Proceedings PaperHomogenization giving rise to unusual metamaterials
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A defining characteristic of metamaterials is that they exhibit behaviour which is not exhibited--either to the same extent or not at all--by their component materials. Prime examples of such metamaterial behaviour may be conceptualized through the process of homogenization. A survey of five different types of metamaterial--each envisaged as a homogenized composite medium (HCM)--is presented. The unusual structures and properties of these HCM-metamaterials are discussed. The constitutive parameters of HCMs may be estimated through the implementation of well-established homogenization formalisms. In particular, those of Maxwell Garnett and Bruggeman, as well as the more comprehensive strong-property-fluctuation theory, are considered. Firstly, we explore bianisotropic HCMs as metamaterials. While bianisotropy is rarely observed in naturally-occurring materials, bianisotropic HCMs may be readily conceptualized, arising from component phases with comparatively simple constitutive properties and simple particulate geometries. Secondly, the issue of Voigt wave propagation is examined. It is demonstrated that this degenerate mode of plane wave propagation can develop in an HCM, even though its component phases do not support such propagation. Thirdly, the topic of plane wave propagation with negative phase velocity is discussed for HCMs. Strategies for achieving negative phase velocities are considered. Fourthly, we illustrate how homogenization can lead to the group velocity in certain HCM-metamaterials exceeding the group velocity in the component materials. Fifthly, the phenomenon of nonlinearity enhancement in weakly nonlinear HCMs is presented.