  We show that if the permittivity profile of a planar dielectric medium is an
analytic function in the upper (lower) half complex position plane then it
won't reflect radiation from the left (right), whatever the angle of incidence.
Consequently, using the spatial Kramers-Kronig relations one can derive a real
part of a permittivity profile from some given imaginary part (or vice versa),
such that the reflection is guaranteed to be zero. This result is valid for
both scalar and vector wave theories, and may have relevance for efficiently
absorbing radiation, or reducing reflection from bodies.
