Transverse and Longitudinal Optic Mode Study in MgF2and ZnF2

Infrared reflectivity measurements have been made on single-crystal Mg${\mathrm{F}}_2$ and Zn${\mathrm{F}}_2$ in the wavelength range 1 to 140 μ. An analysis of the data using Kramers-Kronig analysis and classical dispersion theory gives the transverse optic mode frequencies, strengths, and linewidths. Huang's macroscopic dielectric theory is extended to the case of several modes to study the behavior of the longitudinal optic modes in these fluorides. A generalized Lyddane-Sachs-Teller relation and some additional sum rules are derived for the case of many modes when damping is present. It is shown that the longitudinal mode frequencies are easily obtainable from the reflectivity data analysis. The four longitudinal optic mode frequencies for Mg${\mathrm{F}}_2$ and Zn${\mathrm{F}}_2$ are presented.