  We study the propagation of waves in a quasi 1D homogeneous host medium
filled with various resonators. We first prove that a far field coupling
between the elements explains its dispersive nature. This coupling is
interpreted as a Fano interference between the incoming wave and the waves
re-radiated by each resonator, which experience a phase shift at resonance. We
propose a simple formalism that gives the complete dispersion relation of the
medium in terms of the far field response of a single resonator. We prove that
our approach applies to and unifies various domains such as metamaterials,
hybridization band gap materials and designer's plasmons. Finally we show that
those media, spatially random or organized on a scale larger than the
wavelength, also present very interesting properties, which broadens the range
of man made exotic materials.
