Metalens Array for Complex‐Valued Optical Discrete Fourier Transform

Combined optic system based on polycapillary X-ray optics and single-bounce monocapillary optics for focusing X-rays from a conventional laboratory X-ray source

The rapid rise of machine learning drives demand for extensive matrix-vector multiplication operations, thereby challenging the capacities of traditional von Neumann computing systems. Researchers explore alternatives, such as in-memory computing architecture, to find energy-efficient solutions. In particular, there is renewed interest in optical computing systems, which could potentially handle matrix-vector multiplication in a more energy-efficient way. Despite promising initial results, developing high-throughput optical computing systems to rival electronic hardware remains a challenge. Here, we propose and demonstrate a hyperspectral in-memory computing architecture, which simultaneously utilizes space and frequency multiplexing, using optical frequency combs and programmable optical memories. Our carefully designed three-dimensional opto-electronic computing system offers remarkable parallelism, programmability, and scalability, overcoming typical limitations of optical computing. We have experimentally demonstrated highly parallel, single-shot multiply-accumulate operations with precision exceeding 4 bits in both matrix-vector and matrix-matrix multiplications, suggesting the system’s potential for a wide variety of deep learning and optimization tasks. Our approach presents a realistic pathway to scale beyond peta operations per second, a major stride towards high-throughput, energy-efficient optical computing.

In this paper, we propose an optical scheme of on-chip matrixing for matrix-vector multiplications (MVMs) by configuring each matrix element into a photonic tensor processing unit (TPU) with wavelength division multiplexing and the actively tunable weighting for scalar multiplication. The low loss chalcogenide phase change material of Ge2Sb2Se4Te (GSST) is employed and modeled with intermediate states for multilevel tunable weighting of each TPU. The dynamic electro-thermal process of GSST phase transition using ITO for electrical heating is simulated and well confirms the switchable weighting of TPUs. Simulation results reveal that a 7 V voltage pulse of 500 ns duration followed by a 9 V voltage pulse of 1500 ns duration and another pulse of 14 V voltage and 500 ns duration can set data value of ‘0’ and ‘1’ for each TPU. Taking a set of incident light with varied wavelengths and powers as input vectors, the quantized MVM outputs of photocurrents with varied amplitude are obtained after photoelectric conversion. Finally, the photonic integrated circuit level simulations by Lumerical INTERCONNECT perfectly confirm our scheme of on-chip matrixing for optical MVMs and computing.

The interferometric signal processing method for localizing a broadband moving sound source in shallow water is proposed and studied theoretically and experimentally in the paper. The field of a moving sound source creates in waveguide a stable interference pattern of the intensity distribution (interferogram) in the frequency-time domain. Sound intensity is accumulated along interference fringes over the observation time. The two-dimensional Fourier transform (2D-FT) is applied to analyze the interferogram. The result of the 2D-FT of the interferogram is called the Fourier-hologram (hologram). The mathematical theory of hologram structure is developed in the present paper. It is shown that the hologram allows to coherently accumulate the sound intensity of the interferogram in a relatively small area as focal spots. The presence of these focal spots is the result of interference of acoustic modes with different numbers. The main result of our paper is a simple relationship between the focal spots coordinates on the hologram and the source range, velocity, and motion direction. The proposed interferometric signals processing method for the source localization is validated using the data of acoustic experiment and numerical modeling. [This research was supported by the RFBR (19-29-06075, 19-38-90326).]

We present a number of computational complexity results for an optical model of computation called the continuous space machine. We also describe an implementation for an optical computing algorithm that can be easily defined within the model. Our optical model is designed to model a wide class of optical computers, such as matrix vector multipliers and pattern recognition architectures. It is known that the model solves intractable PSPACE problems in polynomial time, and NC problems in polylogarithmic time. Both of these results use large spatial resolution (number of pixels). Here we look at what happens when we have constant spatial resolution. It turns out that we obtain similar results by exploiting other resources, such as dynamic range and amplitude resolution. However, with certain other restrictions we essentially have a sequential device. Thus we are exploring the border between parallel and sequential computation in optical computing. We describe an optical architecture for the unordered search problem of finding a one in a list of zeros. We argue that our algorithm scales well, and is relatively straightforward to implement. This problem is easily parallelisable and is from the class NC. We go on to argue that the optical computing community should focus their attention on problems within P (and especially NC), rather than developing systems for tackling intractable problems.KeywordsPolynomial TimeDiscrete Fourier TransformTuring MachineSpatial Light ModulatorPolynomial FactorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The formation of a transversally polarized beam by transmitting a tightly focused double-ring-shaped azimuthally polarized beam through a complex spiral phase mask and high numerical aperture lens is presented based on vector diffraction theory. The generation of transversally polarized focal spot segment splitting and multiple focal spots is illustrated numerically. Moreover, we found that a properly designed complex spiral phase mask can move the focal spots along the optical axis in the z direction. Therefore, one can achieve a focal segment of two, three or multiple completely transversely polarized focal spots, which finds applications in optical trapping and in material processing technologies.

Proteins have been utilized in numerous photonic and optoelectronic devices, for example, in optical computation, organic light emitting diodes (OLEDs), waveguides, biomicro/nanolasers, organic field effect transistors (OFETs), and memory devices, because their unique optical, mechanical, electrical, and chemical properties are easily tailored to each application. The performance of as-prepared proteinbased photonic devices has been demonstrated to exceed that of devices that are made with currently available organic materials. The underlying motivation for the use of proteins in microdevices is not only abundance, inexpensiveness, and biodegradability, but also biocompatibility and the capacity to tune their properties through appropriate external stimuli. These features are highly desirable for biologically inspired microdevices, for example delicate miniaturized lenses that are similar to the “camera-type” eyes of human beings, the compound eyes of insects, the photosensitive microlens arrays of brittlestars, or the infrared-sensitive microlens receptor arrays of the fire beetle (Melanophila acuminata). Scientists have been highly motivated to fabricate these lens-like micro/nanostructures with the aim of producing small, multifunctional, artificial eyes by using dynamically adjustable and fully biocompatible proteins. However, the preparation of protein microlenses that have controlled geometry and precise positioning still poses a challenge. Herein, we report a promising approach for the production of biomimetic protein microlenses by facile and rapid maskless femtosecond laser direct writing (FsLDW). FsLDW is a well-known method for producing complicated 3D structures with nanometric resolution. Recently, pioneering work from Shear and co-workers demonstrated that protein hydrogel-based microstructures fabricated by FsLDWexhibit a unique responsiveness to chemical signals. This responsiveness could result in rapid and reversible changes in the size and shape of the structures after stimulation by environmental triggers. However, to our knowledge there are few reports on the development of practical and useful devices, such as a tunable microlens, that are made from this class of proteins. In this study, commercial bovine serum albumin (BSA, 300–500 mgmL 1 in aqueous solution) and a photosensitizer (methylene blue, MB, 0.6 mgmL ) were used to fabricate micro/nanoarchitectures. The cross-linking reaction is initiated through the excitation of photosensitive molecules to their triplet states. The photoexcited molecules then react directly with oxidizable moieties (type I process) or transfer the energy to ground state molecular oxygen (type II process) to form a reactive oxygen species, such as singlet oxygen (O2). In either case, excited-state intermediates catalyze the inter or intramolecular covalent cross-linking of oxidizable protein residues (see Scheme S1 in the Supporting Information). In other words, proteins with photooxidizable groups, such as Tyr, Trp, His, Met, and Cys, can absorb infrared or UV light to form reactive or ionized species that are capable of cross-linking with other oxidizable moieties. This mechanism appears to play a role in the formation of some types of cataracts and in the aging of skin. BSA and other proteins with oxidizable side chains “inherit” this photo-cross-linking ability, and can thus be used for multiphoton fabrication (Figure 1). Proof-of-concept protein microlenses were fabricated by using a FsLDW system of our own construction (Figure 1). The system was composed of a femtosecond titanium/ sapphire laser (Spectra Physics 3960-X1BB), a piezo stage with a precision of 1 nm (Physik Instrumente P-622.ZCD), and a set of two galvano mirrors. The 3D shapes of the microstructures were designed by using 3Ds Max and then the designs were converted into computer processing programs. Prior to the photo-cross-linking of the proteins at the focal spot, the beam from the femtosecond laser (80 MHz repetition rate, 120 fs pulse width, 780 nm central wavelength) was tightly focused by a high-numerical-aperture (NA= 1.35) oilimmersion objective lens (60 ). The horizontal and vertical scanning movements of the focused laser spot were achieved simultaneously by the two-galvano-mirror set and the piezo stage. After cross-linking, the sample was rinsed in water several times to remove unreacted proteins. Then the asformed protein microstructures were left on the chip. Surface topography (shape and roughness) plays an important role in the optical properties of protein microoptics. However, the surface roughness of BSA microstruc[*] Y. L. Sun, Prof. Dr. W. F. Dong, R. Z. Yang, X. Meng, L. Zhang, Prof. Dr. Q. D. Chen, Prof. Dr. H. B. Sun State Key Laboratory on Integrated Optoelectronics College of Electronic Science and Engineering Jilin University, 2699 Qianjin Street Changchun 130012 (China) E-mail: dongwf@jlu.edu.cn hbsun@jlu.edu.cn

Noise remains one of the most significant challenges in the development of reliable and scalable quantum processors. While quantum error correction and mitigation techniques offer potential solutions, they are often limited by the substantial overhead required. To address this, tailored approaches that exploit specific hardware characteristics have emerged. In quantum computing architectures utilizing cat‐qubits, the inherent exponential suppression of bit‐flip errors can significantly reduce the qubit count needed for effective error correction. In this work, how the unique noise bias of cat‐qubits can be harnessed to enhance error mitigation efficiency is explored. Specifically, it is demonstrated that the sampling cost associated with probabilistic error cancellation (PEC) methods can be exponentially reduced with the depth of the circuit when gates act on cat‐qubits and preserve the noise bias. Similar results also hold for Clifford circuits and Pauli channels. The error mitigation scheme is benchmarked across various quantum machine learning circuits, showcasing its practical advantages for near‐term applications on cat‐qubit architectures.

Optical computing is an area of technology for information processing that utilizes excellent features of light. Beginning with some historical background of this technological field, the concept of optical computing is described with respect to definition, motivation, advantages, targets, and classifications. Then two major categories, analog optical computing and digital optical computing, are used to explain concrete instances of this technology. Analog optical computing includes Fourier image processing, acoustooptical signal processing, optical neural computing, and spatiotemporal information processing. Digital optical computing covers logic gates and circuit constructions, computing paradigms, optical computer architectures, and VLSI photonics. Finally, some comments on potential applications of optical computing are added to suggest effective areas for this technological field.

An 8-point inverse discrete cosine transform (IDCT) can be viewed as a matrix multiplication between an 8 X 8 coefficient matrix and an 8 X 1 input vector. It was shown that the matrix computations can be significantly reduced by separating the even and odd elements of the input vector. In this method, the 8 X 8 matrix multiplication is divided into two 4 X 4 matrix multiplications. The output elements are obtained by adding and subtracting the results of two matrix multiplications. On a mediaprocessor that has a large number of multipliers such as MAP1000A from Equator Technologies, we found that the vector-product algorithm yields a faster execution than other fast IDCT algorithms. This is due to the fact that a highly complex operation such as a vector product takes the same number of machine cycles as a simple operation such as a data move. MAP1000A can perform four 4-point vector products with a single instruction. We also found novel approaches to avoid moving data around in separating the even and odd elements of the input vector and in transporting the matrix between the row-wise and column-wise stages. As a result, an 8 X 8 IDCT can be computed in 60 cycles on MAP1000A, which is about 273 ns at 220 MHz clock frequency.

As a significant part in optical computation, analogue optical spatial/temporal differentiators could play a great role in all‐optical signal processing, feature extraction, and optical storage. In the past few years, they have experienced rapid development but mostly for a single function. For many scenarios, optical computation with integrated functionalities is highly desired. In this work, an analogue optical spatiotemporal differentiator utilizing all‐dielectric multilayer is proposed. The film stack is specifically engineered to satisfy the requirements for both spatial and temporal transfer functions of the ideal differentiator. The time‐space performance of the device is numerically examined from the output field profile of the classical Gaussian beam or pulse. A wavelength‐scale high resolution for edge detection is attained using the integrated differentiator. This work may pave a potential way to establish ultracompact, high‐bandwidth, and real‐time optical multiple functional computation systems.

An interferometric signal processing method for localizing a broadband moving sound source in an oceanic waveguide is proposed and studied theoretically and experimentally. The field of a moving sound source in waveguide creates a stable interference pattern of the intensity distribution (interferogram) I(ω,t) in the frequency-time domain. Sound intensity is accumulated along interference fringes over the observation time. The two-dimensional Fourier transform (2D-FT) is applied to analyze the interferogram I(ω,t). The result of the 2D-FT F(τ,ν) is called the Fourier-hologram (hologram). The mathematical theory of hologram structure F(τ,ν) is developed in the present paper. It is shown that the hologram F(τ,ν) allows the coherent accumulation of sound intensity of the interferogram in a relatively small area focal spots. The presence of these focal spots is the result of interference of acoustic modes with different wave numbers. The main result of this paper is a simple relationship between the focal spots coordinates on the hologram and the source range, velocity, and motion direction. The proposed interferometric signals processing method for source localization is validated using experimental observations and numerical modeling in the band 80-120 Hz. The estimations of source range, velocity, and motion direction are performed for different cases of source motion.

Large-scale, highly integrated and low-power-consuming hardware is becoming progressively more important for realizing optical neural networks (ONNs) capable of advanced optical computing. Traditional experimental implementations need N2 units such as Mach-Zehnder interferometers (MZIs) for an input dimension N to realize typical computing operations (convolutions and matrix multiplication), resulting in limited scalability and consuming excessive power. Here, we propose the integrated diffractive optical network for implementing parallel Fourier transforms, convolution operations and application-specific optical computing using two ultracompact diffractive cells (Fourier transform operation) and only N MZIs. The footprint and energy consumption scales linearly with the input data dimension, instead of the quadratic scaling in the traditional ONN framework. A ~10-fold reduction in both footprint and energy consumption, as well as equal high accuracy with previous MZI-based ONNs was experimentally achieved for computations performed on the MNIST and Fashion-MNIST datasets. The integrated diffractive optical network (IDNN) chip demonstrates a promising avenue towards scalable and low-power-consumption optical computational chips for optical-artificial-intelligence.

Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near term. Many state-of-the-art error-mitigation schemes use knowledge of the errors in the quantum processor, which opens up the question of the extent to which inaccuracy in the error model impacts the performance of error mitigation. In this work, we develop a methodology to efficiently compute upper bounds on the impact of error-model inaccuracy in error mitigation. Our protocols require no additional experiments and instead rely on comparisons between the error model and the error-learning data from which the model is generated. We demonstrate the efficacy of our methodology by deploying it on an IBM Quantum superconducting qubit quantum processor, and through numerical simulation of standard error models. We show that our estimated upper bounds are typically close to the worst observed performance of error mitigation on random circuits. Our methodology can also be understood as an operationally meaningful metric to assess the quality of error models and we further extend our methodology to allow for comparison between error models. Finally, contrary to what one might expect, we show that observable error in noisy layered circuits of sufficient depth is not always maximized by a Clifford circuit, which may be of independent interest.

ABSTRACTA hybrid optical processor, utlizing three programmable spatial light modulators and a CCD detector, is presented. Two digital optical architectures based on a binary number encoding technique for multiplematrix multiplication have been implemented in the system. Applications in bilinear transformations arealso described. Several experimental demonstrations are provided. 1. INTRODUCTIONOptical matrix multiplication is one of the prominent areas in optical computing. In early 1970's, Leeet al.[1] proposed a method to perform multiple matrix multiplication using Fourier transform property of lenses. Another technique was later developed by Nakano et al.[2]. They utilized a linear array of LED'salong with a combination of spherical lenses and cylindrical lenses to perform triple matrix multiplication.Several other methods have also been reported to carry out high speed matrix -matrix and triple matrixmultiplication with optics [3 -10].We shall, however, describe an encoding technique for multiple binary number, where the multiplicationsand summations of digits are performed in parallel. Nevertheless, we shall discuss two opticalarchitectures for multiple matrix multiplication (MMM) using this technique. The first architecture employsthe inner -product method to carry out multiple matrix multiplication. Grating masks are introduced intothis architecture to separate the output vectors, so that a fully parallel matrix multiplication can be