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.
The effects of inclusion shape on the quasi-static effective permittivity of a two-phase periodic composite material are discussed in this paper. The lattice is formed from complex-shaped conducting inclusions suspended in a host medium. The effective permittivity is computed using an accurate moment-method-based technique. Numerical results are presented for a variety of particle shapes including circular, square, and "rounded square" cylinders (two dimensional) as well as lattices of spheres and cubes (three dimensional). It was found that among these shapes, lattices of square cylinders and cubes produced nearly the minimal polarization per unit volume possible (à la Maxwell/Maxwell Garnett). It appears that the strong mutual interaction between edges and corners of these particles is responsible for this effect. That is, it was observed that the mutual interaction between square cylinders and cubes caused a decrease in their dipole moments and, hence, the effective permittivity, which is opposite to the usual expectation from mutual interaction between circular cylinders and spheres. Experimental verification of this effect is provided by quasi-static conductivity measurements using an apparatus that simulates an infinite lattice of highly conducting cubes. The methodology and results described in this work can be used to design certain microwave composite materials composed of periodic conductor/dielectric composites.
Composite chiral materials are realized by embedding large numbers of handed inclusions within a host material. In this paper, a computational methodology is presented whereby the effective constitutive parameters of artificial chiral matedals are computed while accounting for all self and mutual iatetactions among the inclusions. This technique combines a full-wave, Monte-Carlo scattering solution for randomly oriented inclusfom together with an analytical solution for the scattering br a canonically-shaped body having a properly chosen constitutive model. It is believed that the effective constitutive parameters shown in this paper are the first full-wave computation of these quantities to appear in the literature.
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