Generalized Mie Theory for Full‐Wave Numerical Calculations of Scattering Near‐Field Optical Microscopy with Arbitrary Geometries

Scattering‐type scanning near‐field optical microscopy (s‐SNOM) is becoming a premier method for the nanoscale optical investigation of materials well beyond the diffraction limit. A number of popular numerical methods exist to predict the near‐field contrast for axisymmetric configurations of scatterers on a surface in the quasi‐electrostatic approximation. Here, a fully electrodynamic approach is given for the calculation of near‐field contrast of several scatterers in arbitrary configuration, based on the generalized Mie scattering method. Examples for the potential of this new approach are given by showing the coupling of hyperbolic phonon polaritons in hexagonal boron nitride (hBN) layers and showing enhanced scattering in core–shell systems. In general, this method enables the numerical calculation of the near‐field contrast in a variety of strongly resonant scatterers and is able to accurately recreate spatial near‐field maps. Generalized Mie scattering theory is used for calculating contrast in scanning near‐field optical microscopy (SNOM). The presented method is capable of the calculation of the scattering properties of several scatterers in arbitrary orientation. Near‐field spectra of filled and unfilled boron nitride nanotubes (BNNTs) is calculated, showing the enhancing effects of the nanotubes for the scattering of the filled material.