Random resonators and prelocalized modes in disordered dielectric films.

We calculate the areal density of disorder-induced resonators with a high quality factor, Q>>1, in a film with fluctuating refraction index. We demonstrate that, for a given kl>1, 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 kl are found.