Dielectric Properties of a Lattice of Anisotropic Particles

The dielectric properties of lattices composed of identical metallic or dielectric elements of various geometries, such as spheres, discs and strips have been investigated from a molecular point of view by Kock, Corkura and others. These investigations have treated two cases, in both of which, the element size and spacings are small compared to the wave length. The first applies to the case where the spacings are large compared to element size and which therefore neglects interaction effects. The second treats interaction for the special case in which the lattice has the structural isotropy of a cubical array and for which the application of the Clausius-Mosotti relation is valid, when the elements are not too closely packed. The main objective of this note will be to extend the treatment to general uniform lattice structures made of identically shaped and oriented particles of general constitutive characteristics. Thus, it will include the most general case of a uniform lattice with structural anisotropy and both element isotropy and anisotropy at the lattice points.