The effect of spatial correlations on the Purcell effect in a bidimensional dispersion of resonant nanoparticles is analyzed. We perform extensive calculations on the fluorescence decay rate of a point emitter embedded in a system of nanoparticles st
atistically distributed according to a simple 2D lattice-gas model near the critical point. For short-range correlations (high temperature thermalization) the Purcell factors present a long-tailed statistic which evolves towards a bimodal distribution when approaching the critical point where the spatial correlation length diverges. Our results suggest long-range correlations as a possible origin of the large fluctuations of experimental decay rates in disordered metal films.
We establish a fundamental relationship between the averaged density of states and the extinction mean free path of wave propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both quantities are
connected by dispersion relations and are constrained by a frequency sum rule. The results are valid under very general conditions and should be helpful in the analysis of measurements of wave transport through complex systems and in the design of randomly or periodically structured materials with specific transport properties.
