Surface structure and polariton interactions in the scattering of electromagnetic waves from a cylinder in front of a conducting grating: theory for the reflection photon scanning tunneling microscope

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Abstract
Exact calculations of the scattering of light and other electromagnetic waves by a tip, metallic or dielectric, in front of surface-relief grating are made by means of the extinction theorem generalized to multiply connected bodies. The configuration addressed is two dimensional; specifically, it pertains to the plane of incidence, and the tip is simulated by a cylinder. The scattered near fields between the surface and the cylinder are calculated, as well as the scattered intensity detected inside the tip as it scans along a line parallel to the interface. Two different regimes of grating parameters are studied, depending on whether the grating period is equal to, or smaller than, the wavelength. The results show that, as a result of multiple scattering, this intensity distribution does not generally follow the surface topography. Tips of diameter not larger than 0.1λ and dielectric permittivity similar to that of glass do not appreciably perturb the field reflected by the grating. The detection of surface polaritons as the tip approaches the interface is also addressed.