Local polariton states in impure ionic crystals

We consider the dynamics of an ionic crystal with a single impurity in the vicinity of the polariton resonance. We show that if the polariton spectrum of the host crystal allows for a gap between polariton branches, the defect gives rise to local states with frequencies within the gap. Despite the atomic size of the impurity we find that the in-gap local states are predominated by long-wavelength polaritons. The properties of these states are shown to be different from the properties of the well-known vibrational local states. The difference is due to the singular behavior of the density of states of polaritons near the low-frequency boundary of the polariton gap. Assuming cubic symmetry of the defect site we consider a complete set of the local states arising near the bottom of the polariton gap.