2D semi-analytical model for optimizing the radiation emission of quantum emitters embedded in a bounded nano-patterned hyperbolic metamaterial

We propose a two dimensional (2D) semi-analytical method to calculate the radiated power and Purcell factor of a quantum emitter (QE) embedded in a medium bounded between a nano-patterned structure and a homogeneous dielectric. We apply our 2D model to optimize a nano-patterned hyperbolic metamaterial (HMM) to increase the QE's quantum efficiency while preserving a high Purcell factor. The low computational cost of this method makes it quite attractive for quantum efficiency optimization, providing initial physical and/or geometrical parameters to be fine-tuned with three-dimension (3D) full-wave techniques such as FDTD.