Connection between phase singularities and the radiation pattern of a slit in a metal plate

We report a new fundamental relation between the minima of the far-zone radiation pattern of a narrow slit in a metal plate and the location of phase singularities in the intermediate field. If a system parameter such as the wavelength is changed, a previously unappreciated singular optics phenomenon occurs: namely, the transition of a near-zone phase singularity into a singularity of the radiation pattern. Our results have significance for the design of novel nanoscale light sources and antennas.