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For many years, optics has been employed in computing, although the major focus has been and remains to be on connecting parts of computers, for communications, or more fundamentally in systems that have some optical function or element (optical pattern recognition, etc.). Optical digital computers are still evolving; however, a variety of components that can eventually lead to true optical computers, such as optical logic gates, optical switches, neural networks, and spatial light modulators have previously been developed and are discussed in this paper. High-performance off-the-shelf computers can accurately simulate and construct more complicated photonic devices and systems. These advancements have developed under unusual circumstances: photonics is an emerging tool for the next generation of computing hardware, while recent advances in digital computers have empowered the design, modeling, and creation of a new class of photonic devices and systems with unparalleled challenges. Thus, the review of the status and perspectives shows that optical technology offers incredible developments in computational efficiency; however, only separately implemented optical operations are known so far, and the launch of the world’s first commercial optical processing system was only recently announced. Most likely, the optical computer has not been put into mass production because there are still no good solutions for optical transistors, optical memory, and much more that acceptance to break the huge inertia of many proven technologies in electronics.

Rapidly growing demands for high-performance computing, powerful data processing, and big data necessitate the advent of novel optical devices to perform demanding computing processes effectively. Due to its unprecedented growth in the past two decades, the field of meta-optics offers a viable solution for spatially, spectrally, and/or even temporally sculpting amplitude, phase, polarization, and/or dispersion of optical wavefronts. In this review, we discuss state-of-the-art developments, as well as emerging trends, in computational metastructures as disruptive platforms for spatial optical analog computation. Two fundamental approaches based on general concepts of spatial Fourier transformation and Green’s function (GF) are discussed in detail. Moreover, numerical investigations and experimental demonstrations of computational optical surfaces and metastructures for solving a diverse set of mathematical problems (e.g., integrodifferentiation and convolution equations) necessary for on-demand information processing (e.g., edge detection) are reviewed. Finally, we explore the current challenges and the potential resolutions in computational meta-optics followed by our perspective on future research directions and possible developments in this promising area.

As a revolutionary observation tool in life science, biomedical, and material science, optical microscopy allows imaging of samples with high spatial resolution and a wide field of view. However, conventional microscopy methods are limited to single imaging and cannot accomplish real-time image processing. The edge detection, image enhancement and phase visualization schemes have attracted great interest with the rapid development of optical analog computing. The two main physical mechanisms that enable optical analog computing originate from two geometric phases: the spin-redirection Rytov-Vlasimirskii-Berry (RVB) phase and the Pancharatnam-Berry (PB) phase. Here, we review the basic principles and recent research progress of the RVB phase and PB phase based optical differentiators. Then we focus on the innovative and emerging applications of optical analog computing in microscopic imaging. Optical analog computing is accelerating the transformation of information processing from classical imaging to quantum techniques. Its intersection with optical microscopy opens opportunities for the development of versatile and compact optical microscopy systems.

Wave-based signal processing has witnessed a significant expansion of interest in a variety of science and engineering disciplines, as it provides new opportunities for achieving high-speed and low-power operations. Although flat optics desires integrable components to perform multiple missions, yet, the current wave-based computational metasurfaces can engineer only the spatial content of the input signal where the processed signal obeys the traditional version of Snell’s law. In this paper, we propose a multi-functional metagrating to modulate both spatial and angular properties of the input signal whereby both symmetric and asymmetric optical transfer functions are realized using high-order space harmonics. The performance of the designed compound metallic grating is validated through several investigations where closed-form expressions are suggested to extract the phase and amplitude information of the diffractive modes. Several illustrative examples are demonstrated to show that the proposed metagrating allows for simultaneous parallel analog computing tasks such as first- and second-order spatial differentiation through a single multichannel structured surface. It is anticipated that the designed platform brings a new twist to the field of optical signal processing and opens up large perspectives for simple integrated image processing systems.

Recently, the study of analog optical computing raised renewed interest due to its natural advantages of parallel, high speed and low energy consumption over conventional digital counterpart, particularly in applications of big data and high-throughput image processing. The emergence of metamaterials or metasurfaces in the last decades offered unprecedented opportunities to arbitrarily manipulate the light waves within subwavelength scale. Metamaterials and metasurfaces with freely controlled optical properties have accelerated the progress of wave-based analog computing and are emerging as a practical, easy-integration platform for optical analog computing. In this review, the recent progress of metamaterial-based spatial analog optical computing is briefly reviewed. We first survey the implementation of classical mathematical operations followed by two fundamental approaches (metasurface approach and Green’s function approach). Then, we discuss recent developments based on different physical mechanisms and the classical optical simulating of quantum algorithms are investigated, which may lead to a new way for high-efficiency signal processing by exploiting quantum behaviors. The challenges and future opportunities in the booming research field are discussed.

Photonic integrated circuits (PICs) have been a research hotspot in recent years. Programmable PICs that have the advantages of versatility and reconfigurability that can realize multiple functions through a common structure have been especially popular. Leveraging on-chip couplers and phase shifters, general-purpose waveguide meshes connected in different topologies can be manipulated at run-time and support a variety of applications. However, current waveguide meshes suffer from relatively a low cell amount and limited bandwidth. Here, we demonstrate a reconfigurable photonic integrated computing chip based on a quadrilateral topology network, where typical analog computing functions, including temporal differentiation, integration, and Hilbert transformation, are implemented with a processing bandwidth of up to 40 GHz. By configuring an optical path and changing the splitting ratio of the optical switches in the network, the functions can be switched and the operation order can be tuned. This approach enables wideband analog computing of large-scale PICs in a cost-effective, ultra-compact architecture.

The burgeoning demand for high-performance computing, robust data processing, and rapid growth of big data necessitates the emergence of novel optical devices to efficiently execute demanding computational processes. The field of meta-devices, such as metamaterial or metasurface, has experienced unprecedented growth over the past two decades. By manipulating the amplitude, phase, polarization, and dispersion of light wavefronts in spatial, spectral, and temporal domains, viable solutions for the implementation of all-optical analog computation and information processing have been provided. In this review, we summarize the latest developments and emerging trends of computational meta-devices as innovative platforms for spatial optical analog differentiators and information processing. Based on the general concepts of spatial Fourier transform and Green’s function, we analyze the physical mechanisms of meta-devices in the application of amplitude differentiation, phase differentiation, and temporal differentiation and summarize their applications in image edge detection, image edge enhancement, and beam shaping. Finally, we explore the current challenges and potential solutions in optical analog differentiators and provide perspectives on future research directions and possible developments.

Optical analog computing has natural advantages of parallel computation, high speed and low energy consumption over traditional digital computing. To date, research in the field of on-chip optical analog computing has mainly focused on classical mathematical operations. Despite the advantages of quantum computing, on-chip quantum analog devices based on metasurfaces have not been demonstrated so far. In this work, based on a silicon-on-insulator (SOI) platform, we illustrated an on-chip quantum searcher with a characteristic size of 60 × 20 μm2. We applied classical waves to simulate the quantum search algorithm based on the superposition principle and interference effect, while combining it with an on-chip metasurface to realize modulation capability. The marked items are found when the incident waves are focused on the marked positions, which is precisely the same as the efficiency of the quantum search algorithm. The proposed on-chip quantum searcher facilitates the miniaturization and integration of wave-based signal processing systems.

Analog optical computing (AOC) has attracted great attention over the past few years, because of its ultra-high speed (potential for real-time processing), ultra-low power consumption, and parallel processing capabilities. In this article, we design an adder and an ordinary differential equation solver (ODE) on chip by Fourier optics and metasurface techniques. The device uses the 4f system consisting of two metalenses on both sides and one middle metasurface (MMS) as the basic structure. The MMS that performs the computing is the core of the device and can be designed for different applications, i.e., the adder and ODE solver in this article. For the adder, through the comparison of the two input and output signals, the effect of the addition can be clearly displayed. For the ODE solver, as a proof-of-concept demonstration, a representative optical signal is well integrated into the desired output distribution. The simulation result fits well with the theoretical expectation, and the similarity coefficient is 98.28%. This solution has the potential to realize more complex and high-speed artificial intelligence computing. Meanwhile, based on the direct-binary-search (DBS) algorithm, we design a signal generator that can achieve power splitting with the phase difference of π between the two output waveguides. The signal generator with the insertion loss of −1.43 dB has an ultra-compact footprint of 3.6 μm× 3.6 μm. It can generate a kind of input signal for experimental verification to replace the hundreds of micrometers of signal generator composed of a multi-mode interference (MMI) combination used in the verification of this type of device in the past.

We review a novel paradigm that has emerged in analogue neuromorphic optical computing. The goal is to implement a reservoir computer in optics, where information is encoded in the intensity and phase of the optical field. Reservoir computing is a bio-inspired approach especially suited for processing time-dependent information. The reservoir’s complex and high-dimensional transient response to the input signal is capable of universal computation. The reservoir does not need to be trained, which makes it very well suited for optics. As such, much of the promise of photonic reservoirs lies in their minimal hardware requirements, a tremendous advantage over other hardware-intensive neural network models. We review the two main approaches to optical reservoir computing: networks implemented with multiple discrete optical nodes and the continuous system of a single nonlinear device coupled to delayed feedback.