Metals support surface plasmons at optical wavelengths and have the ability to localize light to sub-wavelength regions. The field enhancements that occur in these regions set the ultimate limitations on a wide range of nonlinear and quantum optical phenomena. Here we show that the dominant limiting factor is not the resistive loss of the metal, but the intrinsic nonlocality of its dielectric response. A semi-classical model of the electronic response of a metal places strict bounds on the ultimate field enhancement. We demonstrate the accuracy of this model by studying the optical scattering from gold nanoparticles spaced a few angstroms from a gold film. The bounds derived from the models and experiments impose limitations on all nanophotonic systems.

To move nanophotonic devices such as lasers and single-photon sources into the practical realm, a challenging list of requirements must be met, including directional emission 1-5 , room-temperature and broadband operation 6-9 , high radiative quantum efficiency 1,4 and a large spontaneous emission rate 7 . To achieve these features simultaneously, a platform is needed for which the various decay channels of embedded emitters can be fully understood and controlled. Here, we show that all these device requirements can be satisfied by a film-coupled metal nanocube system with emitters embedded in the dielectric gap region. Fluorescence lifetime measurements on ensembles of emitters reveal spontaneous emission rate enhancements exceeding 1,000 while maintaining high quantum efficiency (>0.5) and directional emission (84% collection efficiency). Using angle-resolved fluorescence measurements, we independently determine the orientations of emission dipoles in the nanoscale gap. Incorporating this information with the threedimensional spatial distribution of dipoles into full-wave simulations predicts time-resolved emission in excellent agreement with experiments.Typical luminescent emitters have relatively long emission lifetimes (∼10 ns) and non-directional emission. Unfortunately, these intrinsic optical properties are poorly matched to the requirements of nanophotonic devices. For example, in single-photon sources, fast radiative rates are required for operation at high frequencies, and directionality is needed to achieve a high collection efficiency 10 . In addition, with plasmonic lasers, enhanced spontaneous emission into the cavity mode can reduce the lasing threshold 9 . As a result, much work has focused on modifying the photonic environment of emitters to enhance 11 the spontaneous emission rate, known as the Purcell effect 12 . Early approaches concentrated on integrating emitters into dielectric optical microcavities and showed modest emission rate enhancements [13][14][15] . However, dielectric cavities require high quality factors for large rate enhancements, which makes these cavities mismatched with the spectrally wide emission from inhomogeneously broadened or room-temperature emitters. Plasmonic nanostructures are a natural solution to the spectral mismatch problem because of their relatively broad optical resonances and high field enhancements [16][17][18] . Despite these advantages and the capability for emission rate enhancement 19 , many plasmonic structures suffer from unacceptably high non-radiative decay due to intrinsic losses in the metal, or have low directionality of emission 7 . In plasmonic structures, the Purcell factor (defined as the fractional increase in total emission rate) has contributions from an increased radiative rate and from an increased non-radiative rate due to metal losses. It is therefore critical to specify the fraction of energy emitted as radiation, known as the radiative quantum efficiency (QE). From knowledge of the Purcell factor and the QE, the enhancement in the ...