  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.
