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Deep learning uses multilayered artificial neural networks to learn digitally from large datasets. It then performs advanced identification and classification tasks. To date, these multilayered neural networks have been implemented on a computer. Lin et al. demonstrate all-optical machine learning that uses passive optical components that can be patterned and fabricated with 3D-printing. Their hardware approach comprises stacked layers of diffractive optical elements analogous to an artificial neural network that can be trained to execute complex functions at the speed of light. Science , this issue p. 1004 All-optical deep learning can be implemented with 3D-printed passive optical components. Deep learning has been transforming our ability to execute advanced inference tasks using computers. Here we introduce a physical mechanism to perform machine learning by demonstrating an all-optical diffractive deep neural network (D 2 NN) architecture that can implement various functions following the deep learning–based design of passive diffractive layers that work collectively. We created 3D-printed D 2 NNs that implement classification of images of handwritten digits and fashion products, as well as the function of an imaging lens at a terahertz spectrum. Our all-optical deep learning framework can perform, at the speed of light, various complex functions that computer-based neural networks can execute; will find applications in all-optical image analysis, feature detection, and object classification; and will also enable new camera designs and optical components that perform distinctive tasks using D 2 NNs.

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. Diffractive networks have recently been discussed as an all-optical analogue for performing neural network operations. The authors present a method using deep learning-designed 3D-printed diffractive surfaces to engineer temporal waveforms and perform pulse shaping in the terahertz regime.

Terahertz waves offer advantages for nondestructive detection of hidden objects/defects in materials, as they can penetrate most optically-opaque materials. However, existing terahertz inspection systems face throughput and accuracy restrictions due to their limited imaging speed and resolution. Furthermore, machine-vision-based systems using large-pixel-count imaging encounter bottlenecks due to their data storage, transmission and processing requirements. Here, we report a diffractive sensor that rapidly detects hidden defects/objects within a 3D sample using a single-pixel terahertz detector, eliminating sample scanning or image formation/processing. Leveraging deep-learning-optimized diffractive layers, this diffractive sensor can all-optically probe the 3D structural information of samples by outputting a spectrum, directly indicating the presence/absence of hidden structures or defects. We experimentally validated this framework using a single-pixel terahertz time-domain spectroscopy set-up and 3D-printed diffractive layers, successfully detecting unknown hidden defects inside silicon samples. This technique is valuable for applications including security screening, biomedical sensing and industrial quality control. Researchers showcase a deep learning-designed diffractive terahertz sensor that rapidly detects hidden defects within 3D samples based on the output spectrum measured by a single-pixel detector, eliminating sample scanning or image formation/processing.

As an optical machine learning framework, Diffractive Deep Neural Networks (D NN) take advantage of data-driven training methods used in deep learning to devise light–matter interaction in 3D for performing a desired statistical inference task. Multi-layer optical object recognition platforms designed with this diffractive framework have been shown to generalize to unseen image data achieving, e.g., >98% blind inference accuracy for hand-written digit classification. The multi-layer structure of diffractive networks offers significant advantages in terms of their diffraction efficiency, inference capability and optical signal contrast. However, the use of multiple diffractive layers also brings practical challenges for the fabrication and alignment of these diffractive systems for accurate optical inference. Here, we introduce and experimentally demonstrate a new training scheme that significantly increases the robustness of diffractive networks against 3D misalignments and fabrication tolerances in the physical implementation of a trained diffractive network. By modeling the undesired layer-to-layer misalignments in 3D as continuous random variables in the optical forward model, diffractive networks are trained to maintain their inference accuracy over a large range of misalignments; we term this diffractive network design as D NN (v-D NN). We further extend this vaccination strategy to the training of diffractive networks that use differential detectors at the output plane as well as to jointly-trained hybrid (optical-electronic) networks to reveal that all of these diffractive designs improve their resilience to misalignments by taking into account possible 3D fabrication variations and displacements during their training phase.

Surface states generally degrade semiconductor device performance by raising the charge injection barrier height, introducing localized trap states, inducing surface leakage current, and altering the electric potential. We show that the giant built-in electric field created by the surface states can be harnessed to enable passive wavelength conversion without utilizing any nonlinear optical phenomena. Photo-excited surface plasmons are coupled to the surface states to generate an electron gas, which is routed to a nanoantenna array through the giant electric field created by the surface states. The induced current on the nanoantennas, which contains mixing product of different optical frequency components, generates radiation at the beat frequencies of the incident photons. We utilize the functionalities of plasmon-coupled surface states to demonstrate passive wavelength conversion of nanojoule optical pulses at a 1550 nm center wavelength to terahertz regime with efficiencies that exceed nonlinear optical methods by 4-orders of magnitude. Semiconductor surface states often stand in the way of device performance, but here, the authors take advantage of them for wavelength conversion. They present a compact, passive conversion device insensitive to optical alignment by using plasmon-coupled surface states that enable the efficient conversion without nonlinear phenomena.

Deep learning has been transformative in many fields, motivating the emergence of various optical computing architectures. Diffractive optical network is a recently introduced optical computing framework that merges wave optics with deep-learning methods to design optical neural networks. Diffraction-based all-optical object recognition systems, designed through this framework and fabricated by 3D printing, have been reported to recognize hand-written digits and fashion products, demonstrating all-optical inference and generalization to sub-classes of data. These previous diffractive approaches employed monochromatic coherent light as the illumination source. Here, we report a broadband diffractive optical neural network design that simultaneously processes a continuum of wavelengths generated by a temporally incoherent broadband source to all-optically perform a specific task learned using deep learning. We experimentally validated the success of this broadband diffractive neural network architecture by designing, fabricating and testing seven different multi-layer, diffractive optical systems that transform the optical wavefront generated by a broadband THz pulse to realize (1) a series of tuneable, single-passband and dual-passband spectral filters and (2) spatially controlled wavelength de-multiplexing. Merging the native or engineered dispersion of various material systems with a deep-learning-based design strategy, broadband diffractive neural networks help us engineer the light–matter interaction in 3D, diverging from intuitive and analytical design methods to create task-specific optical components that can all-optically perform deterministic tasks or statistical inference for optical machine learning.

Imaging systems operating in the terahertz part of the electromagnetic spectrum are attractive due to their ability to penetrate many opaque materials and provide unique spectral signatures of various chemicals. However, the use of terahertz imagers in real-world applications has been limited by the slow speed, large size, high cost and complexity of present systems, largely due to the lack of suitable terahertz focal-plane array detectors. Here we report a terahertz focal-plane array that can directly provide the spatial amplitude and phase distributions, along with the ultrafast temporal and spectral information of an imaged object. It consists of a two-dimensional array of ~0.3 million plasmonic photoconductive nanoantennas optimized to rapidly detect broadband terahertz radiation with a high signal-to-noise ratio. We utilized the multispectral nature of the amplitude and phase data captured by these plasmonic nanoantennas to image different objects, including super-resolved etched patterns in a silicon substrate and defects in battery electrodes. By eliminating the need for raster scanning and spatial terahertz modulation, our terahertz focal-plane array offers more than a 1,000-fold increase in the imaging speed compared with the state of the art and potentially suits a broad range of applications in industrial inspection, security screening and medical diagnosis, among others. A terahertz focal-plane array based on a two-dimensional array of plasmonic photoconductive nanoantennas offers high-quality imaging in the terahertz region.

Terahertz waves offer numerous advantages for the nondestructive detection of hidden objects/defects in materials, as they can penetrate through most optically-opaque materials. However, existing terahertz inspection systems are restricted in their throughput and accuracy (especially for detecting small features) due to their limited speed and resolution. Furthermore, machine vision-based continuous sensing systems that use large-pixel-count imaging are generally bottlenecked due to their digital storage, data transmission and image processing requirements. Here, we report a diffractive processor that rapidly detects hidden defects/objects within a target sample using a single-pixel spectroscopic terahertz detector, without scanning the sample or forming/processing its image. This terahertz processor consists of passive diffractive layers that are optimized using deep learning to modify the spectrum of the terahertz radiation according to the absence/presence of hidden structures or defects. After its fabrication, the resulting diffractive processor all-optically probes the structural information of the sample volume and outputs a spectrum that directly indicates the presence or absence of hidden structures, not visible from outside. As a proof-of-concept, we trained a diffractive terahertz processor to sense hidden defects (including subwavelength features) inside test samples, and evaluated its performance by analyzing the detection sensitivity as a function of the size and position of the unknown defects. We validated its feasibility using a single-pixel terahertz time-domain spectroscopy setup and 3D-printed diffractive layers, successfully detecting hidden defects using pulsed terahertz illumination. This technique will be valuable for various applications, e.g., security screening, biomedical sensing, quality control, anti-counterfeiting measures and cultural heritage protection.

As an optical machine learning framework, Diffractive Deep Neural Networks (D2NN) take advantage of data-driven training methods used in deep learning to devise light-matter interaction in 3D for performing a desired statistical inference task. Multi-layer optical object recognition platforms designed with this diffractive framework have been shown to generalize to unseen image data achieving e.g., >98% blind inference accuracy for hand-written digit classification. The multi-layer structure of diffractive networks offers significant advantages in terms of their diffraction efficiency, inference capability and optical signal contrast. However, the use of multiple diffractive layers also brings practical challenges for the fabrication and alignment of these diffractive systems for accurate optical inference. Here, we introduce and experimentally demonstrate a new training scheme that significantly increases the robustness of diffractive networks against 3D misalignments and fabrication tolerances in the physical implementation of a trained diffractive network. By modeling the undesired layer-to-layer misalignments in 3D as continuous random variables in the optical forward model, diffractive networks are trained to maintain their inference accuracy over a large range of misalignments; we term this diffractive network design as vaccinated D2NN (v-D2NN). We further extend this vaccination strategy to the training of diffractive networks that use differential detectors at the output plane as well as to jointly-trained hybrid (optical-electronic) networks to reveal that all of these diffractive designs improve their resilience to misalignments by taking into account possible 3D fabrication variations and displacements during their training phase.