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![Schematic of cascadable all-optical NAND gates using diffractive networks. (a) Design of a cascadable diffractive NAND gate. (b) The input plane intensity profile of the diffractive NAND gate with all the possible combinations of ideal optical logical values, i.e., (x10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{1}^{0}$$\end{document},x20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{2}^{0}$$\end{document}) = (T,T), (T,F), (F,T) and (F,F), as well as the corresponding optical intensity profiles at the output plane of the diffractive network, with output optical logical values of xi1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{i}^{1}$$\end{document}=(F, T, T, T) respectively. (c) Schematic of cascading diffractive NAND gates.](publication/360353056/figure/fig1/AS:1151843384209408@1651632271126/Schematic-of-cascadable-all-optical-NAND-gates-using-diffractive-networks-a-Design-of.png)
Schematic of cascadable all-optical NAND gates using diffractive networks. (a) Design of a cascadable diffractive NAND gate. (b) The input plane intensity profile of the diffractive NAND gate with all the possible combinations of ideal optical logical values, i.e., (x10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{1}^{0}$$\end{document},x20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{2}^{0}$$\end{document}) = (T,T), (T,F), (F,T) and (F,F), as well as the corresponding optical intensity profiles at the output plane of the diffractive network, with output optical logical values of xi1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}_{i}^{1}$$\end{document}=(F, T, T, T) respectively. (c) Schematic of cascading diffractive NAND gates.
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Owing to its potential advantages such as scalability, low latency and power efficiency, optical computing has seen rapid advances over the last decades. Here, we present the design and analysis of cascadable all-optical NAND gates using diffractive neural networks. We encoded the logical values at the input and output planes of a diffractive NAND...
Citations
... As shown in Fig. 1a, this complex field imager is composed of a series of spatially engineered diffractive surfaces (layers), which are jointly optimized using supervised deep learning algorithms to successively perform the modulation of incoming complex fields. This diffractive architecture, known as a diffractive optical neural network, has previously been explored for all-optical information processing covering various applications, including all-optical image classification 41,42 , space-to-spectrum encoding 42,43 , logic operations [44][45][46] , optical phase conjugation 47 , among others [48][49][50][51][52][53][54][55][56][57][58][59][60] . Within the architecture of our diffractive complex field imager, the diffractive surfaces are trained to simultaneously perform two tasks: (1) an amplitude-toamplitude (A → A) transformation and (2) a phase-tointensity (P → I) transformation. ...
Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.
... Diffractive deep neural network (D 2 NN) is known as an optical machine learning framework that utilizes a series of engineered surfaces/layers that are connected by diffraction of light to perform a given inference or computational task [4][5][6][7][8][9]. In a D 2 NN as a coherent optical processor, the input information can be encoded in the phase and/or amplitude channels of the sample/object field of view [4]. ...
Artificial intelligence is a technology for simulating and extending human intelligence and has rapidly altered many aspects of modern society. Optical processors, which compute with photons instead of electrons, can fundamentally accelerate the development of artificial intelligence by offering substantially improved computing performance. Photonic approaches for demonstrating artificial neural networks as one of the most widely used frameworks in artificial intelligence, show extraordinary potential to achieve brain-inspired information processing at the speed of light. Recently, all-optical diffractive deep neural networks have been created that are based on passive structures and can perform complicated functions designed by computer-based neural networks. However, existing passive diffractive deep neural networks are not reconfigurable and once is fabricated, its function is fixed. This work reports an on-chip programmable deep diffractive neural network (OPD²NN), in which the optical neurons are built with Sb2Se3 phase change material, making the network reconfigurable and non-volatile. Using numerical simulations, the performance of the OPD²NN is benchmarked on two machine learning tasks that are learning a multifunctional (AND-OR-NOT) logic gate and classification of images of handwritten digits from the MNIST dataset and the obtained results are validated using FDTD simulations by a commercially available full-wave electromagnetic solver. Both numerical and FDTD simulations indicate that a five-hidden-layer OPD²NN with a footprint of 30μmx150μm can appropriately handle (AND-OR-NOT) logic functions. For handwritten digits (0-1-2-3) classification, a three-hidden-layer OPD²NN with a footprint of 60μmx105μm can achieve numerical testing accuracy of 91.5% on the test dataset and the FDTD verification results show 73% matching with numerical testing results.
... The function approximation capabilities of free-space optical processors are not limited to statistical inference or classification tasks and can be extended to all-optically performing other general-purpose computational tasks, including e.g., logic operations and diffractive NAND gates that can be optically-cascaded 71,72 . ...
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.
... D 2 NNs have been expected to be an alternative to electronic systems as a task-specific computing device owing to its advantages in power efficiency, low latency, and parallelization capabilities. They have been demonstrated remarkable performance in various applications, including object recognition [1], [5]- [8], spectrum control [9], [10], and logical computing [11], [12]. Recent researches has explored ways to enhance the complexity and information processing capabilities of D 2 NNs by introducing polarization [13], wavelength multiplexing [14], and optoelectronic networks [6], [15], [16]. ...
... information is encoded by a pair of square apertures, similarly to the previous work [12]. The decoded binary number is 0 or 1 is determined by the relative power of upper or lower apertures. ...
Diffractive deep neural networks ( D 2 NNs ) have brought significant changes in many fields, motivating the development of diverse optical computing components. However, a crucial downside in the optical computing components is employing diffractive optical elements (DOEs) which were fabricated using commercial 3D printers. DOEs simultaneously suffer from the challenges posed by high-order diffraction and low spatial utilization since the size of individual neuron is comparable to the wavelength scale. Here, we present a design of D 2 NNs based on all-dielectric metasurfaces which substantially reduces the individual neuron size of net to scale significantly smaller than the wavelength. Metasurface-based optical computational elements can offer higher spatial neuron density while completely eliminate high-order diffraction. We numerically simulated an optical half-adder and experimentally verified it in the terahertz frequency. The optical half-adder employed a compact network with only two diffraction layers. Each layer has a size of 2 × 2 cm ² but integrated staggering 40,000 neurons. The metasurface-based D 2 NNs can further facilitate miniaturization and integration of all optical computing devices and will find applications in numerous fields such as terahertz 6G communication, photonics integrated circuits, and intelligent sensors.
... These processes can be employed to implement various logic gates on different platforms [7][8][9], but they require high input power and nonlinear materials which presents a challenge in terms of fabrication. To reduce the power consumption and material requirements, some researchers turn to spatial diffraction [10,11], which is the spatial variation of the refractive index of a material to diffract light beams in different directions. This scheme enables simple and low-cost optical setups, but the cascadability is limited due to encoding and decoding procedures, and the free-space system is bulky. ...
We proposed an inverse-designed compact half adder on a silicon-on-insulator platform with a footprint of ${2}\;\unicode{x00B5}{\rm m} \times {2}\;\unicode{x00B5}{\rm m}$ 2 µ m × 2 µ m . The optical power of SUM and CARRY is controlled by different input combinations, according to the truth table of a half adder. Topology optimization is applied to cope with multiple objective functions in such a combinational logic circuit. The transmittance at 1550 nm for CARRY with 11 input is 170.2%, with extinction ratios (ERs) of 27.1 and 5.8 dB for SUM and CARRY, respectively. The SUM and CARRY outputs have ERs over 22.0 dB and 5.7 dB from 1515 nm to 1600 nm. Phase condition and morphology analysis show that the device has high tolerance on phase fluctuation and fabrication. The proposed device with compact footprint, low insertion loss, and large bandwidth presents a novel, to the best of our knowledge, approach to achieve all-optical combinational logic circuits with inverse design.
... Tentative solutions have been proposed theoretically and experimentally on building cascadable all-optical logic gates based on connected nanowires, 19 polariton fluid in microcavities, 95,96 tandem photonic crystals, 97 topological silicon chips, 92 and diffractive neural networks. 98,99 Due to the high loss and requirement of the extra control light of these solutions, it is still far from building practical optical logic circuits. For guidance on the selection of nanomaterials and heterostructures to observe typical nonlinear processes, the key figures of merit, such as the nonlinear susceptibility and conversion efficiency, have been comprehensively compared in previous review works. ...
In this Perspective, we summarize the current state-of-the-art and the challenges of optical chirality logic computing. We discuss the prospects of its applications in integrated photonics, quantum technologies, and other multifunctional optoelectronics for ultrafast data processing.
... Each pixel point on the diffractive layer is a parameter that can be learned by the computer and can be used for independent complex-valued tuning of the light field. Based on its capabilities in optical information processing, D 2 NN has been applied to image recognition, 11,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] optical logic operations, [41][42][43] terahertz pulse shaping, 44 phase retrieval, 45 and image reconstruction, 15,46-48 etc. ...
As a successful case of combining deep learning with photonics, the research of optical machine learning has recently gained rapid development. Among various optical classification frameworks, diffractive networks have been shown to have unique advantages in all-optical reasoning. As an important property of light, the orbital angular momentum (OAM) of light shows orthogonality and mode-infinity, which can enhance the ability of parallel classification in information processing. However, there have been few all-optical diffractive networks under the OAM mode encoding. Here, we report a strategy of OAM-encoded diffractive deep neural network (OAM-encoded D2NN) that encodes the spatial information of objects into the OAM spectrum of the diffracted light to perform all-optical object classification. We demonstrated three different OAM-encoded D2NNs to realize (1) single detector OAM-encoded D2NN for single task classification, (2) single detector OAM-encoded D2NN for multi task classification and (3) multi-detector OAM-encoded D2NN for repeatable multi task classification, respectively. This work provides a feasible way to improve the performance of all-optical object classification and opens up promising research directions for D2NN by proposing OAM-encoded D2NN.
... Optical neural networks represent a new and exciting direction in deep learning architecture, utilizing the propagation of light waves and modulation of the light field with optical devices to achieve ultra-fast computational speeds. Recent research has proposed various structures, including optical convolution networks [16,17], Mach-Zehnder interferometer-based optical networks [18][19][20], optical spiking neural networks [21,22], and diffractive deep neural networks (D2NNs) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Due to D2NNs' simple structure with high parallel operation and low cost, there has been significant interest in D2NN research over the past few years, including increasing the networks' computation ability [24][25][26][27][28][29] In this study, we investigated the feasibility of using visible light as the light source for the all-optical D2NN. ...
... The detectors collect the final intensity of light, and once the input image is loaded, the distribution of light intensity can be directly seen at the detectors immediately, which represents the result of the network processing. Since the all-optical network has a forward inference speed similar to light, it has been reported in many fields [34][35][36][37][49][50][51]. Table 3. ...
A deep diffractive neural network (D2NN) is a fast optical computing structure that has been widely used in image classification, logical operations, and other fields. Computed tomography (CT) imaging is a reliable method for detecting and analyzing pulmonary nodules. In this paper, we propose using an all-optical D2NN for pulmonary nodule detection and classification based on CT imaging for lung cancer. The network was trained based on the LIDC-IDRI dataset, and the performance was evaluated on a test set. For pulmonary nodule detection, the existence of nodules scanned from CT images were estimated with two-class classification based on the network, achieving a recall rate of 91.08% from the test set. For pulmonary nodule classification, benign and malignant nodules were also classified with two-class classification with an accuracy of 76.77% and an area under the curve (AUC) value of 0.8292. Our numerical simulations show the possibility of using optical neural networks for fast medical image processing and aided diagnosis.
... Despite the fact that on-chip photonic neural networks are robust and have a small footprint, the 3D free-space diffractive optical neural network (DONN) has also become a major platform for photonic artificial intelligence (AI). DONN represents a deep neural network based on freespace optical propagation, diffraction, and scattering [4][5][6][7][8][9][10][11]. It essentially comprises a series of diffractive thin layers that can modulate the wavefront in a pixel-wise fashion to construct a deeply connected network whose preliminary form is an ordinary neural network [4]. ...
... Note that the phase modulation coefficients represent the trainable weights of the DONN. To this end, various DONNs have been successfully applied in image classification [4][5][6][7], quantitative phase imaging [8], holographic display [10], structured beam manipulation and recognition [12][13][14], multichannel interfering [15], on-chip optical neural networks [16,17], single-bit optical logic operations [9], etc. ...
... For instance, it is often desirable to use one set of optical signals to address and/or control another set of optical information [27]. In parallel with the DONN development towards AI inference, DONN-based optical logic gates have been attracting much attention [9,[28][29][30][31]. In practical implementations, the logic values are usually encoded at the input and output planes of the DONN using two spatially separated apertures (e.g., at a relative separation d a ), and the logic operation is defined/judged by the relative power between them. ...
Optical computing has gained much attention due to its high speed, low energy consumption, and the fact that it is naturally parallelizable and multiplexable, etc. Single-bit optical logic gates based on a four-hidden-layer diffractive optical neural network (DONN) have been demonstrated with paired apertures. Here, we show a parallel-logic operation strategy based on two-hidden-layer DONN, showcasing their efficiency by multiple-bit (up to 16-bit) optical logic (e.g., NAND) operations. In addition, we demonstrate how NAND-DONN units can be utilized to achieve NOR and AND operations by flipping and cascading the DONN.
... Computing using diffractive networks possesses the benefits of high speed, parallelism, and low power consumption: the computational task of interest is completed while the incident light passes through passive thin diffractive layers at the speed of light, requiring no energy other than illumination. This framework's success and capabilities were demonstrated numerically and experimentally by achieving various computational tasks, including object classification [28][29][30][31] , hologram reconstruction 32 , quantitative phase imaging 33 , privacy-preserving class-specific imaging 34 , logic operations 35,36 , universal linear transformations 37 , and polarization processing 38 , among others [39][40][41][42][43][44][45][46][47][48] . Diffractive networks can also process and shape the phase and amplitude of broadband input spectra to perform various tasks such as pulse shaping 49 , wavelength-division multiplexing 50 , and single-pixel image classification 51 . ...
Classification of an object behind a random and unknown scattering medium sets a challenging task for computational imaging and machine vision fields. Recent deep learning-based approaches demonstrated the classification of objects using diffuser-distorted patterns collected by an image sensor. These methods demand relatively large-scale computing using deep neural networks running on digital computers. Here, we present an all-optical processor to directly classify unknown objects through unknown, random phase diffusers using broadband illumination detected with a single pixel. A set of transmissive diffractive layers, optimized using deep learning, forms a physical network that all-optically maps the spatial information of an input object behind a random diffuser into the power spectrum of the output light detected through a single pixel at the output plane of the diffractive network. We numerically demonstrated the accuracy of this framework using broadband radiation to classify unknown handwritten digits through random new diffusers, never used during the training phase, and achieved a blind testing accuracy of 87.74 ± 1.12%. We also experimentally validated our single-pixel broadband diffractive network by classifying handwritten digits "0" and "1" through a random diffuser using terahertz waves and a 3D-printed diffractive network. This single-pixel all-optical object classification system through random diffusers is based on passive diffractive layers that process broadband input light and can operate at any part of the electromagnetic spectrum by simply scaling the diffractive features proportional to the wavelength range of interest. These results have various potential applications in, e.g., biomedical imaging, security, robotics, and autonomous driving.
