Polarization sensitivity in scattering-type scanning near-field optical microscopy -- towards nanoellipsometry

Electric field enhancement mediated through sharp tips in scattering-type scanning near-field optical microscopy (s-SNOM) enables optical material analysis down to the 10-nm length scale, and even below. Nevertheless, mostly the out-of-plane electric field component is considered here due to the lightning rod effect of the elongated s-SNOM tip being orders of magnitude stronger as compared to any in-plane field component. Nonetheless, the fundamental understanding of resonantly excited near-field coupled systems clearly allows us to take profit from all vectorial components, especially also from the in-plane ones. In this paper, we theoretically and experimentally explore how linear polarization control of both near-field illumination and detection, can constructively be implemented to (non-)resonantly couple to selected sample permittivity tensor components, e.g. explicitly also to the in-plane directions. When applying the point-dipole model, we show that resonantly excited samples respond with a strong near-field signal, to all linear polarization angles. We then experimentally investigate the polarization-dependent responses for both non-resonant (Au) and phonon-resonant (3C-SiC) sample excitations at a 10.6~$\mu$m and 10.7~$\mu$m incident wavelength using a tabletop CO$_2$ laser. Varying the illumination polarization angle thus allows for quantitatively comparing the scattered near-field signatures for the two wavelengths. Finally, we compare our experimental data to simulation results, and thus gain the fundamental understanding of the polarization's influence on the near-field interaction. As a result, the near-field components parallel and perpendicular to the sample surface can be easily disentangled and quantified through their polarization signatures, connecting them directly to the sample's local permittivity.