Optical vibrations in alkali halide crystals

We consider long-wave phonon-polaritons and longitudinal optical phonons in alkali-halide ionic crystals. The model of point charges that are polarized in the self-consistent electromagnetic field in a dielectric environment is used. The standard dispersion laws for both branches of phonon-polaritons and longitudinal optical phonons are obtained. The transversal optical phonon frequency is found from the electrostatic equilibrium condition. It is proved by comparison with tabular data that the found frequency coincides with the ion plasma frequency multiplied on the relation $\sqrt{(\varepsilon_{\infty}+2)/(3(\varepsilon_0-\varepsilon_\infty))},$ where $\varepsilon_{\infty}$ and $\varepsilon_0$ are the high-frequency dielectric constant and the static one respectively.