New methods for designing invisible and reflectionless materials

In this talk I shall treat wave propagation through a very simple system: an isotropic slab of material that changes permittivity ε over its cross section (see Figure 1). I shall illustrate a method based on the application of complex spatial coordinates for designing inhomogeneous slabs that are invisible, or at least reflectionless from one side; connecting these scattering properties with the branch cuts of the wave in the complex position plane. As an extreme example I shall show that there exist `random' planar media with combinations of loss and gain that always have a transmission coefficient of unity, for all angles of incidence.