Perfect transmission through disordered media

The transmission of a wave through a randomly chosen `pile of plates' typically decreases expo- nentially with the number of plates, a phenomenon closely related to Anderson localisation. In ap- parent contradiction we construct disordered planar permittivity pro les which are complex-valued (i.e. have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way re ectionless for all angles of incidence and exhibit a transmission coe cient of unity. In addition to these complex-valued 'random' planar permittivity pro les, we construct a family of real-valued, two-way re ectionless and perfectly transmitting disordered permittivity pro les that function only for a single angle of incidence and a narrow frequency range.