Exact calculations of the scattering of light and other electromagnetic waves by a dielectric tip in front of corrugated dielectric samples are carried out by means of surface integrals derived from the extinction theorem and related equations. The configuration tackled is two dimensional, and the active part of the probing tip is simulated by a cylinder. The surface under study is illuminated from its dielectric side with a Gaussian beam at different angles of incidence. The transmitted near-field distribution is calculated inside the tip when it scans the surface at a constant distance from its mean plane. Different calculations are performed both for extended corrugated profiles (surface-relief gratings) and for flat dielectric interfaces with topographic subwavelength defects. The results show that the near fields scattered from these two kinds of surface corrugation have a notably different behavior with respect to the profile. Also, the influence of the angle of incidence, the polarization, and the shape of the incident beam on the near-field distribution is studied. It is shown that tips with diameters not larger than 0.1λ and a dielectric permittivity similar to that of glass do not appreciably perturb the near field transmitted by the sample.
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