We theoretically study resonance responses of flat surfaces and sharp edges of the nanostructures that support excitations of phonon-polaritons in mid-infrared range. We focus on two materials: silicon carbide that has a nearly isotropic permittivity and hexagonal boron nitride that has a strong anisotropy and spectral band with hyperbolic dispersion. We aim to predict scattering-type near-field optical microscope (s-SNOM) response and develop a modeling approach that adequately describes the resonant behavior of the nanostructure with phonon-polaritons. The previously employed technique assumes dipole scattering from the tip and allows calculating s-SNOM signal in different demodulation orders by modeling full structure, any tip positions, and vertical scans, which works well for the structures with only one hot spot, e.g. flat surfaces. In the structures of complex shapes, hot-spot places are unknown, and analysis of light absorption in the whole apex is the best way to account for all hot spots and field enhancement. We show that calculation of demodulation orders of light absorption in the tip is an alternative way to predict s-SNOM signal, and it is preferred for the structures of complex shapes with strong resonances, where dipole approximation of the tip is not valid.
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