Three-dimensional isotropic meta-materials

This paper addresses the design and construction of metallic structures, whose induced electric and/or magnetic dipole moments are equal in all three principle directions. These materials can be used to make a 3-dimensional, negative-refractive index metamaterial. Meta-materials are constructed of three-dimensional materials, but the electromagnetic response has only been realized in one or two dimensions. In this paper, when we refer to the dimensionality of a material, we mean the number of directions that have equal and non-trivial response to incident fields. We also consider whether a structure has a polarization dependent response. Although Silveririnha (2004) has shown that the periodic square or cubic grids that are used are not truly isotropic in that the response is angle dependant, the same response in all coordinate directions is a good start