Metamaterials Comprising of Plasmonic Nano-spheres and Nanorods: Modeling Using Dipole Moment and Characteristic Basis Function Methods

This dissertation presents physical modeling and numerically efficient analyses of the interaction between electromagnetic waves and clusters of metamaterials comprising of core-shell nano-particles and plasmonic nanorods. Chapter 1 is the introduction for this thesis. The main idea of chapter 2 is to design an array of core-shell plasmonic nanoparticles manipulating a desired near-field focusing pattern in optical spectrum. The interactions between the array elements are formulated by using Dyadic Green's Function analysis and by employing the closed-form formula for electric polarizability of each plasmonic particle (Dipolar Mode (DM) approach).;In chapter 3 we introduce a set of Macro Basis Functions (MBFs) for efficient representation of the currents induced on metal wires and elements comprising of junctions of wires or strips. The use of these functions leads to a relatively small and well-conditioned matrix, only a 3×3 size for a cross-shaped element. An important advantage of using these basis functions is that the fields they generate can be expressed in close forms.;In chapter 4 we introduce a numerically efficient computational technique to model the problem of scattering from plasmonic nanorod antennas. The key to achieving the numerical efficiency is to utilize MBFs to reduce the size of matrix equation. Closed form formulations are presented for computing the fields by the MBFs that enable us to generate the required matrix elements rapidly.;The goal of chapter 5 is to present a computational scheme to characterize reflection and transmission coefficients for a periodic array of plasmonic nanorods illuminated by an obliquely incident plane wave. The problem is formulated by using the Characteristic Basis Function Method (CBFM) to reduce the number of unknowns. The concept of progressively expanding rings is employed along with Parseval's theorem to evaluate the Galerkin's integrals for the periodic structure.;In chapter 6, by taking advantage of CBFM we solve the scattering problem of finite arrays of plasmonic nanorods for two different cases. In case 1, the elements are arbitrarily tilted (rotated around their centroids). And in case 2, the finite array includes a Fibonacci arrangement of two kinds of nanorods with different lengths and consequently different resonance frequencies.