Optical vibrations in alkali halide crystals

TL;DR

This paper models optical vibrations in alkali halide crystals, deriving dispersion laws for phonon-polaritons and optical phonons using a point charge model within a dielectric environment.

Contribution

It provides a theoretical derivation of dispersion laws and confirms the transverse optical phonon frequency matches the ion plasma frequency scaled by a specific dielectric relation.

Findings

Derived standard dispersion laws for phonon-polaritons and optical phonons.

Confirmed the transverse optical phonon frequency matches the ion plasma frequency scaled by dielectric constants.

Validated the model against tabular data.

Abstract

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.