Homogenization of a set of parallel fibres

Rigorous results concerning the possibility of homogenizing a set of parallel fibres are given from the viewpoint of electromagnetic scattering. We deal with the classical time-harmonic Maxwell problem and distinguish the two cases of polarization, i.e. electric field parallel to the fibres (E∥) and magnetic field parallel to the fibres (H∥). Assuming a low density of fibres, we obtain, in the E∥ case, an effective medium with a possibly negative permittivity, whereas in the H∥ case the fibres disappear completely. On the other hand, for a high density of fibres, the E∥ case leads to a perfectly conducting medium and the H∥ case to a dielectric medium with a surface current on its boundary.