Anisotropy, birefringence, and dispersion in artificial dielectrics

Thin obstacle artificial dielectrics are investigated using a full wave analysis. The artificial dielectrics consist of a number of uniformly or nonuniformly spaced, parallel layers, each layer consisting of periodically arranged thin metallic obstacles. The fields scattered by one layer are expanded in a complete set of space harmonics. The propagating and least attenuating of these space harmonics are then considered as the fields interacting on neighboring layers. The interaction of this finite set of space harmonics is modeled by a set of transmission lines and the mode conversion of these harmonics by the obstacles in each layer is modeled by interconnecting the transmission lines to multiport lumped linear networks. The refractive index is defined in terms of the eigenvalues of the infinite three dimensional periodic structure. An efficient wide-band approximation is formulated for computing refractive index for a dielectric with disk obstacles.