Engineering optical emission in sub-diffraction hyperbolic metamaterial resonators

Sub-diffraction hyperbolic metamaterial resonators are promising structures for engineering light-matter interactions in semiconductor-based emitters and materials. The optical properties of these resonators are determined by a number of device characteristics including the metamaterial permittivity and resonator geometry. In this letter, we develop an optical model based on the modified long wavelength approximation to calculate the radiative and non-radiative photon loss of the resonators. We fabricate and characterize 11 different resonator arrays to demonstrate the effectiveness of model. Using the model, we demonstrate how the radiative properties of the resonators can be engineered via the design of the semiconductor metamaterial and the aspect ratio of the resonator. Over the explored design space, we demonstrate an eightfold increase in the radiative rate compared to the non-radiative rate. Our work reduces the complexity of designing sub-diffraction hyperbolic metamaterial resonators, allowing broader incorporation of these optical structures into novel devices and materials.