Purcell effect in hyperbolic metamaterial resonators

The radiation dynamics of optical emitters can be manipulated by properly designed material structures modifying local density of photonic states, a phenomenon often referred to as the Purcell effect. Plasmonic nanorod metamaterials with hyperbolic dispersion of electromagnetic modes are believed to deliver a significant Purcell enhancement with both broadband and nonresonant nature. Here, we have investigated finite-size resonators formed by nanorod metamaterials and shown that the main mechanism of the Purcell effect in such resonators originates from the supported hyperbolic modes, which stem from the interacting cylindrical surface plasmon modes of the finite number of nanorods forming the resonator. The Purcell factors delivered by these resonator modes reach several hundreds, which is up to 5 times larger than those in the \ensuremath{\epsilon}-near-zero regime. It is shown that while the Purcell factor delivered by the Fabry-P\'erot modes depends on the resonator size, the decay rate in the \ensuremath{\epsilon}-near-zero regime is almost insensitive to geometry. The presented analysis shows a possibility to engineer emission properties in structured metamaterials, taking into account their internal composition.