Unitary learning is a backpropagation that serves to unitary weights update in deep complex-valued neural network with full connections, meeting a physical unitary prior in diffractive deep neural network ([DN]2). However, the square matrix property of unitary weights induces that the function signal has a limited dimension that could not generalize well. To address the overfitting problem that comes from the small samples loaded to [DN]2, an optical phase dropout trick is implemented. Phase dropout in unitary space that is evolved from a complex dropout and has a statistical inference is formulated for the first time. A synthetic mask recreated from random point apertures with random phase-shifting and its smothered modulation tailors the redundant links through incompletely sampling the input optical field at each diffractive layer. The physical features about the synthetic mask using different nonlinear activations are elucidated in detail. The equivalence between digital and diffractive model determines compound modulations that could successfully circumvent the nonlinear activations physically implemented in [DN]2. The numerical experiments verify the superiority of optical phase dropout in [DN]2 to enhance accuracy in 2D classification and recognition tasks-oriented.
In optical devices like diffraction gratings and Fresnel lenses, light wavefront is engineered through the structuring of device surface morphology, within thicknesses comparable to the light wavelength. Fabrication of such diffractive optical elements involves highly accurate multi-step lithographic processes that in fact set into stone both the device morphology and optical functionality. In this work, we introduce shapeshifting diffractive optical elements directly written on an erasable photoresist. We first develop a lithographic configuration that allows writing/erasing cycles of aligned…
Peng Cheng Laboratory（鹏城实验室）；Tianjin University（天津大学）；Beijing Normal University（北京师范大学）；Hebei University of Technology（河北工业大学）
The multiplexing and de-multiplexing of orbital angular momentum (OAM) beams are critical issues in optical communication. Optical diffractive neural networks have been introduced to perform classification, generation, multiplexing and de-multiplexing of OAM beams. However, conventional diffractive neural networks cannot handle OAM modes with a varying spatial distribution of polarization directions. Herein, we propose a polarized optical deep diffractive neural network that is designed based on the concept of rectangular micro-structure meta-material. Our proposed polarized optical diffractiv…
Owing to its potential advantages such as scalability, low latency and power efficiency, optical computing has seen rapid advances over the last decades. A core unit of a potential all-optical processor would be the NAND gate, which can be cascaded to perform an arbitrary logical operation. 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 gate using the relative optical power of two spatially-separated apertures. Based on this architecture, we numer…
Diffractive deep neural network (DNNet) is a novel machine learning framework on the modulation of optical transmission. Diffractive network would get predictions at the speed of light. It's pure passive architecture, no additional power consumption. We improved the accuracy of diffractive network with optical waves at different frequency. Each layers have multiple frequency-channels (optical distributions at different frequency). These channels are merged at the output plane to get final output. The experiment in the fasion-MNIST and EMNIST datasets showed multiple frequency-channels would in…
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute（加州纳米系统研究所）
Diffractive deep neural networks have been introduced earlier as an optical machine learning framework that uses task-specific diffractive surfaces designed by deep learning to all-optically perform inference, achieving promising performance for object classification and imaging. Here we demonstrate systematic improvements in diffractive optical neural networks based on a differential measurement technique that mitigates the non-negativity constraint of light intensity. In this scheme, each class is assigned to a separate pair of photodetectors, behind a diffractive network, and the class infe…
The orbital angular momentum (OAM) of light has recently attracted a growing interest as a new degree of freedom in order to increase the information capacity of today optical networks both for free-space and optical fiber transmission. Here we present our work of design, fabrication and optical characterization of diffractive optical elements for compact OAM-mode division demultiplexing based on optical transformations. Samples have been fabricated with 3D high-resolution electron beam lithography on polymethylmethacrylate (PMMA) resist layer spun over a glass substrate. Their high compactnes…
We propose an efficient inverse design approach for multifunctional optical elements based on adaptive deep diffractive neural networks (a-D$^2$NNs). Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devices that can selectively focus incident radiation over two well-separated spectral bands at desired distances. We investigate focusing efficiencies at two wavelengths and achieve targeted spectral lineshapes and spatial point-spread functions (PSFs) with optimal focusing efficiency. In particular, we demonstrate control of the spectral bandwidths at separate focal position…
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute（加州纳米系统研究所）；David Geffen School of Medicine（戴维·格芬医学院）
Permutation matrices form an important computational building block frequently used in various fields including e.g., communications, information security and data processing. Optical implementation of permutation operators with relatively large number of input-output interconnections based on power-efficient, fast, and compact platforms is highly desirable. Here, we present diffractive optical networks engineered through deep learning to all-optically perform permutation operations that can scale to hundreds of thousands of interconnections between an input and an output field-of-view using p…
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute (CNSI)（加州纳米系统研究所（CNSI））
Research on optical computing has recently attracted significant attention due to the transformative advances in machine learning. Among different approaches, diffractive optical networks composed of spatially-engineered transmissive surfaces have been demonstrated for all-optical statistical inference and performing arbitrary linear transformations using passive, free-space optical layers. Here, we introduce a polarization multiplexed diffractive processor to all-optically perform multiple, arbitrarily-selected linear transformations through a single diffractive network trained using deep lea…
Decision-making and control with diffractive optical networks
School of Physics and Materials Science, Nanchang University（南昌大学物理与材料科学学院）；Institute for Advanced Study, Nanchang University（南昌大学高等研究院）；School of Physics and Electronic Science, East China Normal University（华东师范大学物理与电子科学学院）；School of Engineering and Information Technology, University of New South Wales Canberra（新南威尔士大学堪培拉校区工程与信息技术学院）
In this paper, a novel method is proposed, and employed to design a single diffractive optical element (DOE) for implementing spectrum-splitting and beam-concentration (SSBC) functions simultaneously. We develop an optimization algorithm, through which the SSBC DOE can be optimized within an arbitrary thickness range, according to the limitations of modern photolithography technology. Theoretical simulation results reveal that the designed SSBC DOE has a high optical focusing efficiency. It is expected that the designed SSBC DOE should have practical applications in high-efficiency solar cell …
We characterize the loading, containment and optical properties of all-optical atom traps implemented by diffractive focusing with one-dimensional (1D) microstructures milled on gold films. These on-chip Fresnel lenses with focal lengths of the order of a few hundred microns produce optical-gradient-dipole traps. Cold atoms are loaded from a mirror magneto-optical trap (MMOT) centered a few hundred microns above the gold mirror surface. Details of loading optimization are reported and perspectives for future development of these structures are discussed.
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；California NanoSystems Institute（加州纳米系统研究所）；David Geffen School of Medicine（戴维·格芬医学院）
In their Comment, Wei et al. (arXiv:1809.08360v1 [cs.LG]) claim that our original interpretation of Diffractive Deep Neural Networks (D2NN) represent a mischaracterization of the system due to linearity and passivity. In this Response, we detail how this mischaracterization claim is unwarranted and oblivious to several sections detailed in our original manuscript (Science, DOI: 10.1126/science.aat8084) that specifically introduced and discussed optical nonlinearities and reconfigurability of D2NNs, as part of our proposed framework to enhance its performance. To further refute the mischaracter…
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute（加州纳米系统研究所）；David Geffen School of Medicine（大卫·格芬医学院）
We introduce an all-optical Diffractive Deep Neural Network (D2NN) architecture that can learn to implement various functions after deep learning-based design of passive diffractive layers that work collectively. We experimentally demonstrated the success of this framework by creating 3D-printed D2NNs that learned to implement handwritten digit classification and the function of an imaging lens at terahertz spectrum. With the existing plethora of 3D-printing and other lithographic fabrication methods as well as spatial-light-modulators, this all-optical deep learning framework can perform, at …
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, inferen…
A diffractive optical element (DOE) has been fabricated for creating blue detuned atomic bottle beam traps. The DOE integrates several diffractive lenses for trap creation and imaging of atomic fluorescence. We characterize the performance of the DOE and demonstrate trapping of cold Cesium atoms inside a bottle beam.
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 tunable, single passband as well as dual passband spectral filt…
In recent years, mode-division multiplexing (MDM) has been proposed as a promising solution in order to increase the information capacity of optical networks both in free-space and in optical fiber transmission. Here we present the design, fabrication and test of diffractive optical elements for mode-division multiplexing based on optical transformations in the visible range. Diffractive optics have been fabricated by means of 3D high-resolution electron beam lithography on polymethylmethacrylate resist layer spun over a glass substrate. The same optical sequence was exploited both for input-m…
University of Utah（犹他大学）；Tsinghua University（清华大学）；Purdue University（普渡大学）
Diffractive optical neural networks (DONNs) have been emerging as a high-throughput and energy-efficient hardware platform to perform all-optical machine learning (ML) in machine vision systems. However, the current demonstrated applications of DONNs are largely straightforward image classification tasks, which undermines the prospect of developing and utilizing such hardware for other ML applications. Here, we numerically and experimentally demonstrate the deployment of an all-optical reconfigurable DONNs system for scientific computing, including guiding two-dimensional quantum material synt…
Vector optical vortices exhibit complex polarisation patterns due to the interplay between spin and orbital angular momenta. Here we demonstrate, both analytically and with simulations, that certain polarisation features of optical vortex beams maintain constant transverse spatial dimensions independently of beam divergence due to diffraction. These polarisation features appear in the vicinity of the phase singularity and are associated with the presence of longitudinal electric fields. The predicted effect may prove important in metrology and high resolution imaging applications.
Diffractive optical neural networks have shown promising advantages over electronic circuits for accelerating modern machine learning (ML) algorithms. However, it is challenging to achieve fully programmable all-optical implementation and rapid hardware deployment. Furthermore, understanding the threat of adversarial ML in such system becomes crucial for real-world applications, which remains unexplored. Here, we demonstrate a large-scale, cost-effective, complex-valued, and reconfigurable diffractive all-optical neural networks system in the visible range based on cascaded transmissive twiste…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；California NanoSystems Institute（加州纳米系统研究所）
We report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o represent the number of pixels at the input and output fields-of-view (FOVs), respectively. First, we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach, we also consider a deep learning-…
Atomic systems have long provided a useful material platform with unique quantum properties. The efficient light-matter interaction in atomic vapors has led to numerous seminal scientific achievements including accurate and precise metrology and quantum devices. In the last few decades, the field of thin optical elements with miniscule features has been extensively studied demonstrating an unprecedented ability to control photonic degrees of freedom, both linearly and non-linearly, with applications spanning from photography and spatial light modulators to cataract surgery implants. Hybridizat…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；California NanoSystems Institute (CNSI)（加州纳米系统研究所）
A plethora of research advances have emerged in the fields of optics and photonics that benefit from harnessing the power of machine learning. Specifically, there has been a revival of interest in optical computing hardware, due to its potential advantages for machine learning tasks in terms of parallelization, power efficiency and computation speed. Diffractive Deep Neural Networks (D2NNs) form such an optical computing framework, which benefits from deep learning-based design of successive diffractive layers to all-optically process information as the input light diffracts through these pass…
Several laws are found for the Diffractive Deep Neural Networks (D2NN). They reveal the inner product of any two light fields in D2NN is invariant and the D2NN act as a unitary transformation for optical fields. If the output intensities of the two inputs are separated spatially, the input fields must be orthogonal. These laws imply that the D2NN is not only suitable for the classification of general objects but also more suitable for applications aim to the optical orthogonal modes. Additionally, our simulation shows D2NN do well in applications like mode conversion, mode multiplexer, and opt…
University of California, Los Angeles（加州大学洛杉矶分校）；California NanoSystems Institute (CNSI)（加州纳米系统研究所）
Diffractive deep neural networks (D2NNs) define an all-optical computing framework comprised of spatially engineered passive surfaces that collectively process optical input information by modulating the amplitude and/or the phase of the propagating light. Diffractive optical networks complete their computational tasks at the speed of light propagation through a thin diffractive volume, without any external computing power while exploiting the massive parallelism of optics. Diffractive networks were demonstrated to achieve all-optical classification of objects and perform universal linear tran…
Photonic neural networks perform brain-inspired computations using photons instead of electrons that can achieve substantially improved computing performance. However, existing architectures can only handle data with regular structures, e.g., images or videos, but fail to generalize to graph-structured data beyond Euclidean space, e.g., social networks or document co-citation networks. Here, we propose an all-optical graph representation learning architecture, termed diffractive graph neural network (DGNN), based on the integrated diffractive photonic computing units (DPUs) to address this lim…
We demonstrate a reconfigurable optical filter implemented using a phase-only two-dimensional liquid crystal on silicon spatial light modulator. To achieve this we utilize two different approaches leading to two different configurations in the modulator. The first one, based on a spatially patterned diffractive lens permits to obtain the desired spectrum along the optical axis and, in the second one, based on a generalized spectrometer, it is found outside of the optical axis. Experimental results show good agreement with the theory and indicate the validity of this technique.
Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology, Tsinghua University（清华大学北京国家信息科学与技术研究中心）；Institute for Brain and Cognitive Sciences, Tsinghua University（清华大学脑与认知科学研究所）；Beijing Laboratory of Brain and Cognitive Intelligence, Beijing Municipal Education Commission（北京市脑与认知智能实验室，北京市教育委员会）
Photonic neural networks are brain-inspired information processing technology using photons instead of electrons to perform artificial intelligence (AI) tasks. However, existing architectures are designed for a single task but fail to multiplex different tasks in parallel within a single monolithic system due to the task competition that deteriorates the model performance. This paper proposes a novel optical multi-task learning system by designing multi-wavelength diffractive deep neural networks (D2NNs) with the joint optimization method. By encoding multi-task inputs into multi-wavelength ch…
University of California Los Angeles (UCLA)（加州大学洛杉矶分校）；California NanoSystems Institute (CNSI)（加州纳米系统研究所）
Quantitative phase imaging (QPI) is a label-free computational imaging technique that provides optical path length information of specimens. In modern implementations, the quantitative phase image of an object is reconstructed digitally through numerical methods running in a computer, often using iterative algorithms. Here, we demonstrate a diffractive QPI network that can synthesize the quantitative phase image of an object by converting the input phase information of a scene into intensity variations at the output plane. A diffractive QPI network is a specialized all-optical processor design…
Recent research efforts in optical computing have gravitated towards developing optical neural networks that aim to benefit from the processing speed and parallelism of optics/photonics in machine learning applications. Among these endeavors, Diffractive Deep Neural Networks (D2NNs) harness light-matter interaction over a series of trainable surfaces, designed using deep learning, to compute a desired statistical inference task as the light waves propagate from the input plane to the output field-of-view. Although, earlier studies have demonstrated the generalization capability of diffractive …
We report deep learning-based design of a massively parallel broadband diffractive neural network for all-optically performing a large group of arbitrarily-selected, complex-valued linear transformations between an input and output field-of-view, each with N_i and N_o pixels, respectively. This broadband diffractive processor is composed of N_w wavelength channels, each of which is uniquely assigned to a distinct target transformation. A large set of arbitrarily-selected linear transformations can be individually performed through the same diffractive network at different illumination waveleng…
Fabrication of large area (sub 1 cm cross-section) micro-optical components in a short period of time (approximately 10 min) and with lesser number of processing steps is highly desirable and cost-effective. In the recent years, femtosecond laser fabrication technology has revolutionized the field of manufacturing by offering the above capabilities. In this study, a fundamental diffractive optical element, binary axicon i.e axicon with two phase or amplitude levels, has been designed in three configurations namely conventional axicon, photon sieve axicon (PSA) and sparse PSA and directly mille…
Optical machine learning offers advantages in terms of power efficiency, scalability and computation speed. Recently, an optical machine learning method based on Diffractive Deep Neural Networks (D2NNs) has been introduced to execute a function as the input light diffracts through passive layers, designed by deep learning using a computer. Here we introduce improvements to D2NNs by changing the training loss function and reducing the impact of vanishing gradients in the error back-propagation step. Using five phase-only diffractive layers, we numerically achieved a classification accuracy of 9…
