  Graded index media whose electric susceptibility satisfies the spatial
Kramers-Kronig relations are known to be one-way reflectionless to
electromagnetic radiation, for all angles of incidence. We demonstrate how a
family of these media, in addition to being reflectionless, also have
negligible transmission. To this end, we discuss how the transmission
coefficient for the propagation of waves through a medium whose permittivity is
built from poles in the complex position plane, with residues that sum to
infinity, can be controlled by tuning the positions and residues of the poles.
In particular, we have shown how to make the transmission arbitrarily small,
and hence maximise the absorption of the wave's energy. This behaviour is
confirmed by numerical simulations.
