  In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439
(2015)] showed rather interestingly that planar dielectric media, for which the
real and imaginary parts of the dielectric permittivity are related by spatial
Kramers-Kronig (KK) relations, are one-way reflectionless, whatever the angle
of incidence. Such a fascinating property, besides of extending our
comprehension of the fundamental phenomenon of reflection, may offer new ways
for the design of antireflection surfaces and thin materials with efficient
light absorption. However, KK dielectric media are generally described by
slowly-decaying complex permittivity profiles which may introduce some subtle
issues in the study of the scattering problem. Here we provide a condition on
the imaginary part of the dielectric profile that ensures the existence of
proper scattering states and present a proof of the one-way reflectionless
property in KK dielectric media which is free from loophole. Finally, we show
that instabilities might arise at the interface of KK dielectric media when the
medium is not purely dissipative.
