Linear and Nonlinear Homogenized Composite Mediums as Metamaterials

Abstract

Metamaterials are artificial composites which are characterized by physical properties that are not possessed, either to the same extent or at all, by their component phases. Homogenization provides a means of conceptualizing such metamaterials. The constitutive parameters of homogenized composite mediums (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 discussed here in the context of HCM metamaterials. We present a survey of five generic examples of metamaterials; each example is envisaged as an HCM. The unusual structures and properties of these HCM metamaterials are emphasized. First, we examine bianisotropic HCMs as metamaterials. While bianisotropy is rarely observed in naturally occurring materials, bianisotropic HCMs may be readily conceptualized. Second, an anomalous form of plane wave propagation known as Voigt wave propagation is considered. Under certain conditions, this phenomenon can develop in HCMs, even though the component phases do not support such propagation. Third, the topical issue of plane wave propagation with negative phase velocity is explored for HCMs. Homogenization strategies for achieving negative phase velocities are considered. Fourth, it is shown that homogenization can result in the group velocity in certain HCM metamaterials exceeding the group velocity in the component phases. Fifth, we turn to the weakly nonlinear regime to investigate nonlinearity enhancement.

Keywords:

• bianisotropy
• Voigt waves
• group velocity
• cubic nonlinearity
• strong-property-fluctuation theory

Notes

¹The low volume fraction limitation of the Maxwell Garnett formalism generally emerges from experimental observations (Ward, 1995). Recently it has been suggested that the applicability of the Maxwell Garnett formalism may extend to higher volume fractions if the composite is self-assembled in such a manner that randomness is maintained as the volume fraction increases (Schelm et al., 2004; Smith, 2003). We note that the Maxwell Garnett formalism (as well as the Bruggeman formalism and the SPFT) is based upon the assumption that the component phases are randomly distributed. However, as the volume fraction increases, so the distribution of the component phase particles gradually becomes less random (Lakhtakia & Shanker, 1993).

²When applied in the context of dielectric mediums, the SPFT is known as the strong-permittivity-fluctuation theory