Engineering antenna radiation patterns via quasi-conformal mappings

We use a combination of conformal and quasi-conformal mappings to engineer isotropic electromagnetic devices that modify the omnidirectional radiation pattern of a point source. For TE waves, the designed devices are also non-magnetic. The flexibility offered by the proposed method is much higher than that achieved with conformal mappings. As a result, it is shown that complex radiation patterns can be achieved, which can combine high directivity in a desired number of arbitrary directions and isotropic radiation in other specified angular ranges. In addition, this technique enables us to control the power radiated in each direction to a certain extent. The obtained results are valid for any part of the spectrum. The potential of this method is illustrated with some examples. Finally, we study the frequency dependence of the considered devices and propose a practical dielectric implementation.