Toward a constructive homogenization theory of 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 an effective medium approach which can systematically account for these effects. It involves independently homogenizing rows of wires and planes of resonators as slabs with negative permittivity and permeability respectively. The metamaterial is then treated as a 1D single negative anisotropic stack. Using this approach we show that it is in principle possible to satisfy the requirements of Pendry's superlens, [mu]=[epsilon]=-1 , up to losses. We propose a class of structure geometries which seems promising for achieving this holy grail of metamaterial science.