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.

We report far-field experimental optical extinction spectra of linear chains of gold nanocylinders with interparticle separations close to the particle's surface plasmon resonance (SPR) wavelength λSPR. The spectra reveal non-monotonic shift of the SPR peak position with increase in the distance d. The non-monotonic λSPR(d) dependence is rationalized considering electromagnetic coupling between the particles in the dipole approximation. Simple expressions for the modified SPR frequencies are obtained using the dipole scattered field and taking into account both the retardation and phase lag effects.

We revise the method of periodic metamaterials homogenization initially proposed by Pendry, Holden, Robbins and Stewart (PHRS). The shortcomings of the PHRS derivation of the basic formulae of their method are outlined, subtleties of the method implementation are discussed and the range of validity of both the PHRS method and its later modifications are analyzed. We then give a rigorous derivation of the PHRS averaging formulae in the static approximation and modify the PHRS method to account for the phase advance of an incident wave across the unit cells of metamaterials beyond the quasistatic regime. The advantages of our proposed method are illustrated by numerical calculations of the effective parameters of some periodic metamaterials.