We consider a model of an inhomogeneous dielectric slab first studied by Shvartzburg, Petite and Auby [J. Opt. Soc. Am. B 16, 966 (1999)] and several variations of that model and study the excitation of s-polarized surface electromagnetic waves on the surface of inhomogeneous dielectric media. Using the invariant imbedding theory of wave propagation in stratified media, we calculate the reflectance and the absorptance of an s wave incident obliquely on a dielectric slab in the Otto configuration, as a function of incident angle and frequency. We also calculate the spatial distribution of the electric field intensity in the inhomogeneous region. We find that in all cases we have considered, s-polarized surface waves are excited at certain incident angles and frequencies. We discuss the physical mechanism of the surface wave generation and the possibility of experimental observations of these effects.