Space-Time Superoscillations

A remarkable phenomenon of superoscillations implies that electromagnetic waves can locally oscillate in space or time faster than the fastest spatial and temporal Fourier component of the entire function. This phenomenon allows to focus light into an arbitrary small hotspot enabling superresolution imaging and optical metrology with accuracy far beyond the Abbey-Reileigh diffraction limit. Here we show that the temporal and spatial superoscillations can be observed simultaneously in band-limited supertoroidal light pulses, a set of space-time nonseparable solutions of Maxwell's equations, at a specific region in space-time.