Problem: Polaritons

           

Determine the frequencies of the longitudinal and the transverse waves in a polar insulator or semiconductor, where the limit of the oscillator model, Eq. , describes the dielectric function. Discuss the wavenumber (k) dependence of the transverse waves. Show that the Lyddane-Sachs-Teller relation,

 

holds, where is the real part of the dielectric function, is the longitudinal wave frequency, and is the transverse wave frequency at .