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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 [1]. 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 [2]. 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.
[1] 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).
[2] M. V Berry and S. Popescu, "Evolution of Quantum Superoscillations and Optical Supperresolution without Evanescent Waves," J. Phys. A. Math. Gen. 39, 6965 (2006).
[3] 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).
[4] 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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