Résumé
In the present work, we present a metamaterial made of a periodic collection of dielectric resonators in which a quantum oscillator (denoted QO in the following) is inserted. The geometry at stake here is much more complicated than the textbook 1D cavity usually dealt with theoretically in quantum optics. We do provide a treatment essentially based on the scattering matrix non-perturbative approach, in order to investigate the various effects that could be expected to exist in such structures. The theoretical methods used are the Feshbach projection method associated with multiple scattering theory. First, the phenomenology for one scatterer with a QO inserted is presented, then the collective behavior of a finite periodic set of such scatterers is investigated and it is shown that it is possible to open and close a conduction band according to the state of the oscillators when the inserted quantum oscillators are put in the inversion regime by means of a pump field. They add gain to the system, allowing to reach the amplification regime in the vicinity of the Mie resonances of the dielectric resonators. When the transition frequency is situated at the photonic band gap edge, it creates switchable conducting modes within the bandgap.