We investigated the suitability of three ternary tellurite glass families for use as optical fibre materials. Systematically varied compositions were produced and the scalability of the glass volumes was assessed. Detailed thermal analysis was conducted to provide justification for the observed billet scaling results. Compositional trends in the linear and nonlinear refractive indices were measured and correlated to structural information gained from measured Raman spectra. Physical mechanisms are suggested to explain the observed trends. Finally we explore the suitability of these glasses for optical fibre fabrication.
© 2012 Optical Society of America
In recent times the trend in photonics has been towards the translation of optical components into optical fibre platforms. This trend is driven by the benefits of optical fibres systems over their free space counterparts, namely: compactness, ruggedness, environmental insensitivity and affordability. During this time tellurite glasses have attracted much interest as they possess nonlinear susceptibilities in the order of 10× those found in silica and therefore offer an attractive opportunity for nonlinear applications . Tellurite glasses offer the additional benefit of a broad optical transmission window extending from ≈ 350 nm to ≈5 μm offering the possibility for mid IR transmittance .
There are many reports of tellurite glass compositions with properties that are desirable for optical fibre applications. However, many studies only investigated small glass sample volumes, thus neglecting the difficulties associated with producing bulk glass billets of sufficient size for fabrication into optical fibres [1, 2].
Several compositional families of tellurite glasses have been used in the fabrication of optical fibres. By far the most prominent compositions are variations on the ternary Na2O.ZnO.TeO2 family [3–5]. There have also been reports of quaternary variations of this system such as Na2O.ZnO.Bi2O3.TeO2 and Li2O.ZnO.Bi2O3.TeO2 [6, 7]. Other tellurite compositions that have been sucessfully drawn into optical fibres are the TeO2.BaO.SrO.Nb2O5.WO3 and TeO2.BaO.SrO.Nb2O5. WO3.P2O5 which have been developed for their remarkable Raman gain bandwidth 
We present herein a study of several systematically varied tellurite compositions of the type 10Na2O.xMO.(90 – x)TeO2 with M=Mg, Zn and Ba. The presence of 10 molar% sodium is to increase the glass forming stability of the mixtures . The modifying elements Mg, Zn and Ba were chosen for their reported ability to aid in the formation of stable tellurite glasses [10, 11]. The purpose of this research was twofold: first, to identify those glasses that will be suitable for the fabrication of optical fibres; and second to identify structure-property relationships to advance the understanding of the tellurite glass system.
We focused on assessing the volume scalability of billets and the crystallisation stability of the formed glasses. Further to this, we measured the coefficients of thermal expansion and relevant optical properties such as the linear and nonlinear refractive indices. Raman spectroscopy was utilised to determine the structural changes occurring with variation of composition. These structural data were compared with the compositional trends in the measured properties, from which conclusions are drawn as to the origins of these trends.
2. Experimental details
2.1. Sample preparation
The tellurite glass compositions indicated in Table 1 were fabricated from high purity (99.99% or greater) TeO2, ZnO, MgO and BaO. Na2O was obtained from Na2CO3 which undergoes complete decomposition during melting. The raw materials were melted at 900°C in a gold crucible and cast into preheated brass moulds. The glass melting was performed under an ambient air atmosphere. The samples were then annealed at approximately 5°C below the transition temperature (see Table 2) for 4 hours and cooled to room temperature at a rate of 0.1°C/min. Preliminary tests were conducted by fabricating small billets of 4 cm3. Compositions that formed glasses with no obvious devitrification were then used to produce larger billets of 22 cm3, 42 cm3 and 60 cm3. The data in Table 1 indicates the maximum achieved billet size for each glass composition, where an ‘*’ indicates the largest crystal free billet volume formed.
Samples for optical characterisation were formed from the 4 cm3 blocks by cutting them into 1 mm thick slices which were polished to optical quality.
2.2. Thermal analysis
Thermal characteristics of the glasses were determined using a differential scanning calorimeter (DSC, TA Instruments DSC 2920). Sample sizes of approximately 20 mg were heated in gold pans at a rate of 10 K/min. Measurements were conducted under an air atmosphere to mimic that which is used during the production and processing of the glass.
Tellurite glasses have a coefficient of thermal expansion α, typically in the order of 10−5/°C . This makes the measurement of α via simple mechanical techniques possible. We measured the coefficient of thermal expansion with a heated clamp (illustrated schematically in Fig. 1) and micrometer. Sample lengths were measured over a range of temperatures between ambient and approximately 250°C. The accuracy of this method was first assessed by making measurements on a sample of commercial chalcogenide glass (IG5, Schott Glass Co.) with a coefficient of thermal expansion of similar magnitude to tellurite . Results confirm an accuracy of approximately 1%.
2.3. Linear and nonlinear refractive index measurements
The refractive indices of the glasses were measured using the prism coupler technique . A Metricon prism coupler equipped with a polarised laser source at 1064 nm and a rutile (TiO2) reference prism was used. We determined the absolute accuracy of the prism coupler measurements by measuring the linear refractive index of a sample of commercial lead silicate glass (SF57, Schott Glass co.) and comparing the measured value to that quoted by the manufacturer. The absolute accuracy was determined to be ±0.025%.
Nonlinear refractive indices were measured using the Z-scan technique. 100 fs pulses with energies in the range 0.1 – 1 μJ at 1500 nm were focused to a minimum waist of ω0 ≈ 20 μm. We chose this probe wavelength to be > 3× the UV band edge (approximately 350 nm ) in order to minimise two photon absorption. The experimental configuration, as shown schematically in Fig. 2, allows for the simultaneous measurement of the open and closed aperture channels.
2.4. Raman spectroscopy
Measurements of the Raman spectra were made in the 180° configuration (i.e. backscatter) using 514 nm excitation from an Argon ion laser. Spectra were recorded from 250 cm−1 to 1000 cm−1 with a resolution of 0.25 cm−1. A holographic notch filter was used to filter out the Rayleigh scattered pump light.
3. Results and discussion
3.1. Billet scaling
Billet scaling trials were undertaken to determine the suitability of the glasses under study for use as optical fibre materials. The initial trial involved the formation of a 4 cm3 block. The formed glasses were visually inspected for crystallisation with the assistance of crossed polarisers. Provided a crystal free, homogeneous glass is formed we then preformed the DSC measurements in order to determine the transition temperature. This information is then used for the annealing of subsequent larger glass billets for which proper annealing is critical to avoid cracking of the billet. At present the largest attempted billet volume is 60 cm3 a limit dictated by the size of our crucibles. If this entire volume were to be formed into an optical fibre of 125 μm diameter, the resulting length of that fibre would be approximately 4.9 km, which is sufficient for may applications.
Magnesium containing glasses, TMN1 and TMN3 showed a readiness to crystallise which was in part managed by decreasing the quenching time. This was not effective for billet sizes larger than 4 cm3. In the case of the TMN2 glass we were able to produce a 42 cm3 billet.
TZN with zinc concentrations larger than 20 mole% formed small discrete crystals in the volume of the glass. TZN4, containing 20 mole% presented slight crystallisation in the 42 cm3 billet while all other TZN compositions displayed excellent scalability. As yet we have not found their limit, which indicates that they are well suited to the fabrication scales required to produce optical fibres.
Barium containing tellurite glasses were formed with barium concentrations up to 10 mole%. Mixtures with barium concentrations ≥ 15 mole% were observed to have white coloured spherical inclusions approximately 1 mm in diameter and to shatter during annealing.
3.2. Thermal analysis
3.2.1. Crystallisation stability
Shown in Fig. 3 are the DSC traces for each glass sample, the dashed lines indicate the locations of the important temperatures, namely: the glass transition temperature Tg, crystallisation onset temperature Tx and the peak crystallisation temperature Tc. The inferred values of these temperatures are listed in Table 2.
The glass transition temperatures in the TZN series are not significantly influenced by the concentration of the modifier, whereas the TMN and TBN glasses exhibit an increase as the modifier concentration is raised. A plausible explanation for this observation is that the Ba-O and Mg-O bonds have a much higher polarity than the Zn-O bonds due to the lower electronegativities of these two species. These bonds therefore require greater energy to break. Accordingly the transition temperature increases as these polar bonds are introduced into the glass.
One measure of the suitability of a glass for optical fibre fabrication is its crystallisation stability. This is usually estimated via: ΔT=Tg–Tx, where ΔT is a measure of the ability of the glass to be thermally processed without inducing crystallisation. In other words ΔT is the working range of the glass. A glass with ΔT> 100°C is considered to be stable for fibre drawing . We observe that all of the studied glasses have values of ΔT> 100°C which is consistent with the size of the obtained glass volumes.
By integrating the crystallisation peaks in the DSC data we obtained the enthalpies of crystallisation ΔHc for each glass composition. We note that this parameter corresponds to the the amount of energy released when the glass crystallises and therefore is a measure of the ‘energy pay-off’ for crystallisation. As such glasses that display a smaller ΔHc are less likely to crystallise when being processed at temperatures near the crystallisation temperature such as during casting, extrusion and fibre drawing . Plotted in Fig. 4b are the enthalpies of crystallisation for the glasses as a function of modifier concentration.
The enthalpy data support observations made in the billet scaling experiments. The TMN glasses crystallised readily with the TMN2 glass showing the lowest tendency. This is associated with the TMN glasses having the largest ΔHc of the glasses in this study. TZN glasses were able to be scaled to relatively large billet size.
3.2.2. Coefficient of thermal expansion
The coefficients of thermal expansion are plotted as a function of modifier concentration in Fig. 5 and listed in Table 2. It is note worthy that the TZN series undergoes a gradual decrease in α for increasing zinc concentration, where as the TMN and TBN glasses shows a comparably steeper increase over the range of modifier concentrations.
3.3. Linear and nonlinear index measurements
With reference to Fig. 6a, the tellurite glasses exhibit a decrease in the refractive index as the modifier concentration is increased. Furthermore, for equivalent modifier concentrations, the glasses containing modifiers with higher electronegativities possess lower refractive indices. This is in apparent contradiction to the fact that Ba2+ ions have an electronic polarisability greater than 3× that of Zn2+ . A solution to this contradiction is offered in Section 4.
The Z-scan experimental data was analysed using the techniques described by Sheikh-Bahae at al. yielding the nonlinear phase shift for each sample. A reference phase shift was determined from a sample of SF57 for which the nonlinear refractive index is known to be n2 = 4.10−19 m2/W . This reference data was used to calculate a relative nonlinear refractive index n2, of the tellurite samples. As with the linear refractive index, we observe a decrease in n2 as the concentration of modifying species is increased. This result is in accordance with the empirical Miller’s law, which posits a positive correlation between the linear and nonlinear susceptibilities of a material [18, 19].
3.4. Raman spectra
Sekiya et al. have hypothesised that the Raman spectra of glassy TeO2 can be understood in close analogy to that of the two polymorphs of crystalline tellurium dioxide, α-TeO2 and β-TeO2 [20, 21]. α-TeO2 consists of a three dimensional network of infinite chains comprised of TeO4 trigonal bipyramids (tbp) joined at the corners. In contrast, β-TeO2 contains distorted TeO4 trigonal bipyramids, some of which are connected along common edges to form a Te2O6 unit. Under this interpretation it is understood that the structural subunits present in the glassy state are distorted variants of the TeO4 and TeO3 subunits [20, 21].
Subsequent to the work of Sekiya et al. two additional polymorphs of crystalline TeO2 were identified, γ-TeO2 and δ-TeO2, and convincing evidence for the existence of distorted variant of these subunits in glassy TeO2 has been provided [22, 23].
The two interpretations are similar in a very limited sense. That is the low frequency Raman modes (400 cm−1 – 500 cm−1) are associated with bonds in Te-O-Te bridging configurations and with higher oxygen coordination. Whereas the high frequency modes (600 cm−1 – 800 cm−1) are resultant from predominately Te-O terminal bonds (i.e. non bonding oxygens (NBO)) and therefore lower oxygen coordination.
For this work we have adopted the traditional interpretation provided by Sekiya et al. as this model is more commonly found in the literature and is therefore readily comparable with existing results. Within this model pure tellurite glass is considered to be composed mainly of TeO4 units (left of Fig. 7) joined at corner sharing sites. With the addition of modifying species some TeO4 units have one of their axial bonds stretched, denoted as an intermediate TeO3+1 unit (centre of Fig. 7). In the limit that the axial oxygen bond is cleaved a TeO3 trigonal pyramidal (tp) unit is produced (right of Fig. 7).
Shown in Fig. 8 is a representative Raman spectrum taken from sample TZN2. The spectral envelope has been deconvolved into five Gaussian peaks with approximate centre locations prescribed by the work of Sekiya et al. . The correlation coefficient for the fit (R2) was 0.997 or greater across all samples.
The vibrational modes, labelled A through E, are associated with structural elements as follows: The A band at 450 cm−1 results from the symmetrical bending and stretching modes of continuous chains of corner sharing TeO4, TeO3+1 and TeO3 polyhedra. The B band, located at 610 cm−1, originates from anti-symmetric stretching of continuous networks composed of TeO4 units. These bands are thus a measure of the network connectivity of the glass network. At 660 cm−1 the C band is caused by anti-symmetric vibrations of Te-O-Te bonds constructed from two nonequivalent Te-O bonds. This feature is frequently associated with the presence of TeO4 units. The bands at 715 cm−1 and 775 cm−1, D and E, are attributed to the stretching modes of nonbridging oxygens (NBO) found on the TeO3 and TeO3+1 units, respectively. The Raman bands for tellurite are summarised in Table 3 along with the nomenclature for the assignments to structural elements.
The integrated intensity of each deconvolved Raman band was normalised to the total intensity under the envelope to give a relative band intensity. Based on the quality of the fits to the data the relative intensities are accurate to approximately 1%. We have plotted the relative intensities for each Raman band as a function of modifier concentration for each of the glass series in Fig. 9. It is observed that there are similar trends in the Raman A and B bands for the TMN, TZN and TBN glasses. The interpretation of which is that the network connectivity is being disrupted by the modifying species. Similarly, the Raman C band is decreasing for increasing modifier concentration for all glass series. This indicates that the concentration of TeO4 units is decreasing via conversion into TeO3 subunits. In the case of the TZN series we note that the relative intensity of the Raman E band increases for increasing zinc content, whereas this feature decreases as the modifier concentration is increased for the TMN and TBN glasses.
4. Property-structure relationships
The Raman C and D bands for all three of the glass families under study display the same general trend. That is, as the modifier concentration is increased the relative intensity of the C band decreases, while the D band is observed to increase. This is associated with the progressive shift from predominately TeO4 structural subunits towards higher concentrations of TeO3 via the intermediate TeO3+1 subunit. The rate of conversion is most rapid for the barium containing glasses and least so for the zinc containing glasses. We attribute this to the relative electronegativities of the modifiers and their average coordination numbers. Barium has a preferred coordination number of 8 and an electronegativity of 0.89 whereas zinc typically is coordinated to 6 oxygen atoms and possess an electronegativity of 1.65 (magnesium is intermediate to both) . Accordingly, barium demands more oxygen and with greater vigour than zinc which results in barium perturbing the TeO2 network to a greater degree.
Ab initio quantum chemical calculations performed by others indicate that the polarisability of the TeO3 subunit is substantially less than the TeO4 [25, 26]. Therefore the conversion of TeO4 to TeO3 results in a decrease in the polarisability of the fundamental constituents of the glass network. Similar numerical studies have also revealed the dependence of the nonlinear properties on the polymerisation of the tellurite glass, indicating that the high polarisability of tellurite glass has a significant contribution from nonlocal effects .
With these numerical simulations in mind it is clear that the decrease in the nonlinear refractive index can be understood in terms of the conversion of the highly polarisable TeO4 to the less polarisable TeO3 as well as the reduction in the network connectivity, in particular the decrease in the Raman B band which is specifically associated with the polymerised chains of TeO4 subunits.
Furthermore, an increase of modifier concentration is at the expense of the concentration of Te. Mg, Zn and Ba all possess lower polarisabilities than Te, thus one would expect the net polarisability and consequently the linear and nonlinear refractive indices to decrease, as is observed.
5. Implications for optical fibre fabrication
There exist several techniques for fabricating optical fibre preforms that are compatible with tellurite glass. These include: rotational casting, capillary stacking, core suction, extrusion and ultrasonic drilling [4, 17, 28]. In any case, preforms must be of sufficient size from which to pull practical lengths of optical fibre, i.e. from 100s of meters for research grade optical fibres up to many kilometres for commercial grade optical fibres. Generally speaking, an optical fibre preform will be cylindrical with diameters ranging from 5 mm to 30 mm and will be at least 100 mm in length. This corresponds to preform volumes in the range of 2 to 70 cm3 with the upper end of this range being more realistic as typically some fraction of the preform is not translated into optical fibre. With this consideration in mind it is clear that the TZN glasses have the greatest potential for fibre preform fabrication.
Besides the excellent crystallisation stability possessed by the TZN glasses across the entire composition range there are two key observations to make regarding the trends in the linear and nonlinear refractive indices. First, the variation of the linear refractive index over the explored range of modifier concentration (5 – 20 mol.%) is more than adequate for producing useful refractive index contrasts for core/clad optical fibres where an index contrast (Δn = (n1 – n2)/n1) of between 0.001 and 0.02 is typically required. Second, the decrease in the nonlinear refractive index encountered with increasing modifier is less than 20% over the entire range of modifier concentrations. Despite the variation from composition to composition the magnitude of n2 is significantly higher compared with many other oxide glasses and thus all of these compositions are still attractive for application in nonlinear fibre devices. [1, 29].
The observed trend in the coefficient of thermal expansion is also a significant factor to be considered for the fabrication of an optical fibre. Core/clad fibres are made from two slightly different glasses in order to achieve the necessary refractive index contrast. This will inevitably result in a differential thermal expansion across the interface. This leads to stresses, which can be detrimental for the mechanical stability of the fibre.
In the absence of perfectly matched thermal expansion coefficients it is ideal to have them be as close to one another as possible and to have a core material with a slightly larger coefficient of thermal expansion than the cladding. In this scenario the core will be under compression and the fibre will have a greater mechanical stability . It is generally accepted that a ‘well matched’ pair of materials will have Δα = αc – αcl < 5 × 10−6/°C , were the subscripts ’c’ and ’cl’ indicate core and cladding respectively. For the TZN glass series the variation of α is 2.4−6/°C over the entire range of modifier concentrations. Core glasses, having higher refractive indices than the cladding glasses and thus lower zinc concentrations will also have larger coefficients of thermal expansion than the cladding, thus indicating that the TZN glasses are suitable for core/clad fibre fabrication.
Three ternary tellurite glass systems were produced for the purpose of assessing the suitability of these glasses as optical fibre materials. We focused on the scalability of these glasses and, more generally, their crystallisation stabilities as the primary metric for suitability. Tellurite glass with a composition 10Na2O.15ZnO.75TeO2 were found to be the most suitable compositions. We measured the linear and nonlinear indices of refraction, where it was discovered that increasing the concentration of the modifying species causes these indices to decrease. Analysis of the Raman spectra revealed that one of the contributing factors is the conversion of four coordinated tellurium atoms to three coordinated tellurium atoms and the reduction in polarisability associated with this conversion. Finally, measurements of the coefficients of thermal expansion revealed that the zinc containing glasses display a very small variation over a comparably large composition range, further demonstrating the suitability of TZN glasses for optical fibre fabrication.
This work is supported by an ARC discovery grant (DP0987056) and Tanya Monro acknowledges the support of an ARC Federation Fellowship. Steve Madden at ANU for providing use of the Metricon prism coupler and Z-Scan apparatus. Elizabeth Carter in the School of Chemistry at The University of Sydney acquired the Raman spectra.
References and links
1. J. S. Wang, E. M. Vogel, and E. Snitzer, “Tellurite glass: a new candidate for fiber devices,” Opt. Mater. 3, 187–203 (1994). [CrossRef]
2. V. G. Plotnichenko, V. O. Sokolov, V. V. Koltashev, E. M. Dianov, I. A. Grishin, and M. F. Churbanov, “Raman band intensities of tellurite glasses,” Opt. Lett. 30, 1156–1158 (2005). [CrossRef] [PubMed]
5. M. R. Oermann, H. Ebendorff-Heidepriem, Y. Li, T. Foo, and T. M. Monro, “Index matching between passive and active tellurite glasses for use in microstructured fiber lasers: Erbium doped lanthanum-tellurite glass,” Opt. Express 17, 15578–15584 (2009). [CrossRef] [PubMed]
6. A. Ryasnyanskiy, A. Lin, C. Guintrand, I. Biaggio, and J. Toulouse, “Tunable nonlinear frequency conversion of bismuth-tellurite glass holey fiber,” Optical Fibre Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), pp. 1–3.
7. M. Liao, X. Yan, G. Qin, C. Chaudhari, T. Suzuki, and Y. Ohishi, “A highly non-linear tellurite microstructure fiber with multi-ring holes for supercontinuum generation,” Opt. Express 17, 15481–15490 (2009). [CrossRef] [PubMed]
8. Y. Ohishi, G. Qin, M. Liao, X. Yan, and T. Suzuki, “Recent progress in tellurite fibers,” in “Optical Fiber Communication (OFC), collocated National Fiber Optic Engineers Conference, 2010 Conference on (OFC/NFOEC),” (2010), pp. 1–3.
9. J. C. McLaughlin, S. L. Tagg, J. W. Zwanziger, D. R. Haeffner, and S. D. Shastri, “The structure of tellurite glass: a combined NMR, neutron diffraction, and X-ray diffraction study,” J. Non-Cryst. Solids 274, 1–8 (2000). Physics of Non-Crystalline Solids 9. [CrossRef]
10. T. Nishida, M. Yamada, H. Ide, and Y. Takashima, “Correlation between the structure and glass transition temperature of potassium, magnesium and barium tellurite glasses,” J. Mater. Sci. 25, 3546–3550 (1990). [CrossRef] .
11. J. Lousteau, H. Bookey, X. Jiang, C. Hill, A. Kar, and A. Jha, “Fabrication of multicore tellurite glass optical fibres,” in Transparent Optical Networks, 2007. ICTON ’07. 9th International Conference on, vol. 2 (2007), Vol. 2, pp. 305–308.
12. R. A. H. El-Mallawany, Tellurite Glasses Handbook Physical Properites and Data (CRC Press LLC, 2002).
13. V. S. GmbH, “Infrared chalcogenide glass IG5” (2009).
15. Deepika and N. S. Saxena, “Thermodynamics of glass/crystal transformation in Se58Ge42–xPbx (9 ≤ x ≤ 20) glasses,” J. Phys. Chem. B 114, 28–35 (2010). [CrossRef]
16. A. K. Varshneya, Fundamentals of Inorganic Glasses (Academic Press Inc., 1994).
17. T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. Mater. Res. 36, 467–495 (2006). [CrossRef]
18. R. C. Miller, “Optical second harmonic generation in piezoelectric crystals,” App. Phys. Lett. 5, 17–19 (1964). [CrossRef]
19. C. C. Wang, “Empirical relation between the linear and the third-order nonlinear optical susceptibilities,” Phys. Rev. B 2, 2045–2048 (1970). [CrossRef]
20. T. Sekiya, N. Mochida, A. Ohtsuka, and M. Tonokawa, “Normal vibrations of two polymorphic forms of TeO2 crystals and assignment of Raman peaks of pure TeO2 glass,” Nippon Seramikkusu Kyokai Gakujutsu Ronbunshi 97, 1435–1440 (1989). [CrossRef]
21. T. Sekiya, N. Mochida, A. Ohtsuka, and M. Tonokawa, “Raman spectra of MO1/2TeO2 (M = Li, Na, K, Rb, Cs and Tl) glasses,” J. Non-Cryst. Solids 144, 128–144 (1992). [CrossRef]
22. A. Mirgorodsky, T. Merle-Mjean, J.-C. Champarnaud, P. Thomas, and B. Frit, “Dynamics and structure of TeO2 polymorphs: model treatment of paratellurite and tellurite; Raman scattering evidence for new γ- and δ-phases,” J. Phys. Chem. Solids 61, 501–509 (2000). [CrossRef]
23. O. Noguera, T. Merle-Mjean, A. Mirgorodsky, M. Smirnov, P. Thomas, and J.-C. Champarnaud-Mesjard, “Vibrational and structural properties of glass and crystalline phases of teo2,” J. Non-Cryst. Solids 330, 50–60 (2003). [CrossRef]
24. H. Burger, K. Kneipp, H. Hobert, W. Vogel, V. Kozhukharov, and S. Neov, “Glass formation, properties and structure of glasses in the TeO2-ZnO system,” J. Non-Cryst. Solids 151, 134–142 (1992). [CrossRef]
25. E. Fargin, A. Berthereau, T. Cardinal, G. L. Flem, L. Ducasse, L. Canioni, P. Segonds, L. Sarger, and A. Ducasse, “Optical non-linearity in oxide glasses,” J. Non-Cryst. Solids 203, 96–101 (1996). Optical and Electrical Propertias of Glasses. [CrossRef]
26. S. Suehara, P. Thomas, A. P. Mirgorodsky, T. Merle-Méjean, J. C. Champarnaud-Mesjard, T. Aizawa, S. Hishita, S. Todoroki, T. Konishi, and S. Inoue, “Localized hyperpolarizability approach to the origin of nonlinear optical properties in Teo2-based materials,” Phys. Rev. B 70, 205121 (2004). [CrossRef]
27. A. P. Mirgorodsky, M. Soulis, P. Thomas, T. Merle-Mjean, and M. Smirnov, “Ab initio study of the nonlinear optical susceptibility of TeO2-based glasses,” Phys. Rev. B 73, 1–13 (2006). [CrossRef]
28. X. Feng, A. Mairaj, D. Hewak, and T. Monro, “Nonsilica glasses for holey fibers,” J. Lightwave Technol. 23, 2046–2054 (2005). [CrossRef]
29. V. Dimitrov and T. Komatsu, “Electronic polarizability, optical basicity and non-linear optical properties of oxide glasses,” J. Non-Cryst. Solids 249, 160–179 (1999). [CrossRef]
30. M. D. O’Donnell, K. Richardson, R. Stolen, A. B. Seddon, D. Furniss, V. K. Tikhomirov, C. Rivero, M. Ramme, R. Stegeman, G. Stegeman, M. Couzi, and T. Cardinal, “Tellurite and fluorotellurite glasses for fiberoptic Raman amplifiers: Glass characterization, optical properties, Raman gain, preliminary fiberization, and fiber characterization,” J. Am. Ceram. Soc. 90, 1448–1457 (2007). [CrossRef]
31. J. Wang, J. R. Lincoln, W. S. Brocklesby, R. S. Deol, C. J. Mackechnie, A. Pearson, A. C. Tropper, D. C. Hanna, and D. N. Payne, “Fabrication and optical properties of lead-germanate glasses and a new class of optical fibers doped with tm3+,” J. Appl. Phys. 73, 8066–8075 (1993). [CrossRef]