Using full wave simulations the behavior of two structures composed of split ring resonators (SRRs) and strip wires (SWs) is examined. In the region where the real parts of the permittivity and permeability are both expected to be negative both structures exhibit a transmission peak, a property which is generally assumed to imply a negative index of refraction. However, through an analysis of the dispersion characteristics and insertion phase of the two structures it is shown that only the index in the first structure, in which the SRRs and SWs are printed on opposite sides of a dielectric substrate, is negative in the passband. In the second structure, in which SRRs and SWs are printed on the same side of the substrate, the index in the passband is positive. Therefore the emergence of transmission peaks does not provide sufficient evidence of the existence of a negative index of refraction. To determine the correct sign of the index two methods are investigated. The first uses the transmission phase for propagation through various lengths of the structure and the second utilizes its dispersion diagrams. The dependence of the sign of the index on the dimensions of the unit cell size is also examined.
In this paper we consider the effective electric and magnetic properties of a three-dimensional collection of non-magnetic spheres. Polaritonic materials are used, so that the Mie resonances of the spheres are excited in the long-wavelength regime of the surrounding medium. We consider a simple cubic lattice based on LiTaO<sub>3</sub> and find that it is possible to engineer a fundamental resonant magnetic response. The effective media parameters derived by this approach are isotropic, and closely match those obtained by band structure calculations. Frequency ranges with either negative permittivity or negative permeability are found. Within these ranges a negative group velocity is observed. Coated spheres with a negative index of refraction are also presented.