Large Purcell enhancement without strong field localization

The Purcell effect is defined as the modification of spontaneous decay in the presence of a resonator, and in plasmonics it is usually associated with the large local-field enhancement in "hot spots" due to surface plasmon polaritons. Here we propose a novel strategy for enhancing the Purcell effect through engineering the radiation directivity without a strict requirement of the local field enhancement. Employing this approach, we demonstrate how to enhance the Purcell effect by two orders of magnitude in all-dielectric nanostructures recently suggested as building blocks of low-loss nanophotonics and metamaterials. We support our concept by proof-of-principle microwave experiments with arrays of high-index dielectric resonators.