Effective medium theory of negative index composite metamaterials

In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present a general argument which shows that the homogenization of such metamaterials can be seen as the homogenization of 1D single negative stacks. The sensitivity to the geometrical parameters is due to the fact that light sees the harmonic mean of the dielectric constant when propagating parallel to the layers. Since the dielectric constant is not positive definite the harmonic mean is not bounded and presents abrupt variations. We discuss applications of this remarkable phenomenon.