## 1 Introduction  
Since it is a versatile tool for optical surface characterization and analysis, scattering-type scanning near-field optical microscopy (s-SNOM) has been broadly applied to various material systems, ranging from single crystals [1] to thin films [2], heterostructures [3], semiconductors [4], and biological samples [5]. Generally, s-SNOM can be performed at any wavelength [6; 7; 8; 9; 10; 11], and thus the near-field response strongly depends on the sample's optical characteristics, i.e., frequency-dependent polarizability. Moreover, s-SNOM may couple to different material properties, such as polaritonic responses [12], crystalline structure [13], spins [14], and charge carrier concentrations [10; 13], with the possibility of quantifying all of them via the local optical sample response. Connecting the near-field signal to the local permittivity, therefore, is the primary goal in s-SNOM [15; 16]. Sensitivity to the local in-plane anisotropies has been proven using aperture-type scanning near-field optical microscopy (a-SNOM) [17]. Moreover, a-SNOM-based nanoellipsometry was successfully implemented into transmission [18] and reflection setups [19], thus directly connecting the optical responses to the local permittivity tensor elements. So far, thin films have been the focus of those studies that then mostly were inspected in transmission [18; 19]. In comparison, s-SNOM should support a similar in-plane sensitivity as a-SNOM and moreover offers a much higher and wavelength-independent lateral resolution since it is based on light scattering off a standard scanning force microscopy (SFM) tip. s-SNOM was shown to profit from polarization-sensitive measurements, like mapping plasmonic structures using crossed polarizers [20], polarization-dependent absorption in organic materials [21], and probing in-plane anisotropies [22]. The challenge now lies in extracting the in-plane response as it is commonly assumed to be suppressed due to the enhanced out-of-plane antenna response of the metal-like SFM tip [23]. Various efforts have been made to enhance the in-plane response of standard s-SNOM probes through, for example, optimizing the SFM tip shape [24], or tilt the tip cone with respect to the sample surface normal [25]. Similarly, the sample's in-plane response can be enhanced by patterning dedicated nano-antennas onto the sample surface [26]. Moreover, it has been demonstrated both theoretically [27] and experimentally [28] that excitation close to the sample's optical resonance results in an in-plane signal of significant strength even when using standard s-SNOM tips. As this in-plane response is strongly connected to the resonant excitation, its sensitivity to the local sample properties is enhanced for that frequency interval. Hence, minute changes of the local sample properties related to, e.g., mechanical stress [29] and permittivity anisotropies [22; 28; 30; 31] are expected to have a drastic impact on the in-plane contributions in s-SNOM. This paper explores the possibility of vectorial field analysis under resonant near-field excitation. In particular, we thereby enable the detection of local sample responses excited by an in-plane electric field and describe a universal ellipsometry-like approach for recovering local permittivities. Notably, this is achieved by rotating and analyzing the linear polarization of both incident and detected fields, respectively, thus disentangling the mixed signal contributions of in- and out-of-plane components. Polarization-sensitive measurements are performed on both 3C-SiC and Au at wavelengths of 10.6 \(\upmu\)m and 10.7 \(\upmu\)m. Measurements are compared to simulations that combine the point-dipole model [32] and the Jones matrix formalism [33] to account for any polarization modification in the detection path. We obtain an excellent fit between theory and experiment, which finally allows us to calculate local permittivity values from the sample's polarization point-spectra. The paper is structured as follows:  
_Section 2.