## 9 Highly Directional Emissions  
The computations of Section 8 have been realized for a relative permittivity coefficient \(\varepsilon_{r}\approx 2\), corresponding, for instance, with polyethylene. This is in fact the material that we would like to use in laboratory experiments, due to the possibility of shaping the dielectric through a 3D printing process.  
A further conical metal reflector can be added to the device of Figure 2, obtaining the final antenna schematically represented in Figure 10. The angle at the vertex of the reflector is again \(\pi/2\). In this way, the horizontally spreading signal is driven in the vertical direction. Referring to Figure 1, during the whole process, an annular wave starts inside the dielectric following a path like that shown in the central picture. When exiting the dielectric, the new Poynting vectors are lined up to the vectors \(\mathbf{V}\), as depicted in the picture on the right-hand side of Figure 1. Finally, after the last reflection, the signal is converted into a highly directional beam, such as that of the picture on the left-hand side of Figure 1.  
During all these transitions there is no breaking of the stream lines of the magnetic field, which remain closed curves encircling the \(z\)-axis. After projection on the plane orthogonal to the z-axis, the evolution of the wave displays a central symmetry. This peculiar property is not commonly shared by other devices--for example, parabolic reflectors (when the source is represented by a classical dipole) or horn antennas. These devices actually need to break their initial symmetries in order to radiate [33].  
Preliminary experiments without the presence of the dielectric showed that the signal emerging from the reflector has an annular shape. The fields are thus polarized in a sort of a circular fashion. The signal is absent nearby the \(z\)-axis. The global shape of the emitted wave is that of a torus. The directivity is relatively good, but, due to the lack of the dielectric lens correction, the toroidal wave grows with distance from the source, following a conical pattern. In those tests, the cones were replaced by two conductors having a complicated shape, in order to skip the construction of the dielectric medium \(\Omega\). The outcome was interesting but still far from the directional signal we would like to achieve. The above experiments are however quite crucial in confirming some theoretical predictions. Waves as those just described do not exist in the Maxwellian framework. Indeed, the request that  
Figure 9: Evolution of \(|E|\) by following the classical Maxwell model. Simulation parameters: \(L=1\), \(N=120\), \(T=1.2\) and \(\Delta t=1/1800\). The propagation velocity is \(c=1\).  
the divergence of the electric field must be always zero in a vacuum does not allow the inclusion of such special waves in the solution space. This means that the adoption of the revised model is rather important in the description of antennas already existing, opening the path to the design of a new generation of sustainable, efficient and performant devices.  
It finally has to be noted that, if perfect directional signals exist, where the rays are all parallel, the natural receiver for this kind of antenna is the antenna itself. Indeed, as in a mirror image, the parallel rays are converted back and concentrated at the gap of the cones. There, they can be finally transformed in potentials.