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 ω = ck. This phenomenon is consid-ered to be due to the retardation of the electromagnetic forces among the ions. However, the problem is usually discussed at a phenomeno-logical level, through the introduction of a macroscopic polarization field, so that a microscopic treatment is apparently lacking. A micro-scopic 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 quali-tative 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

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