Purcell effect in Hyperbolic Metamaterial Resonators

TL;DR

This paper investigates how hyperbolic metamaterial resonators can significantly enhance the spontaneous emission rate of optical emitters, revealing the underlying cavity modes and their dependence on structural parameters.

Contribution

It provides a microscopic understanding of the Purcell effect in finite-size hyperbolic nanorod cavities, highlighting the role of Fabry-Perot modes and geometric influences.

Findings

Purcell factors reach several hundred, 4-5 times larger than epsilon near zero frequencies.

Decay rate enhancement depends on emitter polarization and nanorod length.

Purcell enhancement is mainly due to cavity hyperbolic modes and Fabry-Perot resonances.

Abstract

The radiation dynamics of optical emitters can be manipulated by properly designed material structures providing high 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 non-resonant nature. Here, we have investigated finite-size cavities formed by nanorod metamaterials and shown that the main mechanism of the Purcell effect in these hyperbolic resonators originates from the cavity hyperbolic modes, which in a microscopic description stem from the interacting cylindrical surface plasmon modes of the finite number of nanorods forming the cavity. It is found that emitters polarized perpendicular to the nanorods exhibit strong decay rate enhancement, which is predominantly influenced by the rod length. We demonstrate that this enhancement originates from Fabry-Perot modes of the metamaterial cavity. The Purcell factors, delivered by those cavity modes, reach several hundred, which is 4-5 times larger than those emerging at the epsilon near zero transition frequencies. The effect of enhancement is less pronounced for dipoles, polarized along the rods. Furthermore, it was shown that the Purcell factor delivered by Fabry-Perot modes follows the dimension parameters of the array, while the decay rate in the epsilon near-zero regime is almost insensitive to geometry. The presented analysis shows a possibility to engineer emitter properties in the structured metamaterials, addressing their microscopic structure.