Effective Polarizability in Near-Field Microscopy of Phonon-Polariton Resonances

We investigate the resonant characteristics of planar surfaces and distinct edges of structures with the excitation of phonon-polaritons. We analyze two materials supporting phonon-polariton excitations in the mid-infrared spectrum: silicon carbide, characterized by an almost isotropic dielectric constant, and hexagonal boron nitride, notable for its pronounced anisotropy in a spectral region exhibiting hyperbolic dispersion. We formulate a theoretical framework that accurately captures the excitations of the structure involving phonon-polaritons, predicts the response in scattering-type near-field optical microscopy, and is effective for complex resonant geometries where the locations of hot spots are uncertain. We account for the tapping motion of the probe, perform analysis for different heights of the probe, and demodulate the signal using a fast Fourier transform. Using this Fourier demodulation analysis, we show that light enhancement across the entire apex is the most accurate characteristic for describing the response of all resonant excitations and hot spots. We demonstrate that computing the demodulation orders of light enhancement in the microscope probe accurately predicts its imaging.