Electrodynamics of spatial clusters of spheres: Substrate effects

The electrodynamical boundary-value problem for a spatial system of spherical particles located near a semi-infinite substrate is considered in the electrostatic limit. By generalizing the existing technique based on the multipolar expansion for the electrostatic potential, the initial problem is reduced to determining the multipolar coefficients from an infinite set of coupled algebraic equations. 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 polarizability behavior is analyzed. From this analysis, similarities and differences in the effects caused by a sphere and a substrate acting on a trial sphere are elucidated. The substrate influence on the optical properties of a small sphere is studied in the electrostatic approximation by using the Lorentzian dielectric functions. The influence is shown to lead to splitting of the single-sphere resonance into four resonances, a pair of which is red shifted while another one is blue shifted. Analytical expressions for the shifted resonances and the strengths of the corresponding modes are obtained and the main regularities in the substrate influence on optical spectra of a sphere are analyzed.