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Broadband unidirectional visible imaging using wafer-scale nano-fabrication of multi-layer diffractive optical processors

We present a broadband and polarization-insensitive unidirectional imager that operates at the visible part of the spectrum, where image formation occurs in one direction, while in the opposite direction, it is blocked. This approach is enabled by deep learning-driven diffractive optical design with wafer-scale nano-fabrication using high-purity fused silica to ensure optical transparency and thermal stability. Our design achieves unidirectional imaging across three visible wavelengths (covering red, green, and blue parts of the spectrum), and we experimentally validated this broadband unidirectional imager by creating high-fidelity images in the forward direction and generating weak, distorted output patterns in the backward direction, in alignment with our numerical simulations. This work demonstrates wafer-scale production of diffractive optical processors, featuring 16 levels of nanoscale phase features distributed across two axially aligned diffractive layers for visible unidirectional imaging. This approach facilitates mass-scale production of ~0.5 billion nanoscale phase features per wafer, supporting high-throughput manufacturing of hundreds to thousands of multi-layer diffractive processors suitable for large apertures and parallel processing of multiple tasks. Beyond broadband unidirectional imaging in the visible spectrum, this study establishes a pathway for artificial-intelligence-enabled diffractive optics with versatile applications, signaling a new era in optical device functionality with industrial-level, massively scalable fabrication.

36 MATERIALS SCIENCE↗

Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

Nonlinear encoding in diffractive information processing using linear optical materials

Nonlinear encoding of optical information can be achieved using various forms of data representation. Here, we analyze the performances of different nonlinear information encoding strategies that can be employed in diffractive optical processors based on linear materials and shed light on their utility and performance gaps compared to the state-of-the-art digital deep neural networks. For a comprehensive evaluation, we used different datasets to compare the statistical inference performance of simpler-to-implement nonlinear encoding strategies that involve, e.g., phase encoding, against data repetition-based nonlinear encoding strategies. We show that data repetition within a diffractive volume (e.g., through an optical cavity or cascaded introduction of the input data) causes the loss of the universal linear transformation capability of a diffractive optical processor. Therefore, data repetition-based diffractive blocks cannot provide optical analogs to fully connected or convolutional layers commonly employed in digital neural networks. However, they can still be effectively trained for specific inference tasks and achieve enhanced accuracy, benefiting from the nonlinear encoding of the input information. Our results also reveal that phase encoding of input information without data repetition provides a simpler nonlinear encoding strategy with comparable statistical inference accuracy to data repetition-based diffractive processors. Our analyses and conclusions would be of broad interest to explore the push-pull relationship between linear material-based diffractive optical systems and nonlinear encoding strategies in visual information processors.

42 ENGINEERING↗

Universal linear intensity transformations using spatially incoherent diffractive processors

Abstract Under spatially coherent light, a diffractive optical network composed of structured surfaces can be designed to perform any arbitrary complex-valued linear transformation between its input and output fields-of-view (FOVs) if the total number ( N ) of optimizable phase-only diffractive features is ≥~2 N i N o , where N i and N o refer to the number of useful pixels at the input and the output FOVs, respectively. Here we report the design of a spatially incoherent diffractive optical processor that can approximate any arbitrary linear transformation in time-averaged intensity between its input and output FOVs. Under spatially incoherent monochromatic light, the spatially varying intensity point spread function ( H ) of a diffractive network, corresponding to a given, arbitrarily-selected linear intensity transformation, can be written as H ( m , n ; m ′, n ′) = | h ( m , n ; m ′, n ′)| 2 , where h is the spatially coherent point spread function of the same diffractive network, and ( m , n ) and ( m ′, n ′) define the coordinates of the output and input FOVs, respectively. Using numerical simulations and deep learning, supervised through examples of input-output profiles, we demonstrate that a spatially incoherent diffractive network can be trained to all-optically perform any arbitrary linear intensity transformation between its input and output if N ≥ ~2 N i N o . We also report the design of spatially incoherent diffractive networks for linear processing of intensity information at multiple illumination wavelengths, operating simultaneously. Finally, we numerically demonstrate a diffractive network design that performs all-optical classification of handwritten digits under spatially incoherent illumination, achieving a test accuracy of >95%. Spatially incoherent diffractive networks will be broadly useful for designing all-optical visual processors that can work under natural light.

36 MATERIALS SCIENCE↗

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

As an optical processor, a diffractive deep neural network (D2NN) utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing, completing its tasks at the speed of light propagation through thin optical layers. With sufficient degrees of freedom, D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light. Similarly, D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination; however, under spatially incoherent light, these transformations are nonnegative, acting on diffraction-limited optical intensity patterns at the input field of view. Here, we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light. Through simulations, we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products, a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination. The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

36 MATERIALS SCIENCE↗

All-optical image denoising using a diffractive visual processor

Abstract Image denoising, one of the essential inverse problems, targets to remove noise/artifacts from input images. In general, digital image denoising algorithms, executed on computers, present latency due to several iterations implemented in, e.g., graphics processing units (GPUs). While deep learning-enabled methods can operate non-iteratively, they also introduce latency and impose a significant computational burden, leading to increased power consumption. Here, we introduce an analog diffractive image denoiser to all-optically and non-iteratively clean various forms of noise and artifacts from input images – implemented at the speed of light propagation within a thin diffractive visual processor that axially spans <250 × λ, where λ is the wavelength of light. This all-optical image denoiser comprises passive transmissive layers optimized using deep learning to physically scatter the optical modes that represent various noise features, causing them to miss the output image Field-of-View (FoV) while retaining the object features of interest. Our results show that these diffractive denoisers can efficiently remove salt and pepper noise and image rendering-related spatial artifacts from input phase or intensity images while achieving an output power efficiency of ~30–40%. We experimentally demonstrated the effectiveness of this analog denoiser architecture using a 3D-printed diffractive visual processor operating at the terahertz spectrum. Owing to their speed, power-efficiency, and minimal computational overhead, all-optical diffractive denoisers can be transformative for various image display and projection systems, including, e.g., holographic displays.

36 MATERIALS SCIENCE↗

Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network

As a label‐free imaging technique, quantitative phase imaging (QPI) provides optical path length information of transparent specimens for various applications in biology, materials science, and engineering. Multispectral QPI measures quantitative phase information across multiple spectral bands, permitting the examination of wavelength‐specific phase and dispersion characteristics of samples. Herein, the design of a diffractive processor is presented that can all‐optically perform multispectral quantitative phase imaging of transparent phase‐only objects within a snapshot. The design utilizes spatially engineered diffractive layers, optimized through deep learning, to encode the phase profile of the input object at a predetermined set of wavelengths into spatial intensity variations at the output plane, allowing multispectral QPI using a monochrome focal plane array. Through numerical simulations, diffractive multispectral processors are demonstrated to simultaneously perform quantitative phase imaging at 9 and 16 target spectral bands in the visible spectrum. The generalization of these diffractive processor designs is validated through numerical tests on unseen objects, including thin Pap smear images. Due to its all‐optical processing capability using passive dielectric diffractive materials, this diffractive multispectral QPI processor offers a compact and power‐efficient solution for high‐throughput quantitative phase microscopy and spectroscopy.

36 MATERIALS SCIENCE↗

All-optical phase conjugation using diffractive wavefront processing

Abstract Optical phase conjugation (OPC) is a nonlinear technique used for counteracting wavefront distortions, with applications ranging from imaging to beam focusing. Here, we present a diffractive wavefront processor to approximate all-optical phase conjugation. Leveraging deep learning, a set of diffractive layers was optimized to all-optically process an arbitrary phase-aberrated input field, producing an output field with a phase distribution that is the conjugate of the input wave. We experimentally validated this wavefront processor by 3D-fabricating diffractive layers and performing OPC on phase distortions never seen during training. Employing terahertz radiation, our diffractive processor successfully performed OPC through a shallow volume that axially spans tens of wavelengths. We also created a diffractive phase-conjugate mirror by combining deep learning-optimized diffractive layers with a standard mirror. Given its compact, passive and multi-wavelength nature, this diffractive wavefront processor can be used for various applications, e.g., turbidity suppression and aberration correction across different spectral bands.

42 ENGINEERING↗

Time‐Lapse Image Classification Using a Diffractive Neural Network

Diffractive deep neural networks (D 2 NNs), comprised of spatially engineered passive surfaces, collectively process optical input information at the speed of light propagation through a thin diffractive volume, without any external computing power. Diffractive networks were demonstrated to achieve all‐optical object classification and perform universal linear transformations. Herein, a “time‐lapse” image classification scheme using a diffractive network is demonstrated for the first time, significantly advancing its classification accuracy and generalization performance on complex input objects by using the lateral movements of the input objects and/or the diffractive network, relative to each other. In a different context, such relative movements of the objects and/or the camera are routinely being used for image super‐resolution applications; inspired by their success, a time‐lapse diffractive network is designed to benefit from the complementary information content created by controlled or random lateral shifts. The design space and performance limits of time‐lapse diffractive networks are numerically explored, revealing a blind testing accuracy of 62.03% on the optical classification of objects from the CIFAR‐10 dataset. This constitutes the highest inference accuracy achieved so far using a single diffractive network on the CIFAR‐10 dataset. Time‐lapse diffractive networks will be broadly useful for the spatiotemporal analysis of input signals using all‐optical processors.

36 MATERIALS SCIENCE↗

Universal Polarization Transformations: Spatial Programming of Polarization Scattering Matrices Using a Deep Learning‐Designed Diffractive Polarization Transformer

Abstract Controlled synthesis of optical fields having nonuniform polarization distributions presents a challenging task. Here, a universal polarization transformer is demonstrated that can synthesize a large set of arbitrarily‐selected, complex‐valued polarization scattering matrices between the polarization states at different positions within its input and output field‐of‐views (FOVs). This framework comprises 2D arrays of linear polarizers positioned between isotropic diffractive layers, each containing tens of thousands of diffractive features with optimizable transmission coefficients. After its deep learning‐based training, this diffractive polarization transformer can successfully implement N i N o = 10 000 different spatially‐encoded polarization scattering matrices with negligible error, where N i and N o represent the number of pixels in the input and output FOVs, respectively. This universal polarization transformation framework is experimentally validated in the terahertz spectrum by fabricating wire‐grid polarizers and integrating them with 3D‐printed diffractive layers to form a physical polarization transformer. Through this set‐up, an all‐optical polarization permutation operation of spatially‐varying polarization fields is demonstrated, and distinct spatially‐encoded polarization scattering matrices are simultaneously implemented between the input and output FOVs of a compact diffractive processor. This framework opens up new avenues for developing novel devices for universal polarization control and may find applications in, e.g., remote sensing, medical imaging, security, material inspection, and machine vision.

Optical neural networks↗

Diffractive optical computing in free space

Abstract Structured optical materials create new computing paradigms using photons, with transformative impact on various fields, including machine learning, computer vision, imaging, telecommunications, and sensing. This Perspective sheds light on the potential of free-space optical systems based on engineered surfaces for advancing optical computing. Manipulating light in unprecedented ways, emerging structured surfaces enable all-optical implementation of various mathematical functions and machine learning tasks. Diffractive networks, in particular, bring deep-learning principles into the design and operation of free-space optical systems to create new functionalities. Metasurfaces consisting of deeply subwavelength units are achieving exotic optical responses that provide independent control over different properties of light and can bring major advances in computational throughput and data-transfer bandwidth of free-space optical processors. Unlike integrated photonics-based optoelectronic systems that demand preprocessed inputs, free-space optical processors have direct access to all the optical degrees of freedom that carry information about an input scene/object without needing digital recovery or preprocessing of information. To realize the full potential of free-space optical computing architectures, diffractive surfaces and metasurfaces need to advance symbiotically and co-evolve in their designs, 3D fabrication/integration, cascadability, and computing accuracy to serve the needs of next-generation machine vision, computational imaging, mathematical computing, and telecommunication technologies.

36 MATERIALS SCIENCE↗

Atomic Structure, Dynamics, Changes in Chemical Bonding and Semiconductor-Metal Transition in Sb 2 Se 3 : A Remarkable Material for Quantum Networks and Energy Applications

Antimony sesquiselenide has become an outstanding functional material for photovoltaics, energy storage and transformation, memory and photonic applications. Sb 2 Se 3 is one of the most successful emerging solar light absorbers and has also been identified as a highly promising ultralow-loss phase-change material (PCM) for next-generation coherent nanophotonic processors, photonic tensor cores, quantum and neuromorphic networks. Unlike benchmark telluride PCMs, Sb 2 Se 3 features a quasi-one-dimensional (1D) crystalline structure consisting of (Sb 4 Se 6 ) ∞ ribbons, lacks the typical PCM chemical bonding, and undergoes an extended semiconductor-metal transition above the melting point. Consequently, the origin of high optical contrast between crystalline (SET) and amorphous (RESET) logic states remains elusive and presents a significant challenge. Using high-energy X-ray diffraction and Raman spectroscopy over a wide temperature range, supported by first-principles simulations and complemented by thermal, optical and electrical measurements, as well as by 121 Sb-Mossbauer spectroscopy, the quasi-1D network of orthorhombic antimony sesquiselenide was found to undergo significant evolution in amorphous and supercooled Sb 2 Se 3 , leading to lower coordination, shorter interatomic distances and a higher p-electron density on antimony, indicating changes in chemical bonding. The observed novel Sb 2 Se 3 nanocrystalline polymorph, characterized by trigonal antimony coordination and more isolated Sb-Se ribbons, could help reduce multiple trapping defect states in the bandgap, which are typical of orthorhombic Sb 2 Se 3 , thereby enhancing the power-conversion efficiency of photovoltaic devices. Semimetallic and metallic liquid Sb 2 Se 3 exhibit a gradual transformation into a denser 2D and/or 3D network with higher antimony coordination. Localized electron states in the pseudogap are becoming extended, leading to an increase in electronic conductivity σ following the relationship σ ∝ N(E F ) 2 . Liquid Sb 2 Se 3 also appears to be strongly fragile, with a nonmonotonic change in viscosity and higher atomic mobility in the metallic liquid. Furthermore, these results explain extraordinary functionalities of Sb 2 Se 3 for photonic and energy applications.

antimony↗

Nanophotonic waveguide chip-to-world beam scanning

A seamless chip-to-world photonic interface enables broad advancements in optical ranging, display, communication, computation and quantum information science. The ideal solution enables two-dimensional scanning of a diffraction-limited beam from anywhere on a photonic integrated circuit to a large number of resolvable spots. Current beam-scanning technologies are limited by a fundamental trade-off: photonic-integrated-circuits with diffractive optics offer scalability but have poor mode quality, whereas inertially limited micromechanical scanners provide high-quality beams but lack scalable integration. Here we report a photonic ski-jump—a nanoscale waveguide monolithically integrated on a piezoelectric cantilever—to overcome these limitations. It passively curls ~90° out-of-plane within a less-than-0.1 mm 2 footprint, emits a submicrometre, broadband diffraction-limited beam, and exhibits kilohertz-rate mechanical resonances with quality factors of over 10,000. Fabricated in a volume complementary metal–oxide–semiconductor (CMOS) foundry, our device enables scalable two-dimensional beam scanning. Driven on-resonance at CMOS-level voltages, it achieves a footprint-adjusted spot rate of 68.6 mega spots s –1 mm–², exceeding state-of-the-art micro-electro-mechanical systems mirrors by more than 50-fold, which is sufficient for one million pixels at 100 Hz from an approximately 1.5 mm diameter footprint. We demonstrate full-colour image and video projection, and single-photon initialization and readout from silicon vacancy centres in diamond. Finally, by demonstrating uniformity across a 64 ski-jump array, we establish a pathway to achieving greater than one gigaspot resolution at kilohertz rates within a sub-5-cm-diameter footprint, creating a seamless optical pipeline between integrated photonic processors and the free-space world.

Displays↗