## 4 Results
### Analyzing the Near-Field Polarization  
In addition to measuring the integrated signal at a defined illumination polarization, we furthermore investigate the nature of complex far- and near-field mixing by analyzing the polarization distribution of the scattered light. Therefore, the different contributions in the backscattered signal are separated by an analyzer at the angle \(\phi\) with respect to p-polarization. As an exemplary measurement, we excite 3C-SiC resonantly at 10.6 \(\upmu\)m with (\(\theta=45^{\circ}\))-polarized incident light (Figure 4). The overall signal (see Figure 4a) shows a non-trivial polarization state with four lobes, the maxima of which are \(90^{\circ}\) apart. The stronger lobe is oriented along the \(25^{\circ}\) axis, leaving an offset of \(\sim 20^{\circ}\) with respect to the illumination polarization. In order to extract the underlying polarization contributions, the lobe is fitted using Equation (11), resulting in an excellent match. Moreover, the fit allows for a separation of the individual terms and hence for the extraction of individual signal contributions. The corresponding separated p-polarized, s-polarized, and mixed terms are shown in Figure 4b-d, respectively, with the overall signal in grey for comparison. Comparing p- and s-polarized contributions, the out-of-plane field enhancement of the former is apparent, yielding a five times higher signal intensity. However, this comparably small s-polarized contribution causes a significant rotation of the overall light distribution due to the mixed term. Referring to Equation (11), the origin of this enhancement is found in the mixing of the p-polarized far-field term with the s-polarized near-field term and vice versa, resulting in the clover-like polarization response as displayed in Figure 4d. In order to explore the origin of the complex polarization mixing, we extend our measurements to a full set of incident and scattered polarizations as displayed in Figure 5. Here, the intensity distribution in each horizontal line represents one full rotation of the analyzer angle (\(\phi\)), while the vertical axis corresponds to varying incident polarization angles \(\theta\). We refer to the resulting 2D plot as a \"polarization point spectrum\". \begin{table}
\begin{tabular}{c c c} \hline
**Sample** & **Re(\(\epsilon\)); Our Result** & **Re(\(\epsilon\)); Literature** \\ \hline Au @ 10.6 \(\upmu\)m & \(-6521.02\) & \(-5146.8\)[37] \\
3C-SiC @ 10.7 \(\upmu\)m & \(-18.23\pm 1.55\) & \(-1.94\)[38] \\
3C-SiC @ 10.6 \(\upmu\)m & \(-4.27\pm 0.53\) & \(-1.40\)[38] \\ \hline \end{tabular}
\end{table} 
Table 1: \(Re(\epsilon)\) for Au and 3C-SiC as extracted through fitting the experimental results shown in Figure 3 by applying Equation (8). Due to the symmetry of the underlying polarization, the polarization point spectrum (see Figure 5) has a twofold symmetry (and hence self-reproduces every \(180^{\circ}\)). Furthermore, the strongest signal is observed for p-polarized illumination, for \(\theta=0^{\circ},180^{\circ},360^{\circ}\) and p-polarized detection at \(\phi=0^{\circ},180^{\circ},360^{\circ}\), as expected when comparing it to the integrated intensity distribution in Figure 3c. Moreover, side maxima are observed for s-polarized analyzer angles at \(\phi\approx 90^{\circ}\). In order to fit the data, Equation (11) is used, in analogy to the fit for Figure 4a as described above. The function was modified, however, to fit the entire polarization point spectrum recursively. Qualitatively, the resulting fit resembles the experimental data very accurately, including both the global maxima at \(\theta\), \(\phi=0^{\circ},180^{\circ}\), and \(360^{\circ}\), as well as the corresponding side maxima. The latter resembles the creation of side lobes as connected to the mixing of far- and near-field components with different polarization states (see Equation (11)).