Crossover between polariton and phonon local states and effects of anisotropy on the polariton states

We consider local polariton states that are composed from optical phonons and photons localized around atomic impurities. We evaluate a photon contribution into polariton states and investigate the impurity-strength-driven crossover between polariton and phonon local states. The polariton states exhibit a macroscopic spatial size and the absence of the localization threshold. These features are attributed to a negative phonon dispersion, which leads to a nonstandard polariton density of states (DOS). We show that the DOS diverges at the bottom of the polariton gap in an isotropic medium, and it tends to a finite limit in anisotropic polar crystals. This leads to a thresholdless dependence of the frequency of the local state on the impurity strength in both cases.