Semianalytical modeling of arbitrarily distributed quantum emitters embedded in nanopatterned hyperbolic metamaterials

Abstract

Nanopatterned hyperbolic metamaterials (NPHMs) have proven to be efficient structures for enhancing the spontaneous emission rate (Γ) and quantum efficiency (η) of quantum emitters (QEs). However, many of the NPHM designs still rely on computationally costly 3D numerical simulations. In this context, we propose a fast, semianalytical method capable of calculating both Γ and η of QEs placed inside a medium bounded by nanopatterned structures. The low computational cost of our approach makes it attractive for optimizing the NPHMs’ geometrical parameters that maximize η for a desired Γ. Furthermore, we suggest a more realistic procedure to calculate the decay behavior of multiple QEs arbitrarily distributed in the NPHM. This calculation is only feasible with the knowledge of Γ and η mapped for all possible positions of the QEs, which is easily achieved with the proposed model. For the validation procedure, we compare the model results with those obtained by the FDTD method. We apply the proposed model to an NPHM composed of nine Ag/SiO2 layers, with the polymer host layer embedded with rhodamine 6G, to maximize η for a specified tenfold increase of Γ. This procedure allowed η to be increased by 69% and 170% for 1D and 2D nanopatterning, respectively. The time required to build the Γ and η maps (used in the calculation of the decay behavior) is reduced by approximately 96% when compared with those numerically calculated via FDTD.