An overview of the problems involved in the study of electromagnetic power transmission between lossy media is presented. Starting from the well-known problem of the transmission at a dielectric-conductor interface, the different representations of the complex propagation vector of the plane waves are introduced. Analytical expressions to convert from one formulation to the other are obtained. Moreover, the transmission of a plane wave at the interface between two lossy media is taken into account. An explanation of the strange behavior of the transmitted wave is developed by means of power considerations. Finally, the interesting effect of the parallel-attenuated transmitted wave is presented, and its properties as a function of the incident phase vector amplitude are deduced.

In this paper, an introduction to electromagnetic scattering is presented. We introduce the basic concepts needed to face a scattering problem, including the scattering, absorption, and extinction cross sections. We define the vector harmonics and we present some of their properties. Finally, we tackle the two canonical problems of the scattering by an infinitely long circular cylinder, and by a sphere, showing that the introduction of the vector wave function makes the imposition and solution of the boundary conditions particularly simple.

The incidence of an inhomogeneous plane wave on the interface between two lossy media is analyzed. The analytical expressions of the incidence angle of the phase vector, for which the transmitted wave has the phase or the attenuation vector parallel to the interface, are obtained. The transmitted wave with the attenuation vector parallel to the interface is physically interpreted, finding a wave in a lossy medium without attenuation away from the interface. The same effect appears at the interface between a lossless medium and a lossy one.

In this paper, ultra-thin narrow-band, complementary narrow-band, and dual-band metamaterial absorbers (MMAs), exploiting the same electric ring resonator configuration, are investigated at normal and oblique incidence for both transverse electric (TE) and transverse magnetic (TM) polarizations, and with different physical properties in the THz regime. In the analysis of the ultra-thin narrow-band MMA, the limit of applicability of the transmission line model has been overcome with the introduction of a capacitance which considers the z component of the electric field. These absorbing structures have shown a wide angular response and a polarization-insensitive behavior due to the introduction of a conducting ground plane and to the four-fold rotational symmetry of the resonant elements around the propagation axis. We have adopted a retrieval procedure to extract the effective electromagnetic parameters of the proposed MMAs and we have compared the simulated and analytical results through the interference theory.

This paper illustrates how the penetration of electromagnetic waves in lossy media strongly depends on the waveform and not only on the media involved. In particular, the so-called inhomogeneous plane waves are compared against homogeneous plane waves illustrating how the first ones can generate deep penetration effects. Moreover, the paper provides examples showing how such waves may be practically generated. The approach taken here is analytical and it concentrates on the deep penetration conditions obtained by means of incident inhomogeneous plane waves incoming from a lossless medium and impinging on a lossy medium. Both conditions and constraints that the waveforms need to possess to achieve deep penetration are analysed. Some results are finally validated through numerical computations. The theory presented here is of interest in view of a practical implementation of the deep penetration effect.