Dispersion in media containing resonant inclusions: Where does it come from?

Propagation media containing resonant inclusions have been studied for over a century in acoustics, electromagnetism or solid state physics. There exist some in nature, such as dielectrics, which contain enormous amounts of atoms. To calculate those materials permittivities one considers that each atom “sees” the same electromagnetic field and calculates the average field that takes into account an incoming wave as well as the overall response of the ensemble of atoms [1]. This macroscopic view assumes that there is no variations of the electromagnetic field at the scale of the inter-atomic distance.