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Date of Award


Document Type


Degree Name

Doctor of Philosophy in Electrical Engineering (PhD)

College, School or Department Name

Department of Electrical and Computer Engineering

First Advisor

Elena Semouchkina


Metamaterials are artificially-engineered composites comprised of resonant elements with unusual electromagnetic (EM) responses, which couldn’t be found in nature. Effective medium theory is the most widely used approach to characterize the metamaterials behaviors. However, the applicability of the effective medium theory has been pushed to its limits and becomes very questionable, especially near the resonance region. Moreover, it could not reveal the structural resonance phenomena in finite arrays as well as the inter-resonator interaction behind that. Dielectric metamaterials composed of dielectric resonators (DRs) have lower loss and better isotropy than the conventional metamaterials composed of metal resonators. In addition, DRs can support both electric and magnetic-type responses and can serve as the typical resonant elements for metamaterials. The objective of this dissertation is to better understand, characterize and control the inter-resonator interaction in various finite DR arrays under different environments important for practical applications.

In order to realize several options for inter-resonator coupling and to reveal how the coupling affects the EM responses, we have studied finite DR arrays variously positioned with respect to the incident wave in standard waveguides and in free space. It is demonstrated that inter-resonator interaction causes resonance splitting, and as the consequence, the appearance of two transmission modes, i.e. an odd mode and an even mode is detected and analyzed. The effective medium parameters extracted from S parameter spectra for one unit cell representing infinite 2D DR array reflect not only the Lorentz-type resonance response of the resonator, but also the response related to the anti-resonances and the dispersion phenomena in arrays. These effects could cause additional ranges of negativity of the respective effective parameters just below the resonance frequency and, thus, to extend the stop-bands to the low frequency side.

By manipulating the lattice parameters, herein, controlling the inter-resonator coupling in three axes directions, we are able to control the frequency ranges of different components of the array responses in order to make the negative effective permeability and effective permittivity bands overlapped. Consequently, a new design principle of obtaining negative refraction in metamaterials with only one type of resonators is presented and the negativity of the refractive index has been verified.

In order to qualitatively characterize the coupling between DRs in the array, we have employed the equivalent circuit model (ECM) for a 3D DR array under EM wave incidence at magnetic resonance by taking into account inter-resonator coupling along three axes of the lattice. It was shown that the changes of coupling coefficients at the variations of the array lattice parameters explain all the changes of the magnetic resonance band.

Waveguides at frequencies below cut-off can provide unique environment to quantitatively characterize coupling between DRs. For this purpose, the dispersion phenomena of below cut-off waveguides loaded with cylindrical DRs revealed by simulations and experiments are additionally analyzed by using ECMs with accounting for the inter-resonator coupling for DRs at both magnetic and electric resonances. The concepts of magneto-inductive and electro-inductive waves were used to analyze the forward and backward wave propagation. The Transfer Matrix Method was used to analyze the Fabry-Perot resonances and calculate the below cut-off transmission spectra for waveguides loaded with finite DR arrays. By matching these spectra to the spectra obtained by using full-wave simulations and measurements, it was possible to determine the ECM components, including self-inductance, self-capacitance, mutual inductance, and mutual capacitance of DRs at various resonance modes.

In addition, an alternative method—dipole interaction model is used to analyze the dispersion phenomena at below cut-off waveguides loaded with spherical DRs. The analytically calculated dispersion diagrams for spherical DRs having adequately chosen radii at both magnetic and electric dipolar resonances were found to match well the diagrams obtained by using full wave simulations, as well as the ones previously obtained for cylindrical DRs by using the ECMs.