Date of Award

December 2014

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

George W. Hanson

Committee Members

Chiu-Tai Law, Michael Weinert, Arash Mafi, Tzu-Chu Lin


Antenna, Enz, Graphene, Homogenization, Metamaterial, Wire Medium


Artificially engineered materials, known as metamaterials, have attracted the interest of researchers because of the potential for novel applications. Effective modeling of metamaterials is a crucial step for analyzing and synthesizing devices. In this thesis, we focus on wire medium (both isotropic and uniaxial) and validate a novel transport based model for them.

Scattering problems involving wire media are computationally intensive due to the spatially dispersive nature of homogenized wire media. However, it will be shown that using the new model to solve scattering problems can simplify the calculations a great deal.

For scattering problems, an integro-differential equation based on a transport formulation is proposed instead of the convolution-form integral equation that directly comes from spatial dispersion. The integro-differential equation is much faster to solve than the convolution equation form, and its effectiveness is confirmed by solving several examples in one-, two-, and three-dimensions. Both the integro-differential equation formulation and the homogenized wire medium parameters are experimentaly confirmed. To do so, several isotropic connected wire medium spheres have been fabricated using a rapid-prototyping machine, and their measured extinction cross sections are compared with simulation results. Wire parameters (period and diameter) are varied to the point where homogenization theory breaks down, which is observed in the measurements. The same process is done for three-dimensional cubical objects made of a uniaxail wire medium, and their measured results are compared with the numerical results based on the new model. The new method is extremely fast compared to brute-force numerical methods such as FDTD, and provides more physical insight (within the limits of homogenization), including the idea of a Debye length for wire media. The limits of homogenization are examined by comparing homogenization results and measurement.

Then, a novel antenna structure is proposed utilizing an Epsilon Near Zero (ENZ) material and the total internal reflection principle. The epsilon near zero material of the antenna is realized by use of a wire medium which acts as an artificial plasma and exhibits

ENZ condition at a frequency called the plasma frequency. This will lead us the question of whether or not the ENZ condition is realizable using spatially dispersive materials (e.g. wire medium). To answer this question, the momentum-dependent permittivity for a broad class of natural materials and wire-mesh metamaterials with spatial dispersion is determined in real-space, and a new characteristic length parameter is defined, in addition to the Debye length, which governs polarization screening. It is found that in the presence

of spatial dispersion the electric displacement does not vanish at the plasma frequency, in general. However, conditions are investigated under which the permittivity can vanish or be strongly diminished, even in the presence of spatial dispersion, implementing an

epsilon-near-zero material. The thesis will end with a chapter about homogenization of graphene. Although it does not completely follow the subject of the thesis, the last chapter shows another example of homogenization applications. In this last chapter, using periodicity and homogenization, a hyperlens is realized for surface plasmons on graphene. In general, such hyperlens cannot be realized without using periodic structures (metamaterials).