Dipole Mode Analysis of Arrays of Dielectric and Plasmonic Particle Metamaterials

This dissertation presents a theoretical study and numerical evaluations of design and applications of metamaterials. To achieve a metamaterial with desired figure of merit, one needs to create appropriate electric and magnetic dipole moments (in small scale) and then tailor them to the application of interest. Arraying these dipole moments can lead to the required material properties. Since dielectric spheres have the potential to offer both electric and magnetic dipole modes, I consider an array of dielectric spheres. To investigate the behavior, I present a comprehensive method to solve the problem of multiple scattering of a plane wave incident on an arbitrary configuration of N spheres. By using multipole expansion method, I show that, if the spheres are small enough, such that the magnitude of higher order modes are negligible compared to the dipole modes, it is enough to consider only the first electric and magnetic modes.;I then present an analytical solution for the problem of plane-wave scattering by 3D arrays of small spheres. We theoretically investigate the characteristics of electromagnetic (EM) waves supported by three dimensional (3D) periodic arrays of dielectric and magneto-dielectric spheres. It is assumed that either the spheres are sufficiently small or the frequency is such that only the dipole scattered modes are excited. Imposing the boundary conditions, will determine the required equations for obtaining kd -- betad dispersion characteristics. To ease the computer calculations, we transform slowly convergent summations to rapidly ones. A metamaterial constructed from unit-cells of two different spheres is created, where one set of spheres develops electric modes, and the other set establishes magnetic modes.;Metamaterials show potential for several novel applications in electromagnetics and optics. In this thesis, I present novel applications of metamaterials in building antenna devices. This works reviews the performance of small antennas enabled by metamaterials and directive nano-antennas.;I first start with a hemispherical negative permittivity (ENG) resonator fed by a coaxial probe and a hemispherical negative permeability (MNG) resonator antenna using aperture coupling for excitation. For both cases exact and approximated Green's functions for the evaluation of the input impedances are obtained and expressed in a convenient form for numerical computation. It is illustrated how a resonator composed of negative permeability/permittivity medium can successfully establish a small antenna element. To achieve an antenna with higher impedance bandwidths or lower Q, a novel design is proposed. I show that if I embed the dipole antenna inside a core-shell structure, with magnetic shell and dielectric core, a quality factor as low as 1.08 times the Chu limit can be achieved. The Q of the antenna is attained with the use of Green's function analysis and input impedance as a function of frequency. The obtained observations may provide road maps for the future design of metamaterial-based subwavelength antennas.;In addition to the applications of metamaterials in microwave frequencies, I also investigate the design and modeling of nano-antennas using plasmonic particles. To build antennas in optical frequency it has been suggested to use plasmonic particles (negative permittivity). Here, I theoretically characterize the performance of array of plasmonic core-shell nano-radiators located over layered substrates. Engineered substrates are investigated to manipulate the radiation performance of nanoantennas. I developed a rigorous analytical approach for the problem at hand by applying Green's function analysis of dipoles located above layered materials. I highlighted the effect of the dielectric substrate layers on the radiation performance. It is obtained that a dielectric substrate can drastically change the radiation pattern of a plasmonic nanoantenna from what is obtained for that when is located in free space. Integrating a silver layer can reduce the antenna interaction with the dielectric substrate and suppress the back radiation. A composite substrate for an optimized 2D array of four-plasmonic nano core-shell radiators is engineered to tailor the dipolar modes of the nanoantennas and accomplish a pencil beam radiation. I established that by novel arraying of nano-particles and tailoring their multilayer substrates, one can successfully engineer the radiation patterns and beam angles. (Abstract shortened by UMI.)...