## 3 Results and Discussion
### Vitreous Silica
To examine these correlations, Figure 10a plots the relationship between the refractive index at 2 THz and the Boson peak frequency (the value at 2 THz was chosen because it is the region with a low slope and high signal-to-noise ratio). Figure 10b likewise plots the relationship between the Boson peak height and its frequency, where the peak height is calculated as the difference between peak maximum and the baseline at 3 THz. In addition to the seven samples studied in detail above, data from another seven samples are included in Figure 10. The provenance and grade of these samples were not known; therefore, they were not included in the main study. However, the relationships in Figure 10 are made apparent due to the fact that data from a relatively large number of samples (14 in total) are included, unlike previous work where only two to three samples were examined. Figure 8 confirms the existence of strong negative correlations between (a) refractive index and Boson peak frequency, and (b) Boson peak height and its frequency. To our knowledge, this is the first explicit report of these relationships using multiple samples of silica glass. Although it is outside the scope of this work to attempt to explain this behavior, it may be speculated that it arises from polarizability, which is affected by material microstructure and impurities, and in turn, determines the refractive index and influences absorption. As in the case of single-crystal quartz, it is important to compare our data on THz optical parameters of silica with those reported in the literature. Figure 11 presents the data reported in the literature [15; 16; 17; 18; 19; 20; 21; 22; 23; 24] together with the results of this work, shown as the mean and standard deviation of the samples studied. The reported data that falls outside the shown range are excluded. Unlike the case of quartz, the great majority of these results were obtained using FTS [13; 14; 15; 16; 17; 18; 22], while two used TDS [19; 21]; a review of all published data was reported in [20]. Figure 9: The Boson peak in Spectrosil 2000 silica glass samples. Figure 11: THz optical parameters of Spectrosil 2000 silica glass, shown as the mean (heavy blue line) and standard deviation (light blue shading) of the seven samples examined. Data reported in the literature are shown together with the results of this work. (**a**) refractive index; (**b**) absorption coefficient. Figure 10: (**a**) Relationship between the refractive index of silica glasses at 2 THz and their Boson peak frequency. (**b**) Relationship between the Boson peak height and its frequency in silica glasses. The peak height is measured as the difference between peak maximum and its base at 3 THz (see Figure 7). Our results are seen to be in good agreement with the majority of the reported data. However, it is evident that large variations exist in the reported values of both refractive index and absorption coefficient, confirming the necessity for accurate measurements. The open resonator measurements on the seven silica glass samples gave values of refractive index that were consistent within uncertainty. The measured loss of Spectrosil 2000 is noted as being particularly low in comparison with other grades of fused silica [26]. The absorption coefficient, however, is seen to vary by a factor of two between batches. It must, therefore, be concluded that this material is not suitable as a reference material for dielectric loss at microwave and millimeter-wave frequencies. At MHz frequencies, Spectrosil 2000 can be useful as a reference material for dielectric loss because, despite the observed variability, its loss is far below the resolution of typical experiments.