Superoscillations, endfire and supergain

Abstract

Superoscillatory functions vary faster than their fastest Fourier component. Here they are employed to give an alternative description and explicit recipe for creating endfire arrays with supergain, that is ant nnas with radiation patterns concentrated in an arbitrarily narrow angular range and of arbitrary form. Two examples are radiation patterns described by sinc and Gaussian functions. [Editor“s note: for a video of the talk given by Prof. Berry (titled “Weak Value Probabilities”) at the Aharonov-80 conference in 2012 at Chapman U iversity, see quantum.chapman.edu/talk-6.]