Topological analog signal processing

Reconfigurable metamaterial processing units that solve arbitrary linear calculus equations

Calculus equations serve as fundamental frameworks in mathematics, enabling describing an extensive range of natural phenomena and scientific principles, such as thermodynamics and electromagnetics. Analog computing with electromagnetic waves presents an intriguing opportunity to solve calculus equations with unparalleled speed, while facing an inevitable tradeoff in computing density and equation reconfigurability. Here, we propose a reconfigurable metamaterial processing unit (MPU) that solves arbitrary linear calculus equations at a very fast speed. Subwavelength kernels based on inverse-designed pixel metamaterials are used to perform calculus operations on time-domain signals. In addition, feedback mechanisms and reconfigurable components are used to formulate and solve calculus equations with different orders and coefficients. A prototype of this MPU with a compact planar size of 0.93λ0×0.93λ0 (λ0 is the free-space wavelength) is constructed and evaluated in microwave frequencies. Experimental results demonstrate the MPU's ability to successfully solve arbitrary linear calculus equations. With the merits of compactness, easy integration, reconfigurability, and reusability, the proposed MPU provides a potential route for integrated analog computing with high speed of signal processing.

Polarization-independent edge detection based on the spin-orbit interaction of light

In previous edge detection schemes based on the spin-orbit interaction of light, the direction and intensity of the edge-enhanced images are influenced by the incident polarization state. In this study, we develop an edge detection strategy that is insensitive to changes in both the incident polarization and the incident angle. The output intensity and transfer function remain entirely impervious to changes in incident polarization, being explicitly formulated as functions of the incident angle, specifically in terms of cot 2⁡θ i and cot⁡θ i , respectively. This behavior is attributed to the opposing nature of the polarization components E~r H-H and E~r V-V in the x-direction after undergoing mapping through the Glan polarizer, while the sum of polarization components E~r H-V and E~r V-H in the y-direction can be simplified to terms independent of incident polarization. Furthermore, we propose a metasurface design to achieve the required optical properties in order to realize the derived edge detection scheme.

Engineering topological interface states in metal-wire waveguides for broadband terahertz signal processing

Innovative terahertz waveguides are in high demand to serve as a versatile platform for transporting and manipulating terahertz signals for the full deployment of future six-generation (6G) communication systems. Metal-wire waveguides have emerged as promising candidates, offering the crucial advantage of sustaining low-loss and low-dispersion propagation of broadband terahertz pulses. Recent advances have opened up new avenues for implementing signal-processing functionalities within metal-wire waveguides by directly engraving grooves along the wire surfaces. However, the challenge remains to design novel groove structures to unlock unprecedented signal-processing functionalities. In this study, we report a plasmonic signal processor by engineering topological interface states within a terahertz two-wire waveguide. We construct the interface by connecting two multiscale groove structures with distinct topological invariants, i.e., featuring a π-shift difference in the Zak phases. The existence of this topological interface within the waveguide is experimentally validated by investigating the transmission spectrum, revealing a prominent transmission peak in the center of the topological bandgap. Remarkably, we show that this resonance is highly robust against structural disorders, and its quality factor can be flexibly controlled. This unique feature not only facilitates essential functions such as band filtering and isolating but also promises to serve as a linear differential equation solver. Our approach paves the way for the development of new-generation all-optical analog signal processors tailored for future terahertz networks, featuring remarkable structural simplicity, ultrafast processing speeds, as well as highly reliable performance.

Landslide topology uncovers failure movements

The death toll and monetary damages from landslides continue to rise despite advancements in predictive modeling. These models' performances are limited as landslide databases used in developing them often miss crucial information, e.g., underlying movement types. This study introduces a method of discerning landslide movements, such as slides, flows, and falls, by analyzing landslides' 3D shapes. By examining landslide topological properties, we discover distinct patterns in their morphology, indicating different movements including complex ones with multiple coupled movements. We achieve 80-94% accuracy by applying topological properties in identifying landslide movements across diverse geographical and climatic regions, including Italy, the US Pacific Northwest, Denmark, Turkey, and Wenchuan in China. Furthermore, we demonstrate a real-world application on undocumented datasets from Wenchuan. Our work introduces a paradigm for studying landslide shapes to understand their underlying movements through the lens of landslide topology, which could aid landslide predictive models and risk evaluations.

Local Markers for Crystalline Topology

Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches currently used to classify bulk topological crystalline phases cannot predict the existence, localization, or spectral isolation of any resulting boundary-localized modes. While interfaces between materials in different crystalline phases must have topological states at some energy, these states need not appear within the band gap, and thus may not be useful for applications. Here, we derive a class of local markers for identifying material topology due to crystalline symmetries, as well as a corresponding measure of topological protection. As our real-space-based approach is inherently local, it immediately reveals the existence and robustness of topological boundary-localized states, yielding a predictive framework for designing topological crystalline heterostructures. Beyond enabling the optimization of device geometries, we anticipate that our framework will also provide a route forward to deriving local markers for other classes of topology that are reliant upon spatial symmetries.

Dispersion engineered metasurfaces for broadband, high-NA, high-efficiency, dual-polarization analog image processing

Optical metasurfaces performing analog image processing - such as spatial differentiation and edge detection - hold the potential to reduce processing times and power consumption, while avoiding bulky 4 F lens systems. However, current designs have been suffering from trade-offs between spatial resolution, throughput, polarization asymmetry, operational bandwidth, and isotropy. Here, we show that dispersion engineering provides an elegant way to design metasurfaces where all these critical metrics are simultaneously optimized. We experimentally demonstrate silicon metasurfaces performing isotropic and dual-polarization edge detection, with numerical apertures above 0.35 and spectral bandwidths of 35 nm around 1500 nm. Moreover, we introduce quantitative metrics to assess the efficiency of these devices. Thanks to the low loss nature and dual-polarization response, our metasurfaces feature large throughput efficiencies, approaching the theoretical maximum for a given NA. Our results pave the way for low-loss, high-efficiency and broadband optical computing and image processing with free-space metasurfaces.

Uncovering and Experimental Realization of Multimodal 3D Topological Metamaterials for Low-Frequency and Multiband Elastic Wave Control

Topological mechanical metamaterials unlock confined and robust elastic wave control. Recent breakthroughs have precipitated the development of 3D topological metamaterials, which facilitate extraordinary wave manipulation along 2D planar and layer-dependent waveguides. The 3D topological metamaterials studied thus far are constrained to function in single-frequency bandwidths that are typically in a high-frequency regime, and a comprehensive experimental investigation remains elusive. In this paper, these research gaps are addressed and the state of the art is advanced through the synthesis and experimental realization of a 3D topological metamaterial that exploits multimodal local resonance to enable low-frequency elastic wave control over multiple distinct frequency bands. The proposed metamaterial is geometrically configured to create multimodal local resonators whose frequency characteristics govern the emergence of four unique low-frequency topological states. Numerical simulations uncover how these topological states can be employed to achieve polarization-, frequency-, and layer-dependent wave manipulation in 3D structures. An experimental study results in the attainment of complete wave fields that illustrate 2D topological waveguides and multi-polarized wave control in a physical testbed. The outcomes from this work provide insight that will aid future research on 3D topological mechanical metamaterials and reveal the applicability of the proposed metamaterial for wave control applications.

Solving ordinary and partial differential equations using an analog computing system based on ultrasonic metasurfaces

Wave-based analog computing has recently emerged as a promising computing paradigm due to its potential for high computational efficiency and minimal crosstalk. Although low-frequency acoustic analog computing systems exist, their bulky size makes it difficult to integrate them into chips that are compatible with complementary metal-oxide semiconductors (CMOS). This research paper addresses this issue by introducing a compact analog computing system (ACS) that leverages the interactions between ultrasonic waves and metasurfaces to solve ordinary and partial differential equations. The results of our wave propagation simulations, conducted using MATLAB, demonstrate the high accuracy of the ACS in solving such differential equations. Our proposed device has the potential to enhance the prospects of wave-based analog computing systems as the supercomputers of tomorrow.

Time derivatives via interconnected waveguides

Electromagnetic wave-based analogue computing has become an interesting computing paradigm demonstrating the potential for high-throughput, low power, and parallel operations. In this work, we propose a technique for the calculation of derivatives of temporal signals by exploiting transmission line techniques. We consider multiple interconnected waveguides (with some of them being closed-ended stubs) forming junctions. The transmission coefficient of the proposed structure is then tailored by controlling the length and number of stubs at the junction, such that the differentiation operation is applied directly onto the envelope of an incident signal sinusoidally modulated in the time domain. The physics behind the proposed structure is explained in detail and a full theoretical description of this operation is presented, demonstrating how this technique can be used to calculate higher order or even fractional temporal derivatives. We envision that these results may enable the development of further time domain wave-based analogue processors by exploiting waveguide junctions, opening new opportunities for wave-based single operators and systems.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Solving integral equations in free space with inverse-designed ultrathin optical metagratings

As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analogue optical computing enables the processing of large amounts of data at a negligible energy cost and high speeds. Based on these principles, ultrathin optical metasurfaces have been recently explored to process large images in real time, in particular for edge detection. By incorporating feedback, it has also recently been shown that metamaterials can be tailored to solve complex mathematical problems in the analogue domain, although these efforts have so far been limited to guided-wave systems and bulky set-ups. Here, we present an ultrathin Si metasurface-based platform for analogue computing that is able to solve Fredholm integral equations of the second kind using free-space visible radiation. A Si-based metagrating was inverse-designed to implement the scattering matrix synthesizing a prescribed kernel corresponding to the mathematical problem of interest. Next, a semitransparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analogue domain at the speed of light. Visible wavelength operation enables a highly compact, ultrathin device that can be interrogated from free space, implying high processing speeds and the possibility of on-chip integration.

Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification

We report on a class of architected material lattices that exploit multi-stability and kinematic amplification to independently adjust the local effective mass, damping, and stiffness properties, thereby realizing congruent alterations to the acoustic dispersion response post-fabrication. The fundamental structural tuning element permits a broad range in the effective property space; moreover, its particular design carries the benefit of tuning without altering the original size/shape of the emerging structure. The relation between the tuning element geometry and the achieved variability in effective properties is explored. Bloch's theorem facilitates the dynamic analysis of representative one- and two-dimensional (1D/2D) systems, revealing, e.g., bandgap formation, migration, and closure and positive/negative metadamping in accordance with the tuning element configuration. To demonstrate a utility, we improvise a waveguide by appropriately patterning the tuning element configuration within a 2D system. We believe that the proposed strategy offers a new way to expand the range of performance and functionality of architected materials for elastodynamics.

Visualization of transparent particles based on optical spatial differentiation

Optical analog computing operates on the amplitude, phase, polarization, and frequency distributions of the electromagnetic field through the interaction of light and matter. The differentiation operation is widely used in all-optical image processing technology, such as edge detection. Here, we propose a concise way to observe transparent particles, incorporating the optical differential operation that occurs on a single particle. The particle's scattering and cross-polarization components combine into our differentiator. We achieve high-contrast optical images of transparent liquid crystal molecules. The visualization of aleurone grains (the structures that store protein particles in plant cells) in maize seed was experimentally demonstrated with a broadband incoherent light source. Avoiding the interference of stains, our designed method provides the possibility to observe protein particles directly in complex biological tissues.

A metalens-based analog computing system for ultrasonic Fourier transform calculations

Wave-based analog computing is a new computing paradigm heralded as a potentially superior alternative to existing digital computers. Currently, there are optical and low-frequency acoustic analog Fourier transformers. However, the former suffers from phase retrieval issues, and the latter is too physically bulky for integration into CMOS-compatible chips. This paper presents a solution to these problems: the Ultrasonic Fourier Transform Analog Computing System (UFT-ACS), a metalens-based analog computer that utilizes ultrasonic waves to perform Fourier transform calculations. Through wave propagation simulations on MATLAB, the UFT-ACS has been shown to calculate the Fourier transform of various input functions with a high degree of accuracy. Moreover, the optimal selection of parameters through sufficient zero padding and appropriate truncation and bandlimiting to minimize errors is also discussed.

Mathematical operations and equation solving with reconfigurable metadevices

Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical computations or computationally-intensive optimization. Their equation-solving capabilities are applied only to matrices with special spectral (eigenvalue) distribution. Here we report the theory and design of wave-based metastructures using tunable elements capable of solving integral/differential equations in a fully-reconfigurable fashion. We consider two architectures: the Miller architecture, which requires the singular-value decomposition, and an alternative intuitive direct-complex-matrix (DCM) architecture introduced here, which does not require a priori mathematical decomposition. As examples, we demonstrate, using system-level simulation tools, the solutions of integral and differential equations. We then expand the matrix inverting capabilities of both architectures toward evaluating the generalized Moore-Penrose matrix inversion. Therefore, we provide evidence that metadevices can implement generalized matrix inversions and act as the basis for the gradient descent method for solutions to a wide variety of problems. Finally, a general upper bound of the solution convergence time reveals the rich potential that such metadevices can offer for stationary iterative schemes.

Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors

We derive asymptotic formulae describing how the properties of subwavelength devices are changed by the introduction of errors and imperfections. As a demonstrative example, we study a class of cochlea-inspired rainbow sensors. These are graded metamaterials which have been designed to mimic the frequency separation performed by the cochlea. The device considered here has similar dimensions to the cochlea and has a resonant spectrum that falls within the range of audible frequencies. We show that the device’s properties (including its role as a signal filtering device) are stable with respect to small imperfections in the positions and sizes of the resonators. Additionally, under suitable assumptions, if the number of resonators is sufficiently large, then the device’s properties are stable under the removal of a resonator.

All optical divergence and gradient operators using surface plasmon polaritons

In this paper, we propose a plasmonic structure based on Kretschmann configuration capable of performing various computational tasks, i.e. two dimensional isotropic differentiation, gradient and divergence computation. By means of two polarizers, a non-trivial topological charge can be generated in the transfer function of the structure thereby implementing a two dimensional differentiator. By using only one polarizer, on the other hand, the structure is able to compute either the gradient of the field distribution of a polarized light beam or the divergence of the field of an unpolarized light beam. The performance of the proposed structure in two dimensional differentiation has been assessed and compared with its other counterparts by a figure of merit introduced in [Opt. Express28, 898 (2020)10.1364/OE.379492]. The result proves the dominance of our two-dimensional differentiator over similar works in the literature.

Electromagnetic wave-based extreme deep learning with nonlinear time-Floquet entanglement

Wave-based analog signal processing holds the promise of extremely fast, on-the-fly, power-efficient data processing, occurring as a wave propagates through an artificially engineered medium. Yet, due to the fundamentally weak non-linearities of traditional electromagnetic materials, such analog processors have been so far largely confined to simple linear projections such as image edge detection or matrix multiplications. Complex neuromorphic computing tasks, which inherently require strong non-linearities, have so far remained out-of-reach of wave-based solutions, with a few attempts that implemented non-linearities on the digital front, or used weak and inflexible non-linear sensors, restraining the learning performance. Here, we tackle this issue by demonstrating the relevance of time-Floquet physics to induce a strong non-linear entanglement between signal inputs at different frequencies, enabling a power-efficient and versatile wave platform for analog extreme deep learning involving a single, uniformly modulated dielectric layer and a scattering medium. We prove the efficiency of the method for extreme learning machines and reservoir computing to solve a range of challenging learning tasks, from forecasting chaotic time series to the simultaneous classification of distinct datasets. Our results open the way for optical wave-based machine learning with high energy efficiency, speed and scalability.

Metasurface-Based Imagers Enabled Arbitrary Optical Convolution Processing

Using meta-imagers composed of a meta-lens and a complex-amplitude meta-modulator, all-optical convolutional processing that arbitrarily reshapes the point spread function of an optical system can now be implemented.

Meta-programmable analog differentiator

We present wave-based signal differentiation with unprecedented fidelity and flexibility by purposefully perturbing overmoded random scattering systems such that zeros of their scattering matrices lie exactly at the desired locations on the real frequency axis. Our technique overcomes limitations of hitherto existing approaches based on few-mode systems, both regarding their extreme vulnerability to fabrication inaccuracies or environmental perturbations and their inability to maintain high fidelity under in-situ adaptability. We demonstrate our technique experimentally by placing a programmable metasurface with hundreds of degrees of freedom inside a 3D disordered metallic box. Regarding the integrability of wave processors, such repurposing of existing enclosures is an enticing alternative to fabricating miniaturized devices. Our over-the-air differentiator can process in parallel multiple signals on distinct carriers and maintains high fidelity when reprogrammed to different carriers. We also perform programmable higher-order differentiation. Conceivable applications include segmentation or compression of communication or radar signals and machine vision.

Parallel wave-based analog computing using metagratings

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.

Nonlocal Scatterer for Compact Wave-Based Analog Computing

Analog computing based on wave interactions with metamaterials has been raising significant interest as a low-energy, ultrafast platform to process large amounts of data. Engineered materials can be tailored to impart mathematical operations of choice on the spatial distribution of the impinging signals, but they also require extended footprints and precise large-area fabrication, which may hinder their practical applicability. Here we show that the nonlocal response of a compact scatterer can be engineered to impart operations of choice on arbitrary impinging waves, and even to solve integro-differential equations, whose solution is observed in the scattered fields. The lack of strongly resonant phenomena makes the response robust, and the compact nature opens to scalability and cascading of these processes, paving the way to efficient, compact analog computers based on engineered microstructures.

Synthetic Three-Dimensional Z×Z_{2} Topological Insulator in an Elastic Metacrystal

We report a three-dimensional (3D) topological insulator (TI) formed by stacking identical layers of Chern insulators in a hybrid real-synthetic space. By introducing staggered interlayer hopping that respects mirror symmetry, the bulk bands possess an additional Z_{2} topological invariant along the stacking dimension, which, together with the nontrivial Chern numbers, endows the system with a Z×Z_{2} topology. A 4-tuple topological index characterizes the system's bulk bands. Consequently, two distinct types of topological surface modes (TSMs) are found localized on different surfaces. Type-I TSMs are gapless and are protected by Chern numbers, whereas type-II gapped TSMs are protected by Z_{2} bulk polarization in the stacking direction. Remarkably, each type-II TSM band is also topologically nontrivial, giving rise to second-order topological hinge modes (THMs). Both types of TSMs and the THMs are experimentally observed in an elastic metacrystal.

Mechanical computing

Mechanical mechanisms have been used to process information for millennia, with famous examples ranging from the Antikythera mechanism of the Ancient Greeks to the analytical machines of Charles Babbage. More recently, electronic forms of computation and information processing have overtaken these mechanical forms, owing to better potential for miniaturization and integration. However, several unconventional computing approaches have recently been introduced, which blend ideas of information processing, materials science and robotics. This has raised the possibility of new mechanical computing systems that augment traditional electronic computing by interacting with and adapting to their environment. Here we discuss the use of mechanical mechanisms, and associated nonlinearities, as a means of processing information, with a view towards a framework in which adaptable materials and structures act as a distributed information processing network, even enabling information processing to be viewed as a material property, alongside traditional material properties such as strength and stiffness. We focus on approaches to abstract digital logic in mechanical systems, discuss how these systems differ from traditional electronic computing, and highlight the challenges and opportunities that they present.

Recent advances in topological elastic metamaterials

Topological elastic metamaterials have emerged as a new frontier in the quest of topological phases in condensed matter physics. Their exotic topological properties open a wealth of promising engineering-oriented applications that are difficult to realize with traditional elastic metamaterials, such as robust and defect insensitive waveguiding, signal sensing, and splitting. In this review, we retrospectively examine the underlying physical concept of topologically ordered states of elastic waves, starting from the one-dimensional example based on the Su-Schrieffer-Heeger model. We then move on to two-dimensional topological metamaterials, discussing elastic analogues of quantum Hall, pseudospin-Hall, valley-Hall phases. Finally, we survey the latest developments in the field including three-dimensional elastic topological phases and higher-order topological insulators. Altogether, this paper provides a comprehensive overview of the flourishing research frontier on topological elastic metamaterials, and highlights prominent future directions in this field.

Isotropic topological second-order spatial differentiator operating in transmission mode

Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent work demonstrated a topological differentiator in which the transfer function exhibited a topological charge, making the differentiation operation robust to variations in operating conditions. The demonstrated topological differentiator, however, operates in reflection mode at off-normal incidence and is difficult to integrate into compact imaging systems. In this work, we design a topological differentiator that operates isotropically in transmission mode at normal incidence. The device exhibits an optical transfer function with a symmetry-protected topological charge of ±2 and performs second-order differentiation. Our work points to the potential of harnessing topological concepts for optical computing applications.

A single inverse-designed photonic structure that performs parallel computing

In the search for improved computational capabilities, conventional microelectronic computers are facing various problems arising from the miniaturization and concentration of active electronics. Therefore, researchers have explored wave systems, such as photonic or quantum devices, for solving mathematical problems at higher speeds and larger capacities. However, previous devices have not fully exploited the linearity of the wave equation, which as we show here, allows for the simultaneous parallel solution of several independent mathematical problems within the same device. Here we demonstrate that a transmissive cavity filled with a judiciously tailored dielectric distribution and embedded in a multi-frequency feedback loop can calculate the solutions of a number of mathematical problems simultaneously. We design, build, and test a computing structure at microwave frequencies that solves two independent integral equations with any two arbitrary inputs and also provide numerical results for the calculation of the inverse of four 5 x 5 matrices.

Topological optical differentiator

Optical computing holds significant promise of information processing with ultrahigh speed and low power consumption. Recent developments in nanophotonic structures have generated renewed interests due to the prospects of performing analog optical computing with compact devices. As one prominent example, spatial differentiation has been demonstrated with nanophotonic structures and directly applied for edge detection in image processing. However, broadband isotropic two-dimensional differentiation, which is required in most imaging processing applications, has not been experimentally demonstrated yet. Here, we establish a connection between two-dimensional optical spatial differentiation and a nontrivial topological charge in the optical transfer function. Based on this connection, we experimentally demonstrate an isotropic two-dimensional differentiation with a broad spectral bandwidth, by using the simplest photonic device, i.e. a single unpatterned interface. Our work indicates that exploiting concepts from topological photonics can lead to new opportunities in optical computing.

Spatial differentiation is a form of optical computation which has applications in image processing. Here, the authors exploit nontrivial topological charges in the transfer function to realise broadband isotropic two-dimensional differentiation.

Optical Realization of Wave-Based Analog Computing with Metamaterials

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.

Optical analog computing of two-dimensional spatial differentiation based on the Brewster effect

Optical analog computing has attracted widespread attention in recent decades due to its advantages of lower consumption, higher efficiency, and real-time imaging in image processing. Here, we propose a two-dimensional optical analog computing scheme based on the Brewster effect. We experimentally demonstrate two-dimensional edge detection with high efficiency. By combining microscopy, our approach may develop some significant applications in cellular and molecular imaging.

Topological optomechanically induced transparency

The interaction of optical and mechanical degrees of freedom can lead to several interesting effects. A prominent example is the phenomenon of optomechanically induced transparency (OMIT), in which mechanical movements induce a narrow transparency window in the spectrum of an optical mode. In this Letter, we demonstrate the relevance of optomechanical topological insulators for achieving OMIT. More specifically, we show that the strong interaction between optical and mechanical edge modes of a one-dimensional topological optomechanical crystal can render the system transparent within a very narrow frequency range. Since the topology of a system cannot be changed by slight to moderate levels of disorder, the achieved transparency is robust against geometrical perturbations. This is in sharp contrast to trivial OMIT which has a strong dependency on the geometry of the optomechanical system. Our findings hold promise for a wide range of applications such as filtering, signal processing, and slow-light devices.

Sequential Photodamage Driven by Chaotic Systems in NiO Thin Films and Fluorescent Human Cells

A laser ablation process assisted by the feedback of a sensor with chaotic electronic modulation is reported. A synchronous bistable logic circuit was analyzed for switching optical signals in a laser-processing technique. The output of a T-type flip-flop configuration was employed in the photodamage of NiO films. Multiphotonic effects involved in the ablation threshold were evaluated by a vectorial two-wave mixing method. A photoinduced thermal phenomenon was identified as the main physical mechanism responsible for the nonlinearity of index under nanosecond irradiation at 532 nm wavelength. Comparative experiments for destroying highly transparent human cells were carried out. Potential applications for developing hierarchical functions yielding laser-induced controlled explosions with immediate applications for biomedical photothermal processes can be contemplated.

Resonant Coupling Effects in a Double-Layer THz Bandpass Filter

Cascading similar frequency selective surfaces (FSSs) improves the roll-off rate and frequency selectivity of THz bandpass filters. However, resonant coupling between FSS layers causes anomalous transmission peaks. In this work, we have employed an equivalent circuit model to analyze a double-layer FSS structure with periodic cross apertures at different interlayer spacing. We found that the anomalous peaks can be attributed to the resonant coupling between the upper and lower layer FSSs, and their periodic appearance with changing interlayer spacing is related to the half-wavelength repeatability of the circuit. We have fabricated a double-layer FSS sample using femtosecond laser micromachining and measured it using time-domain THz spectroscopy. The results using the equivalent circuit model agree with the Finite-Difference Time-Domain (FDTD) and experimental results.

Disorder-Induced Signal Filtering with Topological Metamaterials

Disorder, ubiquitously present in realistic structures, is generally thought to disturb the performance of analog wave devices, as it often causes strong multiple scattering effects that largely arrest wave transportation. Contrary to this general view, here, it is shown that, in some wave systems with nontrivial topological character, strong randomness can be highly beneficial, acting as a powerful stimulator to enable desired analog filtering operations. This is achieved in a topological Anderson sonic crystal that, in the regime of dominating randomness, provides a well-defined filtering response characterized by a Lorentzian spectral line-shape. The theoretical and experimental results, serving as the first realization of topological Anderson insulator phase in acoustics, suggest the striking possibility of achieving specific, nonrandom analog filtering operations by adding randomness to clean structures.

Randomized resonant metamaterials for single-sensor identification of elastic vibrations

Vibrations carry a wealth of useful physical information in various fields. Identifying the multi-source vibration information generally requires a large number of sensors and complex hardware. Compressive sensing has been shown to be able to bypass the traditional sensing requirements by encoding spatial physical fields, but how to encode vibration information remains unexplored. Here we propose a randomized resonant metamaterial with randomly coupled local resonators for single-sensor compressed identification of elastic vibrations. The disordered effective masses of local resonators lead to highly uncorrelated vibration transmissions, and the spatial vibration information can thus be physically encoded. We demonstrate that the spatial vibration information can be reconstructed via a compressive sensing framework, and this metamaterial can be reconfigured while maintaining desirable performance. This randomized resonant metamaterial presents a new perspective for single-sensor vibration sensing via vibration transmission encoding, and potentially offers an approach to simpler sensing devices for many other physical information.

Designing efficient and flexible metamaterial with uncorrelated transmissions for spatial vibration encoding and identification remains a challenge. Here, the authors propose a randomized resonant metamaterial with randomly coupled local resonators for single-sensor identification of elastic vibrations.

Graphene-assisted electro-optomechanical integration on a silicon-on-insulator platform

Micro- and nano-optomechanics has attracted broad interest for applications of mechanical sensing and coherent signal processing. For nonpiezoelectric materials such as silicon or silicon nitride, electrocapacitive effects with metals patterned on mechanical structures are usually adopted to actuate the mechanical motion of the micro- or nanomechanical devices. However, the metals have deleterious effects on the mechanical structures because they add an additional weight and also introduce considerable mechanical losses. To solve these problems, we have proposed and experimentally demonstrated a new scheme of electro-optomechanical integration on a silicon-on-insulator platform by using single-layer graphene as a highly conductive coating for electromechanical actuation. Mechanical modes of different groups were electrically actuated and optically detected in a micromechanical resonator, with the mechanical Q > 1000 measured in air. Compatible with CMOS technology, our scheme is suitable for large-scale electro-optomechanical integration and will have wide applications in high-speed sensing, communication, and signal processing.

Efficient terahertz polarization conversion with hybrid coupling of chiral metamaterial

We propose an ultrathin terahertz waveplate of bi-layer chiral metamaterial for cross-polarization conversion at asymmetric transmission. The chiral metamaterial is constructed with hybrid coupling plasmonic resonators of a concentric ring and a double-split ring. The terahertz metamaterial can efficiently convert the ${y}$y-polarized wave into the ${x}$x-polarized wave with the cross-polarized transmittance over 97% and the polarization conversion ratio of 99% in simulation. The asymmetric transmission parameter, defined by the difference between two opposite propagating transmittances, can be as high as 0.9. The operation frequency and efficiency are geometrically adjustable with the ring size by exploiting the hybrid coupling effect of electric and magnetic resonances. The presented metamaterial enables the functionality of the nonreciprocal terahertz waveplate with high isolation.

Time response of plasmonic spatial differentiators

We investigate the time response of plasmonic spatial differentiators based on prism coupling configurations. We show that when the incident light is time-modulated, in addition to the spatial differentiation, the output field is also contributed by the signal derivative with respect to time. To reduce this impact, the incident pulse needs a steady time span, and the shortest steady time span is about 100 fs. We further show that the time modulation does not degrade the resolution of the spatial differentiation. Also, we numerically demonstrate the image processing of edge detection by the plasmonic spatial differentiator, with the time-modulated signal.

Nonlinear Second-Order Topological Insulators

We demonstrate, both theoretically and experimentally, the concept of nonlinear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of nonlinearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the intensity. This allows global external control over topological phase transitions and switching to a phase with nonzero bulk polarization, without requiring any structural or geometrical changes. We further show how these nonlinear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.