Ill-posed waveguide discontinuity problem involving metamaterials with impedance boundary conditions on the two ports

It is shown that the presence of double negative metamaterials can affect the traditional well posedness of time-harmonic electromagnetic boundary value problems, even when absorbing boundary conditions are considered on part of the boundary. This is done by considering a simple waveguide discontinuity problem with traditional impedance boundary conditions on the two ports. The theoretical results are then used to introduce some doubts on the reliability of models with sharp interfaces between lossless double positive and double negative materials, when the latter are constructed with arrangements of normal materials; and to explain the anomalous behaviour of many numerical simulators when double negative metamaterials are involved.