In this paper

we extend the theoretic consideration of the electron-phonon inteiaction for a dielectric bilayer system to polar superlattice consisting of two alternately arranged different dielectric layers

assuming that the long wave approximation of the lattice vibration is still suitable for the superlattice.The integral equation characterizing the polarization eigenmodes of the superlattice is derived

as given by(2-3)-(2-5)in the text.One can see from this result that the superlattice can be regarded as an equivelent bilayer system with different boundary condition from simple bilayer.It is also verified that the differential equation satisfied by the polatization vector for the supsrlattice is as the same as for the real bilayer.The dispersion relation is derived from the boundary conditions suited for superlattice

which is given by(4-8).In this expression

a and b are the thickness of each layer

d=a+b

is the periodic length of the superlattice.When N

the number of periodic layers of superlattice

approaches infinity

i.e.N→∞

the dispersion relation is reduced to(4-9).It is droved from calculation that as long as N is larger than 20

such a supeilat-tice can be regarded as one with infinite layer number.If N=0

a→∞ and b→∞

the dispersion relation(4-8)is reduced to(4-11).When a→∞

the dispersion relation(4-8)is reduced to(4-12)

and this is just the case of single qauntum well.The interaction Hamiltonian of the charged particle with SO phonon is obtaind

as given by(3-7)

(4-15)and(4-16).Because the charged particle interacts only with the LO phonon of the dielectric layer in which the charged particle is located

the interaction Hamiltonian of the charged particle with LO phonons for superlattice is as the same as for the bilayer.We also extend the above discussion to the semi-infinite superlattice.We assume that the semiinfinite superlattice occupying the space oi z

>

0

and the space of z

<

0 is vacuum or the third media with dielectric function ε

3

(ω).In this case

the dispersion relation is derived

as given by(5-12).In addition

the interaction Hamiltonain oi the charged particle with SO and LO phonon is completely as the same as for the infinite superlattice.