Random Resonators and Prelocalized Modes in Disordered Dielectric Films

Areal density of disorder-induced resonators with a high quality factor, $Q\gg 1$, in a film with fluctuating refraction index is calculated theoretically. We demonstrate that for a given $kl>1$, where $k$ is the light wave vector, and $l$ is the transport mean free path, when {\em 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 {\em most probable} resonators as functions of $Q$ and $kl$ are found.