Description:

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Sir Michael Berry
Melville Wills Professor of Physics (Emeritus)
H H Wills Physics Laboratory
University of Bristol, UK

"Faster than Fourier: superoscillations, weak measurement, vorticulture..."

Abstract: Band-limited functions can oscillate arbitrarily faster than their fastest Fourier component over arbitrarily long intervals. In quantum mechanics, such ‘superoscillations’ correspond to weak measurements, resulting in ‘weak values’ of observables (e.g photon momenta) far outside the spectrum of the operator being measured. Superoscillations were anticipated in optical vortices and in radar theory. The phenomenon has implications for signal processing, and enable sub-wavelength resolution microscopy without evanescent waves. Where superoscillations occur, functions are exponentially weak and vulnerable to noise. Superoscillations are unexpectedly common: in typical monochromatic optical fields, approximately one-third of the domain is superoscillatory.




Keywords: Physcis, Astronomy, Heilborn