## 3 Results and Discussion
### Vitreous Silica  
It is known that different grades of silica glass have slightly different THz optical properties. In this work, we aimed to test variability among different batches of the same nominal grade and among different samples fabricated from the same batch. Glasses from four different batches of Spectrosil 2000 were examined, designated A, B, C, D. Batch A had two samples; batch D had three samples; batches C and D had one sample each. Their THz optical properties are shown in Figures 7 and 8; their MW properties are listed in Table 1.  
Figure 7: Refractive indices of Spectrosil 2000 silica glass samples. Significant differences are evident among the THz refractive indices of the glasses examined (Figure 7). There is a high consistency between samples A1 and A2; whereas they differ from samples B and C. Samples B and C are closer to each other than they are to samples A1 and A2. Samples D1, D2, and D3 are very similar to samples A1 and A2. Samples D2 and D3 are identical within measurement uncertainty to samples A1 and A2. However, sample D1 differs slightly from D2 and D3. These results, based on the limited number of samples examined, indicate that there is a good consistency between glass samples from the same batch, but that inter-batch variability may be significant in some cases. These should be taken into consideration in employing silica glass as a reference material for THz measurements. The THz absorption coefficients (Figure 8) of all glasses are similar up to about 2 THz, with increasingly significant differences appearing above 3 THz. At THz frequencies absorption in amorphous materials approximates the Debye vibrational density of states (VDOS), described by the relationship \(\alpha\propto\
u^{2}\). In terms of MW loss, this translates into \(\delta\propto\
u\) (see Equations (3)-(6)), which is a well-known behavior in MW measurements [33]. However, it is well known that glasses exhibit low-frequency vibrational modes in excess of the Debye VDOS, termed the Boson peak [34; 35]. The Boson peak can be revealed by plotting \(\alpha/\
u^{2}\) as a function of frequency, where it appears as a broad band. It has been shown that in silica glass the Boson peak occurs at around 1 THz, while in silica glass the Boson peak occurs at around 1 THz. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Material** & \multicolumn{3}{c}{**36 GHz**} & \multicolumn{5}{c}{**144 GHz**} & \multicolumn{2}{c}{**1 THz**} \\ \hline  & \(\epsilon^{\prime}\) & \(\delta\) & **RI** & **Abs (cm\({}^{-1}\))** & \(\epsilon^{\prime}\) & \(\delta\) & **RI** & **Abs (cm\({}^{-1}\))** & **RI** \\  & \(\pm\)**0.012** & **(urad)** & \(\pm\)**0.003** & \(\times\)**10\({}^{-3}\)** & \(\pm\)**0.012** & **(urad)** & \(\pm\)**0.003** & \(\times\)**10\({}^{-3  
1 THz [34; 35; 36; 37; 38] and that it is very sensitive to small variations in the glass properties, and in particular to the presence of OH groups [35; 36; 37; 38; 39]. Figure 9 depicts the Boson peak in the glasses studied, revealing variations in glass absorption properties that cannot be easily distinguished in Figure 8. As in the case of the refractive indices in Figure 7, the glass pair A1 and A2 are very similar; while B and D are close to each other but differ from A1 and A2. However, batch D differs significantly from the other glasses; moreover, unlike the refractive indices, glasses D1 and D2 are very similar, while D3 differs from them. It appears in Figure 9 that the Boson peak height is correlated with its frequency: in glasses where the peaks are at a higher frequency, their heights are reduced. This is consistent with data reported in the literature [35; 36; 37; 38; 39]. Moreover, by considering Figure 9 together with the refractive indices in Figure 7, it appears that glasses with lower refractive indices have Boson peaks shifted to higher frequencies.