## 3 Results and Discussion
### Index of Refraction and Absorption Coefficient  
As mentioned before, we studied two sets of samples: Thin (nominal 0.3 mm) and thick (nominal 0.9 mm); each set contained a different co-polymer as reference and 1-wt% graphene nanocomposite. Since the sample thickness is a very important parameter for calculating \(\hat{n}(\omega)\) and \(\varepsilon(\omega)\), we repeated our measurements several times at different spots on a given sample and used the averaged value for the sample parameter calculation. Spectral dependencies of \(n(\omega)\) and \(\alpha(\omega)\) obtained from the THz-TDS data, using Equations (2) and (3), are presented in Figure 6a,b, respectively.  
One should ignore the low-frequency oscillations in the extracted \(n(\omega)\) and \(\alpha(\omega)\) spectra (Figure 6), that are the most pronounced for the thin samples because these oscillations can be attributed to the approximation error of our simplified model. The methodology behind Equation (1) requires that the time-domain signal be truncated before any secondary peaks (because of internal reflections). This truncation, as well as minor deviation or inaccuracy in the sample thickness determination, introduces an incomplete removal of the Fabry-Perot reflections of the THz signal, resulting in observed oscillations. Note that the oscillations for the thick samples are much smaller and have a smaller period, which is consistent with this approximation error. These errors, while relatively small in the \(n(\omega)\) spectra, were very substantial in the calculated \(\alpha(\omega)\) spectrum for the thin samples and, eventually, prevented us from obtaining a consistent plot in the latter case.  
The \(n(\omega)\) spectra of both neat copolymers, as seen in Figure 6a, are almost flat across the entire measured range, and the values at 1 THz for a thin and a thick polymer are \(\sim\)1.57 and \(\sim\)1.62, respectively, which are close to the values observed earlier for PET polymer [34; 35]. The different \(n(\omega)\) values for the thin and thick samples are caused by the different ratio between the hard and soft segments in the PET-DLA 4060 and PET-DLA 6040 copolymers. The PET-DLA 6040 co-polymer has a higher percentage of PET hard segments and therefore a higher crystallinity, resulting in the increased \(n\) value. When 1 wt% of graphene nanofiller was added into each copolymer, the \(n(\omega)\) dependences of the resultant nanocomposites remained flat in the measurement range, but the values, again evaluated at 1 THz, increased to \(\sim\)1.78 and \(\sim\)1.83 for the thin and thick samples, respectively. Clearly, adding 1 wt% of graphene flakes to a copolymer matrix measurably increased (\(\sim\)10%) the \(n\) of the resultant nanocomposite. Similar results were obtained by other groups [21; 22].  
As explained above, Figure 6b shows \(\alpha(\omega)\) spectra for only the thick samples, i.e., the neat PET-DLA 6040 co-polymer and the corresponding graphene nanocomposite. The addition of 1-wt% graphene into the copolymer matrix increases the \(\alpha(\omega)\), especially at the high-frequency end of the spectrum. The latter result is in good agreement with previously published data [22].