Rayleigh and Raman Scattering by Surface Modes in Ionic Crystals

Abstract

In finite size diatomic cubic crystals there exist three types of long wave optical phonons: (a) Longitudinal bulk modes, (b) Transverse bulk modes, and (c) Surface modes. The features characterizing the surface modes in crystals of arbitrary shape are[1]: Their frequencies form a series lying in the range between ω T and ω T (the transverse and longitudinal frequencies) and converging to an intermediate frequency ω S which satisfies the relation e(ω S) = — 1, where e is the frequency dependent dielectric constant $$\varepsilon \left( \omega \right) = {\varepsilon _\infty } + \frac{{{\varepsilon _O} - {\varepsilon _\infty }}}{{1 - {\omega ^2}/\omega _T^2}}$$ (1) The vibration amplitudes corresponding to the surface modes decay with increasing distance from the surface of the sample. Due to the existence of the long range Coulomb interaction, this decay is rather slow, so that the vibration usually penetrates to the center of the crystal. The number of surface modes is proportional to the number of surface unit cells. These properties of the surface modes still hold when retardation effects are ineluded[2] (in which case the normal modes will be polaritons rather than phonons). The transverse bulk modes, which without retardation are all degenerate with the frequency ω T, form a bulk polariton band lying below ω T. The longitudinal modes are not affected by the inclusion of retardation and remain degenerate with the frequency ω L.