Temporal Pulse Compression Beyond the Fourier Transform Limit

It is a generally known that the Fourier transform limit forbids a function and its Fourier transform to both be sharply localized. Thus, this limit sets a lower bound to the degree to which a band-limited pulse can be temporally compressed. However, seemingly counterintuitive waveforms have been theoretically discovered, which, across finite time intervals, vary faster than their highest frequency components. While these so-called superoscillatory waveforms are very difficult to synthesize due to their high amplitude sidebands and high sensitivity, they open up the possibility toward arbitrarily compressing a temporal pulse, without hindrances from bandwidth limitations. In this paper, we report the design and realization of a class of superoscillatory electromagnetic waveforms for which the sideband amplitudes, and hence, the sensitivity can be regulated. We adapt Schelkunoff´s method for superdirectivity to design such temporally compressed superoscillatory pulses, which we ultimately realize in an experiment, achieving pulse compression 47% improved beyond the Fourier transform limit.