We experimentally broke the temporal Fourier focusing limit of an ultra-short optical pulse and used it to demonstrate temporal super-resolution detection of a temporal event . The envelope function of the pulse is synthesized in the form of a Super-Oscillating Beat (SOB) signal, made of pairs of optical modes (i.e. beat modes) centered around a common carrier frequency. The mathematical form for the synthesis of the SOB signal is based on a known super-oscillatory function . Suited with the right amplitude and phases these beat modes interfere to create a lobe in the temporal waveform of the field’s envelope which can be arbitrarily narrow, at the cost of reduced amplitude at the fast oscillation. In our case, we achieved a temporal feature that is approximately three times shorter than the duration of a transform-limited Gaussian pulse having a comparable bandwidth while maintaining 30% visibility of the super-oscillating feature.
We then used this SOB signal to demonstrate experimentally temporal super-resolution. Specifically, the SOB signal was used to resolve the existence of a temporal double-slit, a pair of adjacent pulses which are detected as a single temporal event by a transform-limited Gaussian pulse having the same bandwidth. Formally, this experiment constitutes a temporal analogue to super resolution imaging by using a super oscillating point-spread-function [3,4]. Numerical simulations analyse in which cases the SOB signal outperform transform-limited signals for detection of short temporal events.
 Y. Eliezer, L. Hareli, L. Lobachinsky, S. Froim and A. Bahabad, “Breaking the Temporal Resolution Limit by Superoscillating Optical Beats”, Physical Review Letters, 119, 043903 (2017).
 M. V Berry and S. Popescu, "Evolution of Quantum Superoscillations and Optical Supperresolution without Evanescent Waves," J. Phys. A. Math. Gen. 39, 6965 (2006).
 A. M. H. Wong and G. V Eleftheriades, "An Optical Super-microscope for Far-field, Real-time Imaging Beyond the Diffraction Limit" Sci. Rep. 3, (2013).
 E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, "A Super-oscillatory Lens Optical Microscope for Subwavelength Imaging," Nat. Mater. 11, 432 (2012).
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