Scattering near-field optical microscopy of optically anisotropic systems

Scattering-type scanning near-field optical microscopy ($s$-SNOM) promises optical resolution down to the $1\mathrm{nm}$ regime. In the present work, we develop a theoretical approach to probing optical anisotropy with $s$-SNOM. We describe the interaction of the scattering probe with the sample in the framework of the well known quasielectrostatic dipole model, which we extend to anisotropic samples and probes by applying the method of image charges. Furthermore, we include reflection of the incident plane wave at the anisotropic sample surface in the analysis. It turns out that it is this latter effect by which the anisotropy modifies the scattering most efficiently. As an example, we discuss the scattering contrast to be expected between ferroelectric domains on barium titanate $\left(\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3\right)$ that differ by the orientation of the anisotropy. Depending on the direction of incidence and the polarization of the illuminating light, a contrast strong enough to be detected experimentally is obtained.