LAUSR

Nanostructures with sizes smaller than or comparable to visible light strongly modify the decay rate of dipole emitters placed in their vicinity. Such modification is usually characterized using the local density of photonic states (LDOS), which quantifies the availability of photonic states at a certain position and frequency in the presence of a nanostructure. Here, we present a detailed analysis of the limits of this quantity through the study of a sum rule that bounds its spectral integral, taking into account both its radiative and nonradiative components. The sum rule studied here relates the integral over the spectrum of the LDOS at a certain point to the field induced by a static dipole placed at that same location. We confirm the validity of this sum rule and investigate its implications for the response of nanostructures by performing rigorous numerical calculations for a variety of systems, including nanospheres, nanodisks, and films, made of different metallic and dielectric materials, as well...