Classical microscopic theory of polaritons in ionic crystals

It is well known that the optical branches of the dispersion curves of ionic crystals exhibit a polaritonic feature, i.e., a splitting about the electromagnetic dispersion line $\omega=ck$. This phenomenon is considered to be due to the retardation of the electromagnetic forces among the ions. However, the problem is usually discussed at a phenomenological level, through the introduction of a macroscopic polarization field, so that a microscopic treatment is apparently lacking. A microscopic first principles deduction is given here, in a classical frame, for a model in which the ions are dealt with as point charges. At a qualitative level it is made apparent that retardation is indeed responsible for the splitting. A quantitative comparison with the empirical data for LiF is also given, showing a fairly good agreement over the whole Brillouin zone.