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 parallel to) and magnetic field parallel to the fibres (H parallel to). Assuming a low density of fibres, we obtain, in the E parallel to case, an effective medium with a possibly negative permittivity, whereas in the H parallel to case the fibres disappear completely. On the other hand, for a high density of fibres, the E parallel to case leads to a perfectly conducting medium and the H parallel to case to a dielectric medium with a surface current on its boundary.