Application of Mie Scattering of Evanescent Waves to Scanning Tunnelling Optical Microscopy Theory

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Abstract
In this paper we present a macroscopic theory for scanning tunnelling optical microscopy where the sample is a grating and the tip is modelled by a dielectric sphere. The sphere is immersed in the near-field above the grating and is excited by the diffracted orders which can be evanescent. The detected signal is supposed to be the diffracted intensity by the sphere which is calculated by using Mie theory. When studying Mie scattering of one evanescent wave we show that the multipolar series is perturbed compared to scattering of a homogeneous wave. Even for a small sphere multipolar terms have to be taken into account. We have then proposed a formula for the intensity leading to calculations of intensity profile and surfaces and to discuss the influence of tip radius on resolution of the images.