  The transmission of a wave through a randomly chosen `pile of plates'
typically decreases exponentially with the number of plates, a phenomenon
closely related to Anderson localisation. In apparent contradiction we
construct disordered planar permittivity profiles which are complex-valued
(i.e. have reactive and dissipative properties) that appear to vary randomly
with position, yet are one-way reflectionless for all angles of incidence and
exhibit a transmission coefficient of unity. We contrast these complex-valued
'random' planar permittivity profiles with a family of real-valued, two-way
reflectionless and perfectly transmitting disordered permittivity profiles that
function only for a single angle of incidence and frequency.

Classical Physics;Optics