A radiator is typically a parabolic mirror illuminated by an electromagnetic source, or a cylindrical transducer of resonant vibrations. Both of these devices are designed to radiate either a beam of parallel rays or a (focused) beam that converges to a point or a line. Consequently, at the worst, the radiation pattern is largely restricted to a {\it half space}, and at the best, to a cone or cylinder-like subspace of this half space. Such devices can therefore be termed unilateral radiators. This study is devoted to the synthesis of the sources that can give rise to such radiation, the underlying motivation being the removal of the material presence of the mirror or transducer casing from which waves coming from other boundaries could reflect or diffract.
