The existence of localised and resonant optical waves in semi-infinite
superlattice with or without a cap layer is reported, considering the
case of s-polarisation (transverse electric modes). These modes appea
r as well defined peaks of the density of states, either inside the mi
nigaps or inside the bulk bands of the superlattice. The density of st
ates, function of the frequency omega and the wave vector k(parallel t
o) (parallel to the interface), are obtained from an analytic determin
ation of the response function for these heterostructures.