The existence of localized and resonant optical waves associated with
the surface of a semi-infinite superlattice or ifs interface with a su
bstrate is reported, considering the case of s-polarization (transvers
e electric modes). These modes appear as well defined peaks of the den
sity of states, either inside the minigaps or inside the bulk bands of
the superlattice. The density of states, function of the frequency om
ega, and the wave vector k(parallel to) (parallel to the interface), a
re obtained from an analytic determination of the response function fo
r a semi-infinite superlattice with or without a cap layer.