Broadband superoscillation brings a wave into perfect three-dimensional

The fundamental properties of a wave precludes it from being localized to subwavelength distances in all dimensions of the wave's existence. The inability to focus electromagnetic waves to an all-direction subwavelength spot limits the 3D resolution of a conventional imaging system to about half the imaging wavelength. A plethora of super-resolution imaging systems have been designed which obtain super-resolution in one or two (but not all) dimensions, but they suffer various restrictions in working distance and the classes of objects they can image. In this paper, we report a first investigation into a wave that is focused to subwavelength dimensions in all directions. After reviewing the physics of wave dispersion and diffraction which seemingly preclude this phenomenon, we sidestep these preclusions using a broadband superoscillation waveform and synthesize an all-direction subwavelength focus. We report the salient spatial and temporal features of this wave, and apply it to achieve 3D super-resolution imaging.