We demonstrate optical networks composed of diffractive layers trained using deep learning to encode the spatial information of objects into the power spectrum of the diffracted light, which are used to classify objects with a single-pixel spectroscopic detector. Using a plasmonic nanoantenna-based detector, we experimentally validated this single-pixel machine vision framework at terahertz spectrum to optically classify the images of handwritten digits by detecting the spectral power of the diffracted light at ten distinct wavelengths, each representing one class/digit. We also coupled this diffractive network-based spectral encoding with a shallow electronic neural network, which was trained to rapidly reconstruct the images of handwritten digits based on solely the spectral power detected at these ten distinct wavelengths, demonstrating task-specific image decompression. This single-pixel machine vision framework can also be extended to other spectral-domain measurement systems to enable new 3D imaging and sensing modalities integrated with diffractive network-based spectral encoding of information.

Recent advances in deep learning have been providing non-intuitive solutions to various inverse problems in optics. At the intersection of machine learning and optics, diffractive networks merge wave-optics with deep learning to design task-specific elements to all-optically perform various tasks such as object classification and machine vision. Here, we present a diffractive network, which is used to shape an arbitrary broadband pulse into a desired optical waveform, forming a compact and passive pulse engineering system. We demonstrate the synthesis of various different pulses by designing diffractive layers that collectively engineer the temporal waveform of an input terahertz pulse. Our results demonstrate direct pulse shaping in terahertz spectrum, where the amplitude and phase of the input wavelengths are independently controlled through a passive diffractive device, without the need for an external pump. Furthermore, a physical transfer learning approach is presented to illustrate pulse-width tunability by replacing part of an existing network with newly trained diffractive layers, demonstrating its modularity. This learning-based diffractive pulse engineering framework can find broad applications in e.g., communications, ultra-fast imaging and spectroscopy.

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