Eur. Phys. J. D (2014) 68: 35
https://doi.org/10.1140/epjd/e2013-40331-y

Regular Article

Classical microscopic theory of polaritons in ionic crystals

¹ School of Physics, Università degli Studi di Milano, 20133 Milano, Italy
² Department of Physics, Università degli Studi di Milano, 20133 Milano, Italy
³ Department of Mathematics, Università degli Studi di Milano, 20133 Milano, Italy

^a e-mail: andrea.carati@unimi.it

Received: 30 May 2013
Received in final form: 29 November 2013
Published online: 27 February 2014

Abstract

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 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.