| Summary: | In this dissertation the proper determination and allowable signs of the effective parameters of metamaterial structures will be examined. First, a method that was commonly used to determine the presence of a negative index of refraction will be discussed. It will be shown that this method, which relies on the appearance of transmission peaks in the region where the real parts of the effective permittivity and permeability are expected to be negative, does not provide sufficient evidence that a negative index exists. Two alternate methods will then be presented that can be used to properly determine the sign of the index. Then, the form of the index in media that exhibit backward wave propagation will be examined from a purely three dimensional wave propagation point of view. It will be shown that in an isotropic medium backward wave propagation requires that the index be negative and in an anisotropic medium it requires that the index be negative along at least one of the three principal axes. In short, the necessary and sufficient condition for the negative index of refraction is the existence of the backward wave. Next, a technique commonly used to retrieve the effective parameters in metamaterials from transmission and reflection data will be considered. It will be shown that this retrieval technique can lead to unphysical claims that the imaginary parts of the effective permittivity or permeability can be negative even though the medium remains passive. By comparing the effective parameters obtained analytically and from the retrieval technique it will be shown that these unphysical claims are the result of error in the numerical simulations. The concepts of causality and analyticity will also be discussed by considering the Lorentzian model and it will be shown that this model does not allow the imaginary parts of the permittivity or permeability to be negative in the metamaterials consisting of split ring resonators and split wires.
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