The boundary problem of linear classical optics about the interaction of
electromagnetic radiation with a thin dielectric film has been solved under
explicit consideration of its discrete structure. The main attention has been
paid to the investigation of the near-zone optical response of dielectrics. The
laws of reflection and refraction for discrete structures in the case of a
regular atomic distribution are studied and the structure of evanescent
harmonics induced by an external plane wave near the surface is investigated in
details. It is shown by means of analytical and numerical calculations that due
to the existence of the evanescent harmonics the laws of reflection and
refraction at the distances from the surface less than two interatomic
distances are principally different from the Fresnel laws. From the practical
point of view the results of this work might be useful for the near-field
optical microscopy of ultrahigh resolution.Comment: 25 pages, 16 figures, LaTeX2.09, to be published in Phys.Rev.
