Mitigating the stochastic noise introduced during the generation, transmission, and detection of temporal optical waveforms remains a significant challenge across many applications, including radio-frequency photonics, light-based telecommunications, spectroscopy, etc. The problem is particularly difficult for the weak-intensity signals often found in practice. Active amplification worsens the signal-to-noise ratio, whereas noise mitigation based on optical bandpass filtering attenuates further the waveform of interest. Additionally, current optical filtering approaches are not optimal for signal bandwidths narrower than just a few GHz. We propose a versatile concept for simultaneous amplification and noise mitigation of temporal waveforms, here successfully demonstrated on optical signals with bandwidths spanning several orders of magnitude, from the kHz to GHz scale. The concept is based on lossless temporal sampling of the incoming coherent waveform through Talbot processing. By reaching high gain factors ( > 100 ), we show the recovery of ultra-weak optical signals, with power levels below the detector threshold, additionally buried under a much stronger noise background. The method is inherently self-tracking, a capability demonstrated by simultaneously denoising four data signals in a dense wavelength division multiplexing scheme.

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A simple, practical method based on electro-optic gating is experimentally shown to improve the temporal resolution of single-photon detection by more than 16 times. Delay times between ultrafast single photons and a reference clock are stretched by a desired programmable sampling gate factor, allowing reconstruction of delay histograms with ≈0.001 photons per pulse to within 60 ps. By transferring the bandwidth of RF electronics to single-photon counting, complex single-photon signals with large time-bandwidth products > 2000 are temporally stretched up so that they can be resolved by slow detectors, irrespective of the quality of the detector instrument response function. This method is also applied to biphotons, in order to reconstruct the 2D histogram of joint detection delays with 15 times better resolution. The phenomenon of nonlocal dispersion, which is not resolvable directly with the slow detectors, is then observable to within the 98 ps level. The proof-of-concept demonstration uses off-the-shelf commercial fiber-integrated LiNbO 3 modulators and RF electronics, and the method is readily integrable on-chip and to speeds >100 GHz, offering a practical solution to ultrafast time-correlated single-photon counting beyond the research laboratory.

We demonstrate gapless and real-time spectral analysis of broadband waveforms with >250 analysis points per spectrum. The concept is based on a discretization of an electro-optic time-lens to implement a phase modulation equivalent to 206.25π.

The ability to detect ultrafast waveforms arising from randomly occurring events is essential to such diverse fields as bioimaging, spectroscopy, radio-astronomy, sensing and telecommunications. However, noise remains a significant challenge to recover the information carried by such waveforms, which are often too weak for detection. The key issue is that most of the undesired noise is contained within the broad frequency band of the ultrafast waveform, such that it cannot be alleviated through conventional methods. In spite of intensive research efforts, no technique can retrieve the complete description of a noise-dominated ultrafast waveform of unknown parameters. Here, we propose a signal denoising concept involving passive enhancement of the coherent content of the signal frequency spectrum, which enables the full recovery of arbitrary ultrafast waveforms buried under noise, in a real-time and single-shot fashion. We experimentally demonstrate the retrieval of picosecond-resolution waveforms that are over an order of magnitude weaker than the in-band noise. By granting access to previously undetectable information, this concept shows promise for advancing various fields dealing with weak or noise-dominated broadband waveforms.