An efficient zero-order description of the fine structure in the infrared reflection band of cubic ionic crystals and the phonon-polariton dispersion using Lorentz gauge.

The reflection of infrared light by ionic crystals with cubic symmetry such as lithium fluoride, LiF, is analyzed in terms of phonon-polaritons. In contrast to the conventional view on phonon-polaritons that uses the Coulomb gauge and assumes a purely local dielectric response of the material, we here develop an alternative description making use of the Lorentz gauge. This involves retarded interactions between charges, implying a non-local response of the material to electromagnetic radiation. The resulting new phonon-polariton dispersion relation features polaritons with negative group velocity in the frequency range in between the transverse (ωT ) and longitudinal frequency (ωL ). By contrast, the conventional description predicts, in zero order, the absence of any propagating polaritons in the frequency interval between ωT and ωL . The new dispersion relation provides an efficient, zero-order description of the fine structure within the reststrahlen band of LiF. The local minimum near the middle of the reflectance band is due to excitation of a phonon-polariton whose energy and momentum matches that of the incoming photon. The Lorentz gauge description can also describe off-normal reflection and accounts for the experimentally observed widening of the reflection band with increasing angle of incidence.