Gozhenko V. Interaction of electromagnetic radiation with regular and irregular structures on solid surfaces

It is proposed a generalization of the microscopic theory of the electrostatic response of a system of spheres on a substrate. The generalized theory allows one to treat spatial systems of spherical particles of different sizes, made of different materials, and located arbitrarily near a boundary surface. For a system of two spheres above a substrate, an analytical expression for the sphere's polarizability is obtained in the dipole approximation, and the substrate influence on the polarizability and the optical properties of a nanodimensional sphere is analyzed. The dipole interaction between the sphere and substrate is shown to lead to splitting of the sphere's eigenmode into a set of four resonances. Expressions for the resonant frequencies, frequency dependence of the sphere's polarizability, and the strengths of the resonant modes are obtained. It is obtained an analytical solution for the problem of electromagnetic wave scattering by a rough surface described by the Weierstrass fractal function.The scattering indicatrix is shown to contain splashes in nonspecular directions, so the specular reflection law is broken for fractal surfaces. Obtained regularities are due to combination of the chaotic character and self-similarity peculiar to fractal surfaces.