Spontaneous emission dynamics of $Eu^{ 3+}$ ions coupled to hyperbolic metamaterials

Sub-wavelength nanostructured systems with tunable electromagnetic properties, such as hyperbolic metamaterials (HMMs), provide a useful platform to tailor spontaneous emission processes. Here, we investigate a system comprising $Eu^{ 3+}(NO_{3})_{3}6H_{2}O$ nanocrystals on an HMM structure featuring a hexagonal array of Ag-nanowires in a porous $Al_{2}O_{3}$ matrix. The HMM-coupled $Eu^{ 3+}$ ions exhibit up to a 2.4-fold increase of their decay rate, accompanied by an enhancement of the emission rate of the $^{ 5}D_{0}\rightarrow$ $^{ 7}F_{2}$ transition. Using finite-difference time-domain modeling, we corroborate these observations with the increase in the photonic density of states seen by the $Eu^{ 3+}$ ions in the proximity of the HMM. Our results indicate HMMs can serve as a valuable tool to control the emission from weak transitions, and hence hint at a route towards more practical applications of rare-earth ions in nanoscale optoelectronics and quantum devices.