorption spectrum and the refractive index of the glass hosts by least-squares ﬁts [25,26]. Fig. 2 shows the compositional dependence of Xt (t = 2, 4, 6) parameters of the glass samples. With increasing Bi2O3 content, the X6 and X2 value parameter ﬁrst increase, reach its maximum at Bi2O3% = 5 mol%, and then decrease, while X4 parameter decreases slightly. 3.2. Fluorescence spectra and cross-sections The stimulated emission cross-section and FWHM are very important parameters for optical ampliﬁers to realize broadband and the gain ampliﬁcation, which
Optical Density (a.u.)
x=15 x=10 x=5 x=0
750 900 Wavelength (nm)
Fig. 1. Absorption spectra of Er3+-doped SBP1, SBP3, SBP5 and SBP7 glasses.
S. Xu et al. / Journal of Non-Crystalline Solids 347 (2004) 197–203
Fig. 2. Compositional dependence of Xt (t = 2, 4, 6) parameters of Er3+ in lead oxyﬂuorosilicate glasses.
can be used to evaluate the gain bandwidth properties of the optical ampliﬁers [26,27]. The normalized emission spectra of the glass samples are shown in Fig. 3. Because of the diﬀerences of the emission spectra in various glass hosts, FWHM is often used as a semiquantitative indication of the bandwidth. Fig. 4 shows the compositional dependence of FWHM of the glass samples. With increasing Bi2O3 content, FWHM of the glass samples ﬁrst increase, reach its maximum at Bi2O3% = 5 mol%, and then decrease. The broadest FWHM value of SBP3 glass is about 64 nm. The absorption cross-section was determined from the measured absorption spectrum and the Er3+ concentration in the glasses, and the stimulated emission crosssection is calculated from McCumber theory . According to the McCumber theory, the absorption and stimulated emission cross-sections are related by re ðkÞ ¼ ra ðkÞ exp½ðe hvÞ=kT ;
Normalized Intensity (a.u.)
x=15 x=13 x=10 x=8 x=5 x=3 x=0
1550 Wavelength (nm)
Fig. 3. The normalized emission spectra of Er3+-doped (50 x)SiO2– xBi2O3–50PbF2 (x = 0, 3, 5, 8, 10, 13, and 15 mol%) glasses.
Fig. 4. Compositional dependence of cross-sections and FWHM of Er3+-doped lead oxyﬂuorosilicate glasses.
where ra and re are absorption and stimulated emission cross-sections, respectively, the h is the planck constant, k is the Boltzmann constant, v is the photon frequency, and e is the net free energy required to excite one Er3+ from the 4I15/2 state to 4I13/2 at temperature T. e was determined using the procedure provided in . Fig. 4 illustrates the peak absorption cross-section rpa of the 4I15/2 ! 4I13/2 transition and the peak stimulated emission cross-section rpe of the 4I13/2 ! 4I15/2 transition of the glass samples. With increasing Bi2O3 content, the rpa and rpe values of the glass samples ﬁrst increase, reach its maximum at Bi2O3% = 5 mol%, and then decrease. The maximum rpa and rpe value of SBP3 glass is 0.64 · 1020 cm2 and 0.73 · 1020 cm2, respectively. 3.3. Lifetimes of 4I13/2 level of Er3+ The lifetime of 4I13/2 level of Er3+ is also an important parameter for broadband optical ampliﬁers. A critical factor in the success of EDFAs in optical communications is the long lifetime of the metastable state that permits the required high population inversions to be obtained under steady-state conditions using modest pump powers . Fig. 5 shows the compositional dependence of the lifetime of 4I13/2 level of the glass samples. The lifetimes of 4I13/2 level of Er3+ decrease slightly with increasing Bi2O3 content. The lifetime is related to the phonon energy of glass hosts. The lower the phonon energy of the glass host, the more phonons are needed to bridge the energy gap between the 4I13/2 level and the next-lower 4I152 level (DE = 6500 cm1), and consequently the lower the probability for non-radiative decay if neglect the energy transfer process between excited ions because of its low concentration of Er3+. In accordance with the simpliﬁed rate relation among total lifetime sm, radiative lifetime sr and the non-radiative lifetime snr, 1/sm = 1/sr + 1/snr, the measured lifetime increases because of the decrease in non-radiative
S. Xu et al. / Journal of Non-Crystalline Solids 347 (2004) 197–203 0.5
0.2 0.1 0.0 -0.1
-0.4 -0.5 -0.6 100
6 8 10 12 Bi 2O3 content (mol%)
Fig. 5. Compositional dependence of lifetime of 4I13/2 level of Er3+ in lead oxyﬂuorosilicate glasses.
decay . SiO2 and Bi2O3 have phonon energies of 1100 and 500 cm1, respectively. Because the phonon energy of Bi2O3 is lower than that of SiO2, the substitution of Bi2O3 for SiO2 leads to a decrease in phonon energy of the glass hosts, which results in an increase in the lifetime of 4I13/2 level of Er3+. Besides, the refractive index of glass host also inﬂuences the lifetime of 4I13/2 level of Er3+. The radiative lifetime calculated by Judd–Ofelt theory is inversely proportional to refractive index of the glass host . From Table 1, it can be seen that refractive index of the glass samples increase with increasing Bi2O3 content, and hence it leads to a decrease in the lifetime of 4I13/2 level of Er3+. That measured lifetime of 4I13/2 level of Er3+ decreases with increasing Bi2O3 content indicates that the refractive index has much more inﬂuence on the measured lifetime than that phonon energy. 3.4. Thermal stabilities of the glass samples A typical DTA curve of Er3+-doped SBP3 glass is illustrated in Fig. 6. The glass transition temperature (Tg) and the crystallization onset temperature (Tx) are marked in Fig. 6. The quantity, DT = Tx Tg has been frequently used as a rough estimate of the glass stability. To achieve a large working range of temperature during our sample ﬁber drawing, it is desirable for a glass host to have DT as large as possible [33,34]. Fig. 7 shows the compositional dependence of Tx, Tg, and DT = Tx Tg of Er3+-doped lead oxyﬂuorosilicate glasses. With increasing Bi2O3 content, the value of Tx, Tg, and DT = Tx Tg decrease. The introduction of Bi2O3 leads to a decrease of Tx, Tg and DT of these glass samples. Such feature was explained as follow: with the substitution of Bi2O3 for SiO2, the network structure of the glasses is broken and the network structure of the
Fig. 6. The DTA curve of Er3+-doped SBP3 glass.
Fig. 7. Compositional dependence of Tx, Tg, and DT = Tx Tg of Er3+-doped lead oxyﬂuorosilicate glasses.
glasses becomes looser. Therefore, it can be deduced that the increases of Bi2O3 content weaken the network structure and then lower thermal stability of the glass. From Fig. 7, it can be seen that all the glass samples have DT value exceeding 100 C, indicating these glass samples are stable against devitriﬁcation . The DT value of SBP3 glass is 215 C, which is larger than those of tellurite (141.5 C) , bismuth (170 C)  and ﬂuoride (105 C)  glasses.
4. Discussion 4.1. Eﬀect of Bi2O3 on Judd–Ofelt parameters Xt The Judd–Ofelt intensity parameters Xt (t = 2, 4, 6) are important for investigations of local structure and bonding in the vicinity of rare-earth ions. According to previous studies [16,18], X2 is related with the symmetry of the glass hosts while X6 decreases with an
S. Xu et al. / Journal of Non-Crystalline Solids 347 (2004) 197–203
increase of the covalency of the Er–O bond, and/or with increase of the fraction of non-bridging oxygen ions. The covalency of Er–O bond is assumed to be related with the local basicity around the rare-earth sites, which can be adjusted by the composition or structure of the glass hosts . With the substitution of Bi2O3 for SiO2, Bi2O3 enters the glass as a network former as well as network modiﬁer, and increases the number of non-bridging oxygen ions in the glass network. Therefore, it leads to a decrease in X6 value. On the other hand, on the basis of the electronegativity theory , the smaller the diﬀerence of electronegativity between cation and anion ions, the stronger the covalency of the bond. The values of electronegativity, for Bi, O, and Si elements, are 1.9, 3.5, and 1.8, respectively. As a result, the covalency of Bi–O bond is stronger than that of Si–O bond. It is expected that the inﬂuence of Bi–O bond on the local ligand environments around Er3+ increases with increasing Bi2O3 content. Consequently, the covalency of Er–O bond decreases, which leads to an increase in X6 value. From Fig. 2, it can be seen that the X6 value ﬁrst increases and then decreases, which indicates that the covalency of the Er–O bond has much more inﬂuence on the X6 value than that the non-bridging oxygen ions at ﬁst, and then has less inﬂuence on the X6 value than that non-bridging oxygen ions. 4.2. Relationship FWHM of 1.5 lm emission band and Judd–Ofelt parameters X6 In the case of the 4I13/2 ! 4I15/2 transition of Er3+, because the diﬀerence in the total angular momentum DJ equals 1, there exists the contribution of magnetic dipole transitions (Smd) . In order to obtain broadband and ﬂat emission spectrum, it will be eﬀective to increase the relative contribution of electric dipole transition (Sed) . Smd is independent of the ligand ﬁelds and is characteristic to the transition determined by the quantum numbers, while Sed is a function of the ligand ﬁelds, and it is possible to increase Sed by modifying the structure and compositions of the glass hosts. According to the Judd–Ofelt theory, the line strength of Sed of the 1.55 lm 4I13/2 ! 4I15/2 transition of Er3+ is given in  S ed ½4 I 13=2 ;4 I 15=2 ¼ 0:0188X2 þ 0:1176X4 þ 1:4617X6 : ð2Þ Consequently, for Sed of 4I13/2 ! 4I15/2 transition of Er3+, the X6 parameter is dominant and consequently is also dominant for 1.55 lm emission. Therefore, increasing the X6 value is helpful in increasing the bandwidth 1.55 lm emission. Fig. 8 shows the relationship between FWHM and the X6 value in Er3+-doped lead oxyﬂuorosilicate glasses. The X6 value shows a strong dependence on FWHM of the 1.55 lm emission band,
Fig. 8. The relationship between FWHM and the X6 value in Er3+doped lead oxyﬂuorosilicate glasses.
and the glass sample with a large X6 value generally possesses a broad FWHM. In addition, FWHM could be related to coordination numbers of bismuth. Bi3+ act as network modiﬁers in threefold and fourfold coordination duo to adding small amounts of Bi2O3, while Bi3+ act as network formers in sixfold coordination owing to adding large amounts of Bi2O3 . It can be concluded that the glass sample of Bi3+ with sixfold coordination possesses a broad FWHM. Therefore, it can be deduced that in lead oxyﬂuorosilicate glasses, keeping a optimal Bi2O3 content will be helpful to the broadband optical ampliﬁers. 4.3. The stimulated emission cross-section and the gain bandwidth properties Previous studies have shown that glass composition has an important eﬀect on the stimulated emission cross-section re of rare-earth ions. The re value is expected to increase with increase refractive index of the glass host, because re that is due to the electric dipole transition of rare-earth ions increase as the refractive index of the glass host [re (n2 + 2)2/n] increases . From Fig. 4, it can be seen that rpe is more than 0.7 · 1020 cm2 when Bi2O3% P 5 mol%, mainly because of the high refractive index of the glass host. The rpe value changes only slightly with increasing Bi2O3 content over the range 5–15 mol%, which suggests that rpe is not linearly proportional to the refractive index of the glass host. The peak stimulated emission cross-section rpe and FWHM are very important parameters in optical ampliﬁers to realize broadband and the gain ampliﬁcation. The gain bandwidth properties of optical ampliﬁers can be evaluated by FWHM · rpe product . The bigger the product, the better the property. Table 2 lists FWHM, rpe and FWHM · rpe of Er3+ in various glass
S. Xu et al. / Journal of Non-Crystalline Solids 347 (2004) 197–203
Table 2 Comparisons of rpe , FWHM and rpe · FWHM of Er3+ in diﬀerent glass hosts Glass
rpe (1020 cm2)
rpe · FWHM
Bismuth  Tellurite  Silicate  Phosphate  Germante  SBP3
0.70 0.75 0.55 0.64 0.57 0.73
79 65 40 37 42 64
55.4 48.8 22.0 23.7 23.9 46.7
hosts for comparison of the gain bandwidth properties. It is clear that FWHM · rpe of Er3+ in SBP3 glass is close to those of tellurite and bismuth glasses, and larger than those of germanate, silicate and phosphate glasses. Consequently, the SBP3 glass can be used as potential host material for developing broadband optical ampliﬁers in WDM.
5. Conclusion Eﬀect of Bi2O3 on spectroscopic properties and thermal stability of Er3+-doped lead oxyﬂuorosilicate glasses were analyzed. SBP3 glass showed broad emission spectra of 1.55 lm with a large stimulated emission cross-section and good thermal stability. The gain bandwidth properties were evaluated by FWHM · rpe product, and the FWHM · rpe value of SBP3 glass is 46.7 which is close to those of tellurite glass (48.8) and bismuth glasses (55.4), and is larger than those of silicate glasses (22.0) phosphate glasses (23.7) and germante glasses (23.9). The large stimulated emission cross-section of Er3+-doped SBP3 glass (rpe ¼ 0:73 1020 cm2) results from the large refractive index of the glass host. According to the Judd–Ofelt theory, the FWHM value is related to the X6 parameter, and the lager the X6 parameter, the broader the FWHM. DT has been used as a rough estimate of the glass formation ability or glass stability, and the DT value of SBP3 glass is 215 C, which is larger than those of tellurite (141.5 C), bismuth (170 C) and ﬂuoride (105 C) glasses.
Acknowledgments The authors would like to thank Dr Jianghu Yang and Nengli Dai for their helpful discussions. This research is supported by the Project of the National Nature Science Foundation of China (Grant no. 60207006 and 60307004) and Optical Science and Technology of Shanghai (Grant no. 022261046).
References  S. Tanabe, N. Sugimoto, S. Ito, T. Hanada, J. Lumin. 87&89 (2000) 670.  S. Tanabe, J. Non-Cryst. Solids 259 (1999) 1.  M. Yamada, A. Mori, K. Kobayashi, H. Ono, IEEE Photon. Technol. Lett. 10 (1998) 1244.  Y. Ding, S.B. Jiang, B.C. Hwang, T. Luo, N. Peyghambarian, Y. Himei, T. Ito, Y. Miura, Optical Mater. 15 (2000) 123.  C.G. Atking, J.F. Massicott, J.P. Armitage, R. Wyatt, B.J. Ainslie, S.P. Craig-Ryan, Electron. Lett. 25 (1989) 910.  J.F. Massicott, J.P. Armitage, R. Wyatt, B.J. Ainslie, S.P. CraigRyan, Electron. Lett. 26 (1990) 1645.  Y. Ohishi, A. Mori, M. Yamada, H. Ono, Y. Nishida, K. Oikawa, Opt. Lett. 23 (1998) 274.  A. Buxens, H.N. Poulsen, A.T. Clausen, P. Jeppesen, Electron. Lett. 36 (2000) 821.  M.A. Mahdi, F.R. Mahamd, P. Poopalan, S. Selvakennedy, H. Ahmad, IEEE Photon. Technol. Lett. 12 (2000) 1468.  Y.B. Lu, P.L. Chu, IEEE Photon. Technol. Lett. 12 (2000) 1616.  S. Jiang, T. Luo, B.C. Hwang, F. Smekatala, K. Seneschal, J. Lucas, N. Peyghambarian, J. Non-Cryst. Solids 263&264 (2000) 364.  B.C. Hwang, S. Jiang, T. Luo, K. Seneschal, G. Sorbello, M. Morrell, F. Smektala, S. Honkanen, J. Lucas, N. Peyghambarian, IEEE. Photo. Tech. Lett. 13 (2001) 197.  S. Tanabe, S. Yoshii, K. Hirao, N. Soga, Phys. Rev. B 45 (1992) 4620.  K. Soga, H. Inoue, A. Makishima, J. Non-Cryst. Solids 274 (2000) 69.  H. Lin, E.Y.B. Pun, S.Q. Man, X.R. Liu, J. Opt. Soc. Am. B 18 (2001) 602.  X. Feng, S. Tanabe, T. Hanada, J. Am. Ceram. Soc. 84 (2001) 165.  A. Mori, K. Kobayashi, M. Yamada, Electron. Lett. 34 (1998) 887.  J. Yang, S. Dai, Y. Zhou, L. Wen, L. Hu, Z. Jiang, J. Appl. Phys. 93 (2003) 977.  J.S. Wang, E.M. Vogel, E. Snitzer, Opt. Mater. 3 (1994) 187.  F. Guinhos, P. Nobrega, P. Santa-Cruz, J. Alloys Compd. 323&324 (2001) 358.  S. Xu, Z. Yang, S. Dai, J. Yang, L. Wei, L. Hu, Z. Jiang, Chin. Phys. Lett. 20 (2003) 905.  S. Xu, Z. Yang, S. Dai, J. Yang, L. Hu, Z. Jiang, J. Alloys Compd. 361 (2003) 313; B.R. Judd, Phys. Rev. 127 (1962) 70.  G.S. Ofelt, J. Chem. Phys. 37 (1962) 511.  S. Tanabe, T. Ohyagi, N. Soga, T. Hanada, Phys. Rev. B: Condens. Matter. 46 (1992) 3305.  H. Takebe, Y. Nageno, K. Morinaga, J. Am. Ceram. Soc. 78 (1995) 1161.  A. Mori, Y. Ohishi, S. Sudov, Electron. Lett. 33 (1997) 863.  S. Shen, M. Naftaly, A. Jha, Proc. SPIE 3489 (1999) 103.  D.E. McCuber, Phys. Rev. A 134 (1964) 299.  W.J. Miniscalo, R.S. Quimby, Opt. Lett. 16 (1992) 258.  R. Rolli, A. Chiasera, M. Montagna, Proc. SPIE 4282 (2001) 109.  L. Petit, T. Cardinal, J.J. Videau, G.L. Flem, Y. Guyot, G. Boulon, M. Couzi, T. Buﬀeteau, J. Non-Cryst. Solids 298 (2002) 76.  M.J. Weber, J.D. Myers, D.H. Blackbum, J. Appl. Phys. 52 (1981) 2944.  L.L. Neindre, S.B. Jiang, B.C. Hwang, T. Luo, J. Watson, N. Peyghambarian, J. Non-Cryst. Solids 255 (1999) 97.  M.G. Drexhage, O.H. El Bayoumi, C.T. Moyniyan, J. Am. Ceram. Soc. C 65 (1982) 168.
S. Xu et al. / Journal of Non-Crystalline Solids 347 (2004) 197–203  J.S. Wang, E.M. Vogel, E. Snitzer, J. Non-Cryst. Solids 178 (1994) 109.  L. Pauling, J. Am. Chem. Soc. 51 (1929) 1010.  S. Tanabe, T. Hanada, J. Non-Cryst. Solids 196 (1996) 101.  M.J. Weber, Phys. Rev. 157 (1967) 262.
 W.H. Dumbaugh, J.C. Lapp, J. Am. Ceram. Soc. 75 (1992) 2315.  R. Reisfeld, Struct. Bond. 22 (1975) 123.  G.C. Righini, S. Pelli, M. Fossi, M. Brenci, A.A. Lipovskii, E.V. Kolobkova, A. Speghini, M. Bettinelli, Proc. SPIE 4282 (2001) 210.