Near-field polarization of a high-refractive-index dielectric nanosphere on a dielectric substrate

The near-field polarization structure of a high-refractive-index dielectric nanosphere in a nonmagnetic and nonabsorbing medium is studied numerically in free space and in the vicinity of a flat dielectric substrate. Polarization patterns of the near field are obtained for linear and circular polarizations of the incident light and visualized using the polarization degree and three-dimensional Stokes parameters. Calculations are performed using the finite-element method and verified analytically using the Mie solution for scattering by a sphere with an extension of Weyl's method allowing description of reflection by a flat substrate. It is shown that the nanosphere drastically affects the polarization leading to a complex butterflylike structure. For instance, the near-field polarization is found to be qualitatively modified near the Mie electric and magnetic dipole and quadrupole resonances: linear polarization of the incident field results in circular polarization in some areas around the particle and vice versa. The areas of strong polarization change are found to be spatially localized in certain places around the particle making it possible to perform an experimental mapping. It is shown how a dielectric substrate affects the polarization distribution of the near-field of the particle. Also, several schemes of potential experiments to map the near-field intensity and polarization have been discussed.