Representations and Transforms of Vector Field as the Basis of Near-Field Optics*

Abstract

We report the novel mathematical description of the vector mode functions which provide a useful basis for theoretical treatment of near-field optical microscope and related phenomena. The vector planar, spherical, and cylindrical mode functions and transforms are formulated on the bases of spatial rotational functions and angular spectrum representations. It is demonstrated that the formulation provides the bases to evaluate the range and locality of optical near-field interaction of sub-wavelength sized matter with an example of electric dipole interaction.