Superoscillations, Endfire and Supergain
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 antennas 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 University, see quantum.chapman.edu/talk-6.]
KeywordsRadiation Pattern Forward Direction Line Source Hermite Polynomial Excitation Amplitude
I thank Professor Stephen Lipson for introducing me to supergain, Professor Sandu Popescu for a helpful suggestion, Chapman University for generous hospitality while this work was begun, and the Leverhulme Trust for research support—and of course Yakir Aharonov for continuing inspiration.
- 4.M.V. Berry, in Faster than Fourier in Quantum Coherence and Reality; in Celebration of the 60th Birthday of Yakir Aharonov, ed. by J.S. Anandan, J.L. Safko (World Scientific, Singapore, 1994), pp. 55–65 Google Scholar