The integral and differential equations of the polarization eigenmodes in dielectric bilayer systems were straightforwardly deduced by means of macroscopic electric potential caused by the surface and bulk polarization charges. It is shown that the polarization eigenmodes should be normalized according to (18) described in the text. The operator representations for the Hamiltonian of the polarization eigenmodes and the interaction between the charged particles and the polarizable media were also deduced which are

respectively

given in (24) and (28).In the section IV

we assume that the dielectric media are filled in the half-space of x

3

>

0 and x

3

<

0

respectively

and are in contact at x

3

=0. It is shown that there are three kinds of phonons coiresponding to the p-polarized wave. They are surface longitudinal optical (SO)

surfacen transverse optical (TO) and longitudinal optical (LO) phonons. The interaction of the charged particles with p-polarized SO phonons is equivalent to SO phonons with an effective frequency of ω

eff

±

SO

and can be described by introducing a Frölich-like coupling constant α

±

SO

The interaction of the charged particles with LO phonons is

in essence

that with the bulk LO phonons

but is weakened by the surface effects.