Case of Strongly Polar Species LO-TO Splitting

A material exhibiting vibrational IR absorption at frequency coojln can be described by a dielectric function of the type [24] 

Eor weakly polar (e small) or dilute (N small) IR-active species, the vibrational contribution to g is much smaller than 1 for every co, so that g +g  

The two functions Im(l/g) and -Im(g) are then proportional to each other, and the absorption shapes associated with the three components of the interface electric field are similar. 

In the case of strongly polar or concentrated species (which is typically the case for an oxide), the vibrational contribution to e(co) may become larger than Boo in the region of the resonance. The shapes of the functions -lm[g( )] and lm[l/g( )] then become different, the former exhibiting its maximum for (o=(Oo, whereas for the latter the maximum turns out to be shifted to a o=(coo+Ne lBoBcoR). If one considers the phonon modes in the infinite 3D material, the two modes o coq appear as the zero-wavevector limit of the transverse-optical (TO) and longitudinal-optical (LO) phonon branches, and for that reason are generally termed TO mode and LO mode [94]. 

It is noteworthy that these two modes actually correspond to the same molecular vibration. This occurs, though the material is isotropic, just because it has been put in the form of a thin layer. The origin of the effect can be intuitively explained as follows (Eig. 6.13a) in a homogeneous isotropic material, the synchronous vibration of the polar species produces a dielectric polarization P= Ne Sz in the medium (where Sz represents the instantaneous value of the normal coordinate associated with the vibration mode under consideration). If the sample is shaped in the form of a thin layer and the direction of the vibration is perpendicular to the layer, a depolarizing field -PIb Bq will appear, acting as a restoring force -e PlBa ,Bo on the vibrators (Eig. 6.13a). This amounts to increasing the usual 

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