  Electromagnetic waves at grazing incidence onto a planar medium are analogous
to zero energy quantum particles incident onto a potential well. In this limit
waves are typically completely reflected. Here we explore dielectric profiles
supporting optical analogues of `half-bound states', allowing for zero
reflection at grazing incidence. To obtain these profiles we use two different
theoretical approaches: supersymmetric quantum mechanics, and direct inversion
of the Helmholtz equation.
