Modelling of the Fluctuation and Coherent Dynamics in Active Metamaterial Devices

Active metamaterials, i.e., coupled systems consist of metamaterials and active or gain media. Modelling the interaction between unconventional electromagnetic response in metamolecules and quantum dynamics of active media in active metamaterials requires the development of a unified and efficient semiclassical model. Here, we propose a semiclassical model based on Langevin Maxwell-Bloch equations and simplified rate equations for a multi-level quantum system. Using the semiclassical model and the finite-difference time-domain (FDTD) algorithm, a methodology for the self-consistent descriptions of both the coherent lasing process and the spatio-temporal spontaneous noise dynamics in active metamaterials is developed. To validate the proposed method, we numerically study the luminescence of QDs hybridized with plasmonic and all-dielectric metasurfaces and compare with the experimental results. The proposed semiclassical method reveals a new approach for developing new types of nanodevices based on active metasurfaces.