Random Resonators and Prelocalized Modes in Disordered Dielectric Films

We calculate the areal density of disorder-induced resonators with a high quality factor, $Q\gg 1$, in a film with fluctuating refraction index. We demonstrate that, for a given $\mathrm{kl}>\mathrm{}1\mathrm{}$, where $k$ is the light wave vector and $l$ is the transport mean-free path, when on average the light propagation is diffusive, the likelihood for finding a random resonator increases dramatically with increasing the correlation radius of the disorder. Parameters of most probable resonators as functions of $Q$ and $\mathrm{kl}$ are found.