The long-wavelength optical vibration in a trilayer system of polar cr
ystals is studied by using a continuum model. The optical polarization
modes of the lattice vibration and the Hamiltonian of the interaction
between an electron and the optical phonons are derived. It is found
that there are six branches of interface optical modes in a trilayer s
ystem. The numerical results for several practical systems are given.
The dispersion relations, eigenvectors of the polarization modes and t
he electron-phonon coupling functions are discussed. The results indic
ate that some surprising experimental phenomena are expected.