We have studied the formation of near-field fringes when sharp edges of materials are imaged using scattering-type scanning near-field optical microscope (s-SNOM). Materials we have investigated include dielectrics, metals, near-perfect conductor, and those that possess anisotropic permittivity and hyperbolic dispersion. For our theoretical analysis, we use a technique that combines full-wave numerical simulations of tip-sample near-field interaction and signal demodulation at higher orders akin to what is done in typical s-SNOM experiments. Unlike previous tip-sample interaction near-field models, our advanced technique allows simulation of the realistic tip and sample structure. Our analysis clarifies edge imaging of recently emerged layered materials such as hexagonal boron nitride and transition metal dichalcogenides (in particular, molybdenum disulfide), as well as traditional plasmonic materials such as gold. Hexagonal boron nitride is studied at several wavelengths, including the wavelength where it possesses excitation of phonon-polaritons and hyperbolic dispersion. Based on our results of s-SNOM imaging in different demodulation orders, we specify resonant and non-resonant types of edges and describe the edge fringes for each case. We clarify near-field edge-fringe formation at material sharp boundaries, both outside bright fringes and the low-contrast region at the edge, and elaborate on the necessity of separating them from propagating waves on the surface of polaritonic materials.
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