Crossover between polariton and phonon local states. Anisotropy-induced localization threshold

We consider the impurity-induced polariton local states in a dipole-active medium. These states present the local optical vibrations which are coherently coupled with the induced electromagnetic field. We show that the crossover between the polariton and phonon local states takes place within the relativistically narrow interval near the bottom of the polariton gap. However, the resonant phonon-photon interaction leads to the absence of the lower threshold of the impurity strength. These results are due to the singularity of the density of the polariton states, which is generic for any isotropic dipole-active phonon mode with the negative dispersion. We show that a weak anisotropy removes this singularity and sets a finite threshold for the local polariton states.