Electromagnetic media with no Fresnel (dispersion) equation and novel jump (boundary) conditions

At a boundary that separates two insulators, the components of the electric field strength E and of the magnetic field excitation H parallel to the interface are continuous; moreover, the same is true for the components of the magnetic field strength B and of the electric field excitation D that are perpendicular to the interface. Because these jump conditions are an immediate consequence of Maxwell’s equations, they are valid for all electromagnetic materials [1]; in the statement above, electric conductors were ruled out as a matter of simplicity. Numerous recent works discuss further jump conditions, whose role in the foundations of electrodynamics is secondary, but which have unique technological properties. For example, the boundary separating a perfect electromagnetic conductor (PEMC) and vacuum can act as a twist polariser. More in detail, for a specific choice of the key material parameter, the electric field of a wave being reflected off the interface is totally cross-polarised [2]. Another possibility is to require that the components of the magnetic field strength B and of the electric field excitation D orthogonal to the interface vanish. Such “DB ” jump conditions can be used to achieve invisibility to the monostatic radar, whose transmitter and receiver are located at the same point. More in detail, by engineering an appropriate material coating, it is possible to reduce the back-scattering cross-section of any object that is endowed with certain symmetries [3]. The PEMC an