We cosider the elementary excitations in quantum wells of arbitrary sh
ape, as they result from the coupling between excitons and electromagn
etic radiation. The exciton states are obtained from a two-band model
[1]. The solutions of Maxwell equations with the appropriate exciton d
ependent nonlocal susceptibility are obtained by using a mean field ap
proach [2] based on the fact that the radiation wavelength lambda is m
uch larger than the well width L. Application to asymmetric wells give
s the polariton dispersion modes and the radiative linewidths for all
possible well shapes. The splitting of the Z-mode and the values of th
e radiative lifetimes strongly depend on the well width L and its asym
metry. The reflectivity and absorption are computed and are shown to g
ive strong evidence of polariton modes.