Investigation of properties of materials with negative permittivity and permeability: negative refraction

Abstract

This thesis provides a study of electromagnetic wave properties of a uniform isotropic material with negative permittivity and permeability. No natural material has been found with this property, and none is expected. However, artificial materials made of periodic metallic structure have been shown to exhibit this behavior and have motivated much of this study. The acronym NIM for negative index medium is often used to denote such a metamaterial.Chapter 2 provides interpretation of the meaning of permittivity and permeability in terms of measured values of reflection and transmission coefficients through a planar slab of an arbitrary homogeneous isotropic medium. Permittivity and permeability are frequency dependent. Consequently, this chapter and much of what follows are in the frequency domain.Chapter 3 provides a comprehensive categorization of wave types at the boundary of a lossless normal dielectric with a half space of arbitrary permittivity and permeability in the low-loss limit. New wave types of backward surface waves and backward lateral waves are found for certain NIM combinations of permittivity and permeability.Chapter 4 calculates the negative refraction expected at the interface with a NIM. The plane wave result given by Snell's law is shown to extend to a beam wave (a wave packet in the time domain) if the dominant beam wave frequencies are within a band in which the NIM is not too dispersive. Both an analytic approximate solution and numerical examples calculated from exact Fourier transform solutions are obtained.Chapter 5 presents details of the phenomenon of negative index focusing by a planar NIM layer when the relative permittivity and permeability of the layer are both close to -1. Both an analytic approximation, based on expansions and asymptotics, and numerical results based on exact Fourier transform solutions are derived. Results of both approaches show good agreement in the appropriate parameter ranges.Chapter 6 documents an approach to calculating reflection and transmission from a periodic layer of cylinders. This approach was not found to be useful for the challenge of calculating the properties of a metamaterial, nor in fact for any 3-dimensional structure.