Oral: Reconstructing Superoscillations Buried Deeply in Noise

Superoscillations are local oscillations in a signal that can be many times faster than the signal's fastest global Fourier component. In trade, these superoscillations can be many orders of magnitude smaller than the average amplitude of the signal. This makes noise highly probematic when attempting to transmit a superoscillating signal. We demonstrate a method using frequency combs to create superoscillating regions that mimic any analytic function - even ones well outside the bandlimits - to an arbitrary degree of accuracy. We mathematically and experimentally show that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. Using simple tools and lab equipment, we additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit.