A Class of Focusing Waves With Controllable Spatial Extension and Directivity

Slepian's concentration operator is applied in order to define a set of focusing waves with finite angular spread and the highest spatial focusing possible. These waves can be used as building blocks for the definition of any wave that requires to ensure both angular and spatial resolution, as an optimal tradeoff within the bounds imposed by the uncertainty principle. Applications of these results can be expected in the form of focusing waves yielding higher energy efficiency for antenna characterization, electromagnetic compatibility (EMC) radiative-immunity tests, electronic warfare, as well as spatially resolved beamforming.