Topological Dark Spots of Electric Near Field in Metal Structures

Electric dark spots are point singularities at which the electric field amplitude vanishes. These singularities usually emerge in real space accidentally and are unstable due to the vectorial property of the electric field. In this paper, we show that topologically protected electric dark spots can emerge in metal scatterers under external excitation. The material property of metal imposes a boundary condition that reduces the vectorial electric field on the metal surface to a scalar field. The phase singularity of this scalar field has zero amplitude and carries a well-defined topological charge corresponding to an electric dark spot. The topological electric dark spots give rise to the superoscillation phenomenon with a divergent local wavenumber. We uncover the global charge conservation property of the dark spots on the scatterers' surfaces and demonstrate their stability under different perturbations. We also demonstrate the manipulation of the dark spots' topological charge and spatial location. The results open a new avenue for nanophotonic near-field manipulations and may find applications in optical metrology, optical sensing, and super-resolution imaging.