Cooperative electromagnetic interactions and linwidth narrowing in discrete metamaterial systems

Summary form only given. Multiple scattering of the electromagnetic (EM) field from an ensemble of resonators generates interactions which can lead to a cooperative response. In atomic gases, the cooperative response is often washed out due to fluctuations in atomic positions. When these fluctuations are restricted, as in an optical lattice in a Mott-insulator state with precisely one atom per lattice site, a cooperative response can be observed. The ability to fabricate metamaterials whose constituent circuit elements, meta-atoms at fixed positions, interact in prescribed ways with EM fields also permits the construction of systems in which cooperative phenomena emerge. In this work, we show that the cooperative response of an ensemble of discrete resonators can result in a transmission resonance whose quality factor increases with the size of the system. This behaviour arises from the formation of a collective eigenmode of excitation that possesses a suppressed, or subradiant, emission rate. To describe the metamaterial, we developed a model in which one dynamic variable represents a meta-atom interacting with the EM fields. Collective modes emerge from interactions between meta-atoms mediated by the EM field, each mode with its own resonance frequency and decay rate.