In the present paper we consider nonlinear dimers and trimers (more
generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where
the nonlinear sites are of saturable type. We examine the stationary states of
such chains in the form of plane waves, and analytically compute their
reflection and transmission coefficients through the nonlinear oligomer, as
well as the corresponding rectification factors which clearly illustrate the
asymmetry between left and right propagation in such systems. We examine not
only the existence but also the dynamical stability of the plane wave states.
Lastly, we generalize our numerical considerations to the more physically
relevant case of Gaussian initial wavepackets and confirm that the asymmetry in
the transmission properties also persists in the case of such wavepackets.