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Advancing Fourier: space-time concepts in ultrafast optics, imaging and photonic neural networks

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 Added by Daniel Brunner
 Publication date 2019
  fields Physics
and research's language is English




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The concepts of Fourier optics were established in France in the 1940s by Pierre-Michel Duffieux, and laid the foundations of an extensive series of activities in the French research community that have touched on nearly every aspect of contemporary optics and photonics. In this paper, we review a selection of results where applications of the Fourier transform and transfer functions in optics have been applied to yield significant advances in unexpected areas of optics, including the spatial shaping of complex laser beams in amplitude and in phase, real-time ultrafast measurements, novel ghost imaging techniques, and the development of parallel processing methodologies for photonic artificial intelligence.



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We present theoretical formulation and experimental demonstration of a novel technique for the fast compression-less terahertz imaging based on the broadband Fourier optics. The technique exploits k-vector/frequency duality in Fourier optics which allows using a single-pixel detector to perform angular scan along a circular path, while the broadband spectrum is used to scan along the radial dimension in Fourier domain. The proposed compression-less image reconstruction technique (hybrid inverse transform) requires only a small number of measurements that scales linearly with the image linear size, thus promising real-time acquisition of high-resolution THz images. Additionally, our imaging technique handles equally well and on the equal theoretical footing the amplitude contrast and the phase contrast images, which makes this technique useful for many practical applications. A detailed analysis of the novel technique advantages and limitations is presented, as well as its place among other existing THz imaging techniques is clearly identified
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The ultrafast response of metals to light is governed by intriguing non-equilibrium dynamics involving the interplay of excited electrons and phonons. The coupling between them gives rise to nonlinear diffusion behavior on ultrashort timescales. Here, we use scanning ultrafast thermo-modulation microscopy to image the spatio-temporal hot-electron diffusion in a thin gold film. By tracking local transient reflectivity with 20 nm and 0.25 ps resolution, we reveal two distinct diffusion regimes, consisting of an initial rapid diffusion during the first few picoseconds after optical excitation, followed by about 100-fold slower diffusion at longer times. We simulate the thermo-optical response of the gold film with a comprehensive three-dimensional model, and identify the two regimes as hot-electron and phonon-limited thermal diffusion, respectively.
With recent rapid advances in photonic integrated circuits, it has been demonstrated that programmable photonic chips can be used to implement artificial neural networks. Convolutional neural networks (CNN) are a class of deep learning methods that have been highly successful in applications such as image classification and speech processing. We present an architecture to implement a photonic CNN using the Fourier transform property of integrated star couplers. We show, in computer simulation, high accuracy image classification using the MNIST dataset. We also model component imperfections in photonic CNN and show that the performance degradation can be recovered in a programmable chip. Our proposed architecture provides a large reduction in physical footprint compared to current implementations as it utilizes the natural advantages of optics and hence offers a scalable pathway towards integrated photonic deep learning processors.
The propagation of ultrashort pulses in optical fibre displays complex nonlinear dynamics that find important applications in fields such as high power pulse compression and broadband supercontinuum generation. Such nonlinear evolution however, depends sensitively on both the input pulse and fibre characteristics, and optimizing propagation for application purposes requires extensive numerical simulations based on generalizations of a nonlinear Schrodinger-type equation. This is computationally-demanding and creates a severe bottleneck in using numerical techniques to design and optimize experiments in real-time. Here, we present a solution to this problem using a machine-learning based paradigm to predict complex nonlinear propagation in optical fibres with a recurrent neural network, bypassing the need for direct numerical solution of a governing propagation model. Specifically, we show how a recurrent neural network with long short-term memory accurately predicts the temporal and spectral evolution of higher-order soliton compression and supercontinuum generation, solely from a given transform-limited input pulse intensity profile. Comparison with experiments for the case of soliton compression shows remarkable agreement in both temporal and spectral domains. In optics, our results apply readily to the optimization of pulse compression and broadband light sources, and more generally in physics, they open up new perspectives for studies in all nonlinear Schrodinger-type systems in studies of Bose-Einstein condensates, plasma physics, and hydrodynamics.
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