Electromagnetic eigenstates applied to the theoretical discussion of meta-materials with negative refraction

The electromagnetic (EM) eigenstates of a thin, long circular cylinder, for which a very good approximate closed form expression wasderived earlier, are used to set up a numerical computation of the EM eigenstates of a cluster of parallel cylinders. Detailed results are presented for a pair of identical cylinders, as well as for a cluster of three identical cylinders, where the cylinder axes are situated at the vertices of an equilateral triangle. The aim is to find an eigenstate that has an electric dipole moment and a magnetic dipole moment of comparable magnitudes. By operating the system near such an isolated resonance, it should be possible to tweak the macroscopic response so as to have both the macroscopic electric permittivity ε_e and the macroscopic magnetic permeability μ_e attain desirable values, e.g., values that are almost real and negative. It is argued that a three-cylinder cluster is a good configuration for achieving this goal, but a two-cylinder cluster is not.