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Abstract
Dielectric properties of oxyfluorosilicate (OFS) glasses have been characterized using Terahertz (THz)-time domain spectroscopy in the sub-THz region as well as optical reflection measurement. OFS glass containing 20 mol% of Nb2O5, which is termed ZNbKLSNd glass, has the highest refractive index of 3.70 in the sub-THz region. The THz and optical refractive indices of various silicate oxide glasses, including OFS glasses, have been confirmed to be correlated by a unified relationship utilizing a parameter defined by the ratio of ionic to electronic polarizability. Additionally, the frequency dependence of the THz dielectric constant has been interpreted by a single oscillator model for all silicate oxide glasses including OFS glasses. On the basis of the present unified dielectric model, the very high refractive index of ZNbKLSNd glass has been attributed to the lowering of oscillator resonance wavelength originated from the incorporation of Nb2O5 intermediate network former.
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1. Introduction
Terahertz (THz) wave technology, which typically covers a frequency range of sub-THz to tens-THz, is demanded for the applications to a variety of systems including spectroscopy, communications, sensing and imaging due to the characteristic transmission and propagation properties of THz waves in various media [1–3]. Recent developments are widening the application field to cover materials, telecommunications, and variety of equipments in production, bio-medicine, environment, security, etc. [4–6]. In constructing practical THz and sub-THz components and systems, glasses are indispensable materials. Particularly, glasses having high-refractive index and low-loss properties are prerequisite for forming basic passive components such as lenses and waveguides as well as active components based on high nonlinearity of glasses in the THz and sub-THz regions [7,8]. If empirical Miller’s rule [9,10] can be applied in the THz range, high refractive index glasses are also expected to exhibit a high nonlinearity, which merits their application to THz nonlinear functions including modulation, switching and wavelength conversion [11–13].
So far, a variety of silicate oxide glasses with metal oxide modifiers and chalcogenide glasses which have high chemical/mechanical stability and desirable dielectric properties, e.g., high refractive index, high transparency and high optical nonlinearity, have been developed for the application in visible and mid-infrared wavelength regions [14,15]. Investigation on dielectric properties of glass materials in the THz frequency range has first been carried out by means of far-infrared absorption measurements, and fairly limited kinds of glasses such as fused silica, soda-lime glass and As-S/Se glasses have been studied [16–20]. Detailed studies on THz dielectric properties have been started fairly recently by using THz-time domain spectroscopy (THz-TDS) technique on various materials [21–24]. The use of THz-TDS technique has been extended to detailed characterization of a variety of glass materials such as silicate oxides [25–28] and chalcogenides [29–31]. Naftaly has reported a study of THz refractive index and absorption properties of a series of commercial silicate oxide glasses and found their relationships with the optical refractive index and other various material properties including the density and thermal expansion coefficient [27]. Ravagli has carried out a study on sub-THz refractive index and absorption coefficient in a selection of chalcogenide and La:chalcogenide glasses with varied compositions, and discussed the absorption mechanism [29]. We have recently conducted sub-THz characterization of oxyfluorosilicate (OFS) glasses as a new group of silicate oxide glasses [32], in which fluorides (ZnF2, PbF2 and LiF) and rare-earth ions (Nd3+) are introduced in the silicate glass host, along with the incorporation of alkali ions (K+ and Na+) and/or metal oxide based intermediate network former (Nb2O5) on the basis of our previous studies on various OFS glasses [33,34]. An OFS glass containing 20 mol % of Nb2O5, which is termed ZNbKLSNd glass, has achieved the simultaneous realization of the highest refractive index and lowest absorption loss among silicate oxide glass family in sub-THz frequency region [32]. Comparative analysis of THz properties has indicated that the very low absorption loss achieved in OFS glass is attributed to the effect of fluorine to relax structural disordering, which reduces charge fluctuation and eventually minimizes the absorption loss in the glass.
In view of either applying existing glasses in practice or developing new glasses for advanced systems, it is essential to understand the mechanism of how the THz dielectric properties of those glasses are determined. However, there has been no fully comprehensive description of THz dielectric property even within the silicate oxide glass family.
In this study, we carry out detailed characterization of dielectric property of OFS glasses using the same glasses as used in our recent work [32]. THz dielectric properties of these glasses are analyzed by using THz-TDS data [32], and optical reflectivity measurement is performed for optical refractive index determination. We compare THz properties of these series of OFS glasses with those of different multicomponent silicate oxide glasses [27] and chalcogenide glasses, particularly La3+:chalcogenides [29], for which detailed THz dielectric property data are available. For a comparative study, we first focus on the difference between the optical and THz refractive indices, from which the electronic and ionic polarizabilities are determined. This analysis gives a unified relationship between the optical and THz refractive indices for all the silicate oxide glasses examined. Next, we analyze the THz frequency dependence of refractive index using a single oscillator model, so that the characteristic oscillator parameters are determined for different glasses. While all those data confirm the validity of the single oscillator model, they also indicate the difference in characteristic parameters for different glass groups. We discuss possible mechanism behind the high THz refractive index properties of the present OFS glasses.
2. Experimental methods
2.1 Glass preparation
The OFS glass samples employed in our experiment involve two glass groups [32]; one is ZNbKLSNd: (20-x)ZnF2 + 20Nb2O5 + 20K2CO3 + 10LiF + 30SiO2 + xNd2O3, and the other is PbNKLSNd: (20-x)PbF2 + 5Na2O + 20K2CO3 +10LiF + 45SiO2 + xNd2O3, where x = 1, 5 and 10 mol%. Glasses were prepared by the melt-quenching technique [32]. A batch composition (weight: ∼15 g) was thoroughly crushed in an agate mortar and the homogeneous mixture was taken into a platinum crucible and heated at 1250 °C for 3 hours in an ambient. The melt was then annealed at 400 °C for 10 hrs to remove thermal strains. After cooling down, glasses were polished and formed into disks with the thickness of ∼ 1.6 mm for measurements.
2.2 Characterization and analyzing techniques
The THz optical constants of OFS glasses were determined by using a photoconductive-antenna-based transmission type THz-TDS system [3,24,32]. A Ti-sapphire laser (wavelength: 800 nm) with duration of 60 fs, average optical power of 380 mW was used for exciting GaAs photoconductive antennae for THz generation and detection in an ambient.
The THz electric fields were recorded in the time domain with (Esam(t)) and without (Eref(t)) the glass sample, which was placed in the collimated THz beam path of the THz-TDS system. By Fourier-transforming the measured time-domain electric field data, we then retrieved the complex amplitude and phase of the transmitted THz waves in the frequency domain. The THz refractive index n(ν) and extinction coefficient κ(ν) at the frequency ν are related to the electric field E(ν) and phase ϕ(ν) measured after transmission through a reference (air in our case)(suffix: ref) and through the sample (suffix: sam) by the following equations [27];
The optical transmission and reflectivity r were measured by using the conventional Fourier transform infrared (FTIR) spectroscopy system in the visible to near-infrared range. The optical refractive index nopt was determined at the wavelength of 1.5 μm using the standard equation:
3. Results and discussions
3.1 THz refractive index and polarizability
Figure 1 shows the frequency dependence of the refractive index n(ν) and extinction coefficient k(ν) of OFS glasses determined in the frequency range from 0.2 to 0.8 THz by using the same original THz-TDS data as used in [32]. The extinction coefficient is found to be smaller by more than 40 times compared with the refractive index within the measured frequency range. General behavior of frequency dependence as observed here is consistent with those of previously reported oxide-based silicate and chalcogenide glasses in the sub-THz frequency band [27–30]. The refractive indices measured in the present glasses are comparatively high, and ZNbKLSNd glasses particularly exhibit refractive indices as high as 3.70, being the highest among silicate glasses reported to date and close to those of La3+:chalcogenide glasses [32]. It should be reemphasized that the absorption coefficients (α(ν)=4πνκ/c) at 0.5 THz (5.6-8.7 cm−1 for ZNbKLSNd glasses and 7.6-8.9 cm−1 for PbNKLSNd glasses) are significantly low as compared with other high-refractive index glasses [32]. This is interpreted to be caused primarily due to the structural relaxation effect of fluorine in OFS glasses as discussed in our previous work [32]. Figure 2 shows the wavenumber/wavelength dependence of the optical reflection measured in the infrared region and the optical refractive index calculated by using Eq. (3) for both of OFS glasses. It is observed that the reflection and refractive index are nearly constant at the wavenumber greater than 4000 cm−1 (wavelength < 2.5 μm) in both OFS glasses, and we use the refractive index values at the wavelength of 1.5 μm as the optical refractive indices for later discussion. Table 1 summarizes the THz and optical refractive index data for the present OFS glasses as well as selected silicate oxide and chalcogenide glasses taken from Refs. [27,29]. The compositions of the glasses selected in Table 1 are listed together with respective Refs. [35–38], in Table 2.
Fig. 1. Refractive index and extinction coefficient for (a),(c)ZNbKLSNd glasses and (b),(d) PbNKLSNd glasses determined by THz-TDS measurements.
Fig. 2. Optical reflectance and refractive index spectra for (a),(c)ZNbKLSNd glasses and (b),(d) PbNKLSNd glasses.
Table 1. Material, THz, and optical parameters determined for a variety of glasses selected in the present analysis.
Table 2. Compositions of a variety of glasses selected in the present analysis.
In order to compare dielectric properties of the present OFS glasses with other silicate oxide and chalcogenide glasses, we analyze the data by using the Clausius-Mossotti equation (Lorentz-Lorentz equation) [27,32,39,40]. The dielectric constant ɛopt in the optical frequency range is determined by the polarizability of electrons associated with constituent molecules in the glass. On the other hand, the dielectric constant ɛTHz in the sub-THz frequency range is determined by the total polarizability including contributions not only of fast response electrons (Pe) but also of slow response ions (Pi) in the glass. Thus the dielectric constants, ɛopt and ɛTHz, are related to the molar electronic polarizability, Pe, molar ionic polarizability, Pi, and molar total polarizability, Ptot = Pe+Pi, as shown in the following relations:
Figure 3 shows the total, electronic and ionic polarizabilities thus obtained as functions of the molar volume for the present OFS glasses, in which data for other silicate oxide and La:chalcogenide glasses (S1-S5 in Table 1 and 2) as well as other chalcogenide glasses (IG series) (S6, S7 in Tables 1 and 2) taken from the literature [27,29] are also plotted. The compositions of glasses used in Fig. 3 are listed in Table 2, and their physical and dielectric parameters are summarized in Table 1. The straight line in Fig. 3 shows a guide line corresponding to the THz refractive index of 3.7. THz plots of ZNbKLSNd glasses and La:chalcogenide glasses show a slope similar to this guide line being consistent with the THz refractive index very close to 3.7 as confirmed in Table 1.
Fig. 3. Electronic, ionic and total molar polarizabilities versus molar volume for all glasses selected for the present comparison. A straight line indicates a slope corresponding to a refractive index of 3.70.
In Fig. 3, it is found that the electronic and ionic contributions to the total polarizability are different for different glass groups; both contributions are comparable in silicate oxide glass group, and electronic contribution is much larger than ionic contribution in chalcogenide glasses. This implies that the total polarizability of different glass systems is characterized in view of the ionic and electronic polarizability ratio which is defined by a = Pi/Pe. By using this ratio a, the electronic molar refraction $R_m^e$ and the molar volume Vm, the optical refractive index (nopt) and THz refractive index (nTHz) can be expressed by the following equations:
Figure 4 shows the relationships between the THz refractive index and optical refractive index for the silicate oxide glass group and La:chalcogenide glass group. Curves shown in the figure have been calculated from Eqs. (6) and (7) by using $R_m^e/{V_m}$ as a parameter with assumptions of a = 0.95 for silicate oxide and a = 0.35 for La:chalcogenide glass groups, respectively. As seen in this result, different glass groups are classified by the polarizability ratio a. This classification applies to a variety of additives incorporated in the silicate oxide glasses. Slight deviation of the experimental data from the calculation is interpreted by considering an appropriate shift of a from 0.95, for example a = 0.85-0.95 for ZNbKLSNd glasses and a = 1.10-1.38 for PbNKLSNd glasses, as shown in Table 1. The same trend is observed for La:chalcogenide glass group. These results support the applicability of the polarizability ratio a in characterizing chemical composition/structure of the glass within the same glass family, e.g., silicate oxide glasses in which the oxygen ion O2- governs the dielectric property. Naftaly et al. reported a linear relationship between the optical and THz refractive indices in high-refractive index silicate oxide glasses, but the linear relationship does not hold for low-refractive index glasses such as Pyrex and fused silica [27]. This allows us to confirm that the polarizability ratio a is useful to characterize dielectric properties of glasses with a wider range of compositions.Fig. 4. Relationship of THz refractive index as functions of optical refractive index for various glasses. Curves shown have been calculated by using Eqs. (6) and (7) for fixed values of a = Pi/Pe.
3.2 Ionic contribution to the dielectric characteristics of silicate oxide glasses
In the previous section we have shown that the electronic and ionic contributions to the dielectric properties are correlated by a unified relationship for all silicate oxide glasses. In the following, we focus on the ionic contribution to the dielectric property and discuss its relation with physical properties of glasses. In the present analysis, we adopt a simplified model of dielectric material. The dielectric constant (ɛ) at a given frequency (ν) in the THz and far-infrared (FIR) region, ɛν, is assumed to be expressed by the classical single oscillator model (Lorentz model) for displacement of a pair of anion and cation as shown by the following equation [40–42]:
In the present analysis, the values of $\varepsilon (0 )$ have been determined from the refractive indices measured at the optical wavelength (λ=1.5 µm) by using the relation $\varepsilon (0 )= {\varepsilon _{\textrm{opt}}} = n_{\textrm{opt}}^2$. For $\; \varepsilon (\infty )$, we have used the value of $\varepsilon ({0.2\textrm{THz}} )= {\varepsilon _{\textrm{THz}}} = n_{\textrm{THz}}^2$ since $\; \varepsilon (\lambda )$ virtually saturates at 0.2 THz (Fig. 1). Figure 5 shows $1/[\varepsilon (\lambda )- \varepsilon (0 )]$ as functions of 1/λ2 for ZNbKLSNdx (x = 1, 5, 10) and PbNKLSNdx (x = 1, 5, 10) glass series, which show good linear dependences. The g factor and λ0 are readily determined from these graphs, and the results are included in Table 1. The same analysis has been carried out for other silicate oxide glass groups by using the data reported in the literature [27]. Figure 6 shows plots of selected silicate oxide glasses. Some THz-TDS data show weak frequency dependences (e.g. silica and Pyrex) and those data have been excluded for accuracy in the present analysis. All data plotted in Fig. 6 show linear relationships and the values of g and λ0 determined for all glasses (including La:chalcogenide glasses) are listed in Table 1.
Fig. 5. 1/[ɛ(λ)- ɛ(0)] versus 1/λ2 plots for ZNbKLSNd and PbNKLSNd glasses with different compositions.
Figures 5 and 6 show that THz dielectric properties of all glasses analyzed here can be interpreted by the single oscillator model. Equation (12) indicates that $\varepsilon (\infty )- \varepsilon (0 )$, which corresponds to the ionic contribution to the dielectric constant, is governed by Vm, g and λ0 all of which are characteristic to each glass material. To see the ionic contribution in different glass groups, we plot the dielectric constant difference ${\varepsilon _{\textrm{THz}}} - {\varepsilon _{\textrm{opt}}}$ .as a function of gλ02/Vm in Fig. 7. Here we use ɛ(v = 0.2 THz) for the ɛTHz value for determining the dielectric constant difference, and all parameters are determined basically from the experimental data as described above. As is seen clearly in Fig. 7, a linear relationship has been obtained without regard to the difference of glass groups (including La:chalcogenide glasses: not shown). This confirms a wide applicability of the single oscillator model for characterizing THz dielectric properties of all glass materials examined.
Fig. 7. Relationship between ɛTHz - ɛopt versus gλ02/Vm for selected chalcogenide and silicate oxide glasses. Plots show experimental data determined from the single oscillator analysis and the straight line shows a slope of unity.
Next question is what parameters are governing the overall dielectric property in each glass. In order to find out such dominant parameters, ${\varepsilon _{\textrm{THz}}} - {\varepsilon _{\textrm{opt}}}$ has been plotted as functions of each parameter: 1/Vm, g and λ02, as shown in Fig. 8. Here 1/Vm is regarded to be proportional to the number of ion pairs in a unit volume. Other parameters, g and λ02, are used to characterize nature of the oscillator. As shown in Fig. 8(a), over a wide range of variation in the dielectric constant difference, 1/Vm does not show too much change. In contrast, Fig. 8(b) and (c) show that the dielectric constant difference increases in proportion to g as well as λ02, which is consistent with the indication of Eq. (12). If we look into these g and λ02 dependences more closely, they can be categorized into two classes: ZNbKLSNd glasses, and all other silicate oxide glasses. A distinct difference is observed between these classes. In ZNbKLSNd glasses, the very large dielectric constant difference (>10) is achieved by the large value of g (rather than by λ02). By contrast, in other silicate oxide glasses including PbNKLSNd glasses, the increase of the dielectric constant difference is caused by the increase of λ02 (rather than of g). Thus the present single oscillator model analysis has revealed that the different physical parameter is responsible for the increase of ionic contribution to the dielectric constant in different glass groups, e.g., the large g is predominantly responsible in ZNbKLSNd glasses and the large λ02 is predominantly responsible in other silicate oxide glasses.
Fig. 8. The dielectric constant difference ɛTHz - ɛopt as functions of 1/Vm, g and λ02 for silicate oxide glasses including PbNKLSNd (Pb) and ZNbKLSNd (ZN) glasses. A significant behavior difference is found between ZNbKLSNd glasses and other silicate oxide glasses.
3.3 Effects of compositional properties on the dielectric characteristics of silicate oxide glasses
In this section we discuss how OFS glasses, particularly ZNbKLSNd glasses exhibit high THz refractive indices by comparing their THz properties with those of other silicate oxide glasses. We thus focus on the contribution of ionic vibration to the dielectric property of glasses. Dielectric characteristics revealed by the present THz analysis should be correlated with the physical property of specific glasses. According to the simple diatomic chain oscillator model as we used in the THz analysis, the resonant wavelength λ0 of the oscillator is determined by the mass of atoms and the interatomic force within the groups of atoms comprising the glass network. The resonant wavelength is given by [43,44]:
where c is the speed of light, μ is the reduced mass, and D is the force constant of cation-anion pair. The resonant oscillator in a silicate oxide glass presumably results from a low-frequency vibrational mode of O-Si-O chains in the glass network, but the particular modifiers and intermediates introduced in the glass structure will perturb the O-Si-O vibration. Hence the resulting low-frequency vibrational mode will depend strongly on the structure and composition of the glass. Thus, it can safely be assumed that the resonant wavelength λ0 represents the dominant wavelength of all the low-frequency vibrational modes and that λ0 can be used as a measure to know the variations in μ and/or D which are caused by the addition of modifiers and intermediates.In silicate oxide glasses, as is shown in Fig. 8(c), λ0 shows the largest value for SF series, the intermediate values for PbNKLSNd series and SK10 glass, and the smallest for ZNbKLSNd series and BK7 glass. We first discuss the effects of μ and D by comparing ZNbKLSNd glasses and SF glasses, both of which have similarly large dielectric constant differences up to 10. Here it can be noted that the THz refractive index has a one-to-one correspondence with the optical refractive index as shown in Fig. 4 and, in addition, that the optical refractive index, as well as the electronic polarizability as its cause, has an unambiguous, empirical relationships with the energy bandgap as have been reported for a variety of oxide glass materials [45–47]. Also, the energy bandgap of silicate oxide glasses is considered to be determined by the coupling strength of the dominant cation-anion pair. Taking into account that the optical bandgap energies of ZNbKLSNd glasses and SF glasses are not too much different (our visible region transmission experiment indicated the bandgap energy to be 3.18 eV for ZNbKLSNd05 glass, 3.15 eV for SF10 and 3.06 eV for SF6 glass), the cation-anion coupling strength and therefore the force constant D would not be significantly different for a first approximation. In consequence, the difference of λ0 value between these two glass series is most likely resulted from the difference in the reduced mass μ. The SF series glasses involve large amount (molar fraction >50%) of modifier PbO and would contribute to effectively increase μ and eventually increase λ0. On the other hand, ZNbKLSNd series glasses have considerable amount (molar fraction of 20%) of intermediate network former Nb2O5, and this would contribute to the effective decrease of the reduced mass due to the atomic number of Nb comparatively smaller than Pb, leading to a λ0 value smaller than that for SF series. These tendencies are consistent with the observation in Fig. 8(c) as mentioned above. The inclusion of large amount of Nb2O5 is also considered to contribute to the increase of the refractive indices due to the high oxygen-to-cation ratio of Nb2O5 which can provide sufficient oxygen ions leading to the generation of non-bridging oxygens in the glass structure.
When we turn to focus on a comparison between ZNbKLSNd glasses and BK7 glass both of which have similarly small λ0 (Fig. 8(c)), BK7 glass has a much smaller g factor than ZNbKLSNd glasses (Fig. 8(b)). If we can assume that g∝1/μ (Eq. (10)) and λ0∝(μ/D)1/2 Eq. (13) hold in these glasses (presuming no severe influence of other factors in Eq. (10)), the above feature (small g and small λ0) is only possible when BK7 glass possesses a significantly large force constant D. Actually BK7 glass has small amount of additives and the bandgap energy estimated from the transmission data is as large as ∼3.80 eV, indicating a stronger coupling and a larger D than in other oxide glasses. Consequently the small λ0 in BK7 glass is attributable to a large force constant. This interpretation seems to provide qualitative agreement with the experimental results of dielectric properties in silicate oxide glasses.
Following the discussion based on Eqs. (10) and (13) as described above, a couple of comparatively distinctive features have been realized for certain groups of glasses: ZNbKLSNd glasses are characterized by small reduced mass primarily caused by the intermediates Nb2O5, SF series glasses have large reduced mass primarily due to modifiers PbO, and BK7 glass exhibits a large force constant due to strong cation-anion coupling. Other glasses (PbNKLSNd, SK10) likely locate in intermediate range in terms of the reduced mass and force constant.
The THz polarizability is linked with the optical polarizability through Eqs. (4) and (5) together with a parameter a = Pi/Pe which seems to be characteristic to each group of glasses as is noticed in Table 1. The more ionic bonds are incorporated in the glass, the more ionic contribution would be expected to dominate the molar polalizability. Noticing that bonding of chalcogenide glasses is highly covalent and also silica has high covalency among silicate oxide glasses, it would be reasonable that these glasses have small a (0.37 for La:chalcogenide; 0.82 for silica, being smaller than for most of other silicate oxide glasses). The present hypothesis is likely supported by fairly high a values for BK7 (1.15) and SK10 (1.03) glasses in which alkaline cations such as Na+, K+, Ba2+ introduce ionic bondings. The a values found in FSO glasses (0.85-0.947 for ZNbKLSNd and 1.10-1.38 for PbNKLSNd series) are greater than that of silica. This seems to indicate the significance of ionic nature of the glass material, but further study is required for approaching to a precise mechanism of “a” parameter determination.
4. Conclusion
The THz dielectric properties of two (ZNbKLSNd and PbNKLSNd) series of OFS glasses have been characterized by THz-TDS and optical reflection measurements and discussed through a comparison with previously reported data on selected silicate oxide and chalcogenide glasses. The present OFS glasses, in particular, ZNbKLSNd glass has shown the highest THz (ν=0.5 THz) refractive index around 3.70. On the basis of Clausius-Mossotti relationship, THz and optical (λ=1.5 μm) dielectric constants have been correlated by a unified relationship using a parameter a which is defined by the ratio of the ionic polarizability to electronic polarizability for each glass series. This parameter a has been shown to be determined uniquely for each of the glass groups.
The dielectric constant difference estimated between the sub-THz and optical frequency ranges (ɛTHz –ɛopt= nTHz2 –nopt2), which correspond to the ionic contribution to the polarizability, has been analyzed in the sub-THz frequency region by using a simplified single oscillator model. The result has confirmed that the dielectric constant difference is well explained by the single oscillator model for all silicate oxide glasses examined, and the glass dependent factors such as the resonance wavelength λ0 and amplitude factor g have been evaluated. Analysis has shown that the increase of the dielectric constant difference, which leads to high THz refractive index (e.g. SF series glasses), is supported by large λ0 and small g in all silicate oxide glasses except ZNbKLSNd glasses. In contrast, ZNbKLSNd glasses have shown a distinctive feature with small λ0 and large g.
Effects of the glass composition have been discussed to understand the origin of large ionic polarizability in OFS glasses, particularly ZNbKLSNd glasses. The small λ0 found in ZNbKLSNd glass has been attributed to the effects of large amount of intermediate network former Nb2O5 incorporated in the glass structure. Incorporation of Nb2O5, instead of heavy PbO in SF series glasses, effectively suppresses the reduced mass of cation-anion pair, leading to the small λ0 as observed. It has also been suggested that the high oxygen-to-anion ratio of Nb2O5 helps introducing sufficient oxygen ions, which results in the enhancement of the total polarizability and THz refractive index.
In this study, THz dielectric properties of silicate oxide glasses, with a focus on OFS glasses, have been systematically interpreted in a unified approach. The high THz refractive index properties of OFS glasses, particularly ZNbKLSNd glasses, have been interpreted consistently with their physical properties.
Funding
Ministry of Science and Technology, Taiwan (# MOST 106-2112-M-007-022-MY2).
Acknowledgments
Dr. Doddoji Ramachari is thankful to Ministry of Science and Technology, Taiwan for the award of Postdoctoral Fellowship. The authors thank Chao-Kai Wang and Chun-Ling Yen for taking the THz-TDS data of the samples reported in this work.
Disclosures
The authors declare no conflicts of interest.
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