Optimisation of colour generation from dielectric nanostructures using reinforcement learning

Machine Learning-Driven Design Optimization of Buckling-Induced Quasi-Zero Stiffness Metastructures for Low-Frequency Vibration Isolation

Metastructures, artificial arrangements of micro/macrostructures, possess unique properties and are of significant interest in aerospace, stealth technology, and various other applications. Recent studies have focused on quasi-zero stiffness metastructures, providing an outstanding vibration isolation capability. However, existing methods are constrained to low preloads and lack the consideration of structural analysis, despite their intended use in practical structures. This study introduces metastructures with quasi-zero stiffness characteristics under high preloads by inducing local buckling. An optimization framework combining deep reinforcement learning and finite-element analysis is employed to derive an optimal model that considers both structural safety and quasi-zero stiffness characteristics. To validate the optimization results, quasi-zero stiffness metastructures are fabricated via 3D printing, and compression and vibration experiments are conducted. The fabricated metastructures exhibit quasi-zero stiffness characteristics under a high target preload along with outstanding vibration reduction performance, even in the low-frequency range.

Hybrid supervised and reinforcement learning for the design and optimization of nanophotonic structures

From higher computational efficiency to enabling the discovery of novel and complex structures, deep learning has emerged as a powerful framework for the design and optimization of nanophotonic circuits and components. However, both data-driven and exploration-based machine learning strategies have limitations in their effectiveness for nanophotonic inverse design. Supervised machine learning approaches require large quantities of training data to produce high-performance models and have difficulty generalizing beyond training data given the complexity of the design space. Unsupervised and reinforcement learning-based approaches on the other hand can have very lengthy training or optimization times associated with them. Here we demonstrate a hybrid supervised learning and reinforcement learning approach to the inverse design of nanophotonic structures and show this approach can reduce training data dependence, improve the generalizability of model predictions, and significantly shorten exploratory training times. The presented strategy thus addresses several contemporary deep learning-based challenges, while opening the door for new design methodologies that leverage multiple classes of machine learning algorithms to produce more effective and practical solutions for photonic design.

A deep learning method for empirical spectral prediction and inverse design of all-optical nonlinear plasmonic ring resonator switches

All-optical plasmonic switches (AOPSs) utilizing surface plasmon polaritons are well-suited for integration into photonic integrated circuits (PICs) and play a crucial role in advancing all-optical signal processing. The current AOPS design methods still rely on trial-and-error or empirical approaches. In contrast, recent deep learning (DL) advances have proven highly effective as computational tools, offering an alternative means to accelerate nanophotonics simulations. This paper proposes an innovative approach utilizing DL for spectrum prediction and inverse design of AOPS. The switches employ circular nonlinear plasmonic ring resonators (NPRRs) composed of interconnected metal-insulator-metal waveguides with a ring resonator. The NPRR switching performance is shown using the nonlinear Kerr effect. The forward model presented in this study demonstrates superior computational efficiency when compared to the finite-difference time-domain method. The model analyzes various structural parameters to predict transmission spectra with a distinctive dip. Inverse modeling enables the prediction of design parameters for desired transmission spectra. This model provides a rapid estimation of design parameters, offering a clear advantage over time-intensive conventional optimization approaches. The loss of prediction for both the forward and inverse models, when compared to simulations, is exceedingly low and on the order of 10-4. The results confirm the suitability of employing DL for forward and inverse design of AOPSs in PICs.

General deep learning framework for emissivity engineering

Wavelength-selective thermal emitters (WS-TEs) have been frequently designed to achieve desired target emissivity spectra, as a typical emissivity engineering, for broad applications such as thermal camouflage, radiative cooling, and gas sensing, etc. However, previous designs require prior knowledge of materials or structures for different applications and the designed WS-TEs usually vary from applications to applications in terms of materials and structures, thus lacking of a general design framework for emissivity engineering across different applications. Moreover, previous designs fail to tackle the simultaneous design of both materials and structures, as they either fix materials to design structures or fix structures to select suitable materials. Herein, we employ the deep Q-learning network algorithm, a reinforcement learning method based on deep learning framework, to design multilayer WS-TEs. To demonstrate the general validity, three WS-TEs are designed for various applications, including thermal camouflage, radiative cooling and gas sensing, which are then fabricated and measured. The merits of the deep Q-learning algorithm include that it can (1) offer a general design framework for WS-TEs beyond one-dimensional multilayer structures; (2) autonomously select suitable materials from a self-built material library and (3) autonomously optimize structural parameters for the target emissivity spectra. The present framework is demonstrated to be feasible and efficient in designing WS-TEs across different applications, and the design parameters are highly scalable in materials, structures, dimensions, and the target functions, offering a general framework for emissivity engineering and paving the way for efficient design of nonlinear optimization problems beyond thermal metamaterials.

Accelerating the Design of Multishell Upconverting Nanoparticles through Bayesian Optimization

The photon upconverting properties of lanthanide-doped nanoparticles drive their applications in imaging, optoelectronics, and additive manufacturing. To maximize their brightness, these upconverting nanoparticles (UCNPs) are often synthesized as core/shell heterostructures. However, the large numbers of compositional and structural parameters in multishell heterostructures make optimizing optical properties challenging. Here, we demonstrate the use of Bayesian optimization (BO) to learn the structure and design rules for multishell UCNPs with bright ultraviolet and violet emission. We leverage an automated workflow that iteratively recommends candidate UCNP structures and then simulates their emission spectra using kinetic Monte Carlo. Yb3+/Er3+- and Yb3+/Er3+/Tm3+-codoped UCNP nanostructures optimized with this BO workflow achieve 10- and 110-fold brighter emission within 22 and 40 iterations, respectively. This workflow can be expanded to structures with higher compositional and structural complexity, accelerating the discovery of novel UCNPs while domain-specific knowledge is being developed.

Deep learning-based inverse design optimization of efficient multilayer thermal emitters in the near-infrared broad spectrum

This study proposes a deep learning architecture for automatic modeling and optimization of multilayer thin film structures to address the need for specific spectral emitters and achieve rapid design of geometric parameters for an ideal spectral response. Multilayer film structures are ideal thermal emitter structures for thermophotovoltaic application systems because they combine the advantages of large area preparation and controllable costs. However, achieving good spectral response performance requires stacking more layers, which makes it more difficult to achieve fine spectral inverse design using forward calculation of the dimensional parameters of each layer of the structure. Deep learning is the main method for solving complex data-driven problems in artificial intelligence and provides an efficient solution for the inverse design of structural parameters for a target waveband. In this study, an eight-layer thin film structure composed of SiO₂/Ti and SiO₂/W is rapidly reverse engineered using a deep learning method to achieve a structural design with an emissivity better than 0.8 in the near-infrared band. Additionally, an eight-layer thin film structure composed of 3 × 3 cm SiO₂/Ti is experimentally measured using magnetron sputtering, and the emissivity in the 1-4 µm band was better than 0.68. This research provides implications for the design and application of micro-nano structures, can be widely used in the fields of thermal imaging and thermal regulation, and will contribute to developing a new paradigm for optical nanophotonic structures with a fast target-oriented inverse design of structural parameters, such as required spectral emissivity, phase, and polarization.

Artificial Intelligence and Advanced Materials

Artificial intelligence (AI) is gaining strength, and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems, and processes can be devised and optimized thanks to machine learning (ML) techniques, and such progress can be turned into innovative computing platforms. Future materials scientists will profit from understanding how ML can boost the conception of advanced materials. This review covers aspects of computation from the fundamentals to directions taken and repercussions produced by computation to account for the origins, procedures, and applications of AI. ML and its methods are reviewed to provide basic knowledge of its implementation and its potential. The materials and systems used to implement AI with electric charges are finding serious competition from other information-carrying and processing agents. The impact these techniques have on the inception of new advanced materials is so deep that a new paradigm is developing where implicit knowledge is being mined to conceive materials and systems for functions instead of finding applications to found materials. How far this trend can be carried is hard to fathom, as exemplified by the power to discover unheard of materials or physical laws buried in data.

Machine learning for nanoplasmonics

Plasmonic nanomaterials have outstanding optoelectronic properties potentially enabling the next generation of catalysts, sensors, lasers and photothermal devices. Owing to optical and electron techniques, modern nanoplasmonics research generates large datasets characterizing features across length scales. Furthermore, optimizing syntheses leading to specific nanostructures requires time-consuming multiparametric approaches. These complex datasets and trial-and-error practices make nanoplasmonics research ripe for the application of machine learning (ML) and advanced data processing methods. ML algorithms capture relationships between synthesis, structure and performance in a way that far exceeds conventional simulation and theory approaches, enabling effective performance optimization. For example, neural networks can tailor the nanostructure morphology to target desired properties, identify synthetic conditions and extract quantitative information from complex data. Here we discuss the nascent field of ML for nanoplasmonics, describe the opportunities and limitations of ML in nanoplasmonic research, and conclude that ML is potentially transformative, especially if the community curates and shares its big data.

Neural Inverse Design of Nanostructures (NIDN)

In the recent decade, computational tools have become central in material design, allowing rapid development cycles at reduced costs. Machine learning tools are especially on the rise in photonics. However, the inversion of the Maxwell equations needed for the design is particularly challenging from an optimization standpoint, requiring sophisticated software. We present an innovative, open-source software tool called Neural Inverse Design of Nanostructures (NIDN) that allows designing complex, stacked material nanostructures using a physics-based deep learning approach. Instead of a derivative-free or data-driven optimization or learning method, we perform a gradient-based neural network training where we directly optimize the material and its structure based on its spectral characteristics. NIDN supports two different solvers, rigorous coupled-wave analysis and a finite-difference time-domain method. The utility and validity of NIDN are demonstrated on several synthetic examples as well as the design of a 1550 nm filter and anti-reflection coating. Results match experimental baselines, other simulation tools, and the desired spectral characteristics. Given its full modularity in regard to network architectures and Maxwell solvers as well as open-source, permissive availability, NIDN will be able to support computational material design processes in a broad range of applications.

A unique physics-inspired deep-learning-based platform introducing a generalized tool for rapid optical-response prediction and parametric-optimization for all-dielectric metasurfaces

Metasurfaces are composed of a two-dimensional array of carefully engineered subwavelength structures. They provide a novel compact alternative to conventional voluminous optical components. However, their design involves a time-consuming hit and trial procedure, requiring many iterative electromagnetic simulations through expensive commercial solvers. To overcome this non-practical design strategy, recently, various deep-learning-based fast and low computational cost networks have been proposed to design and optimize individual meta-atoms and complete metasurfaces. Most of them focus on optimizing the amplitude response of nanostructures, whereas mapping the phase response is a much more challenging problem that needs to be addressed. Since the metaatom's optical response is entirely reliant on and vulnerable to its geometrical structure, underlying material, and operating wavelength, changing any of these parameters changes the entire physics of the problem in hand. Here, we propose novel deep-learning-based generalized forward and inverse design approaches to optimize all-dielectric transmissive metasurfaces. The proposed forward predicting neural networks take all the geometrical parameters and the physical properties of the bar-shaped dielectric nano-resonators as the input and predict the cross-polarized transmission amplitude and modulated phase at eight distinct rotation angles of the nano-bar. These networks are generalized to predict the electromagnetic (EM) response of different dielectric materials at different operating wavelengths. An inverse design neural network is also proposed that takes the target transmission amplitude and phase at eight discrete orientation angles of the nano-bar as the primary input. The underlying physics of the problem is also incorporated by feeding the intrinsic material properties and the operating wavelength of the nano-bar as a second input to the inverse neural network. It predicts the optimum set of geometrical parameters to achieve maximum cross-polarized transmission and complete Pancharatnam-Berry (PB) phase coverage from 0 to 2π. The average test data mean square error (MSE) achieved for the forward predicting neural network is 1.8 × 10^-3 and that of the inverse design neural network is 2.8 × 10^-1. The average MSEs for different material's test samples are demonstrated to validate the generalizability of the proposed models in terms of seen and unseen materials. A comparative analysis of the proposed approach with conventional EM software optimization tools is performed to prove that the proposed inverse design works much faster than the conventional methods, also it can handle a comparatively larger range of parameters and predicts the results in a single run with high accuracy.

Inverse design of core-shell particles with discrete material classes using neural networks

The design of scatterers on demand is a challenging task that requires the investigation and development of novel and flexible approaches. In this paper, we propose a machine learning-assisted optimization framework to design multi-layered core-shell particles that provide a scattering response on demand. Artificial neural networks can learn to predict the scattering spectrum of core-shell particles with high accuracy and can act as fully differentiable surrogate models for a gradient-based design approach. To enable the fabrication of the particles, we consider existing materials and introduce a novel two-step optimization to treat continuous geometric parameters and discrete feasible materials simultaneously. Moreover, we overcome the non-uniqueness of the problem and expand the design space to particles of varying numbers of shells, i.e., different number of optimization parameters, with a classification network. Our method is 1-2 orders of magnitudes faster than conventional approaches in both forward prediction and inverse design and is potentially scalable to even larger and more complex scatterers.

Intelligent design of the chiral metasurfaces for flexible targets: combining a deep neural network with a policy proximal optimization algorithm

Recently, deep reinforcement learning (DRL) for metasurface design has received increased attention for its excellent decision-making ability in complex problems. However, time-consuming numerical simulation has hindered the adoption of DRL-based design method. Here we apply the Deep learning-based virtual Environment Proximal Policy Optimization (DE-PPO) method to design the 3D chiral plasmonic metasurfaces for flexible targets and model the metasurface design process as a Markov decision process to help the training. A well trained DRL agent designs chiral metasurfaces that exhibit the optimal absolute circular dichroism value (typically, ∼ 0.4) at various target wavelengths such as 930 nm, 1000 nm, 1035 nm, and 1100 nm with great time efficiency. Besides, the training process of the PPO agent is exceptionally fast with the help of the deep neural network (DNN) auxiliary virtual environment. Also, this method changes all variable parameters of nanostructures simultaneously, reducing the size of the action vector and thus the output size of the DNN. Our proposed approach could find applications in efficient and intelligent design of nanophotonic devices.

Machine Learning in Interpolation and Extrapolation for Nanophotonic Inverse Design

The algorithmic design of nanophotonic structures promises to significantly improve the efficiency of nanophotonic components due to the strong dependence of electromagnetic function on geometry and the unintuitive connection between structure and response. Such approaches, however, can be highly computationally intensive and do not ensure a globally optimal solution. Recent theoretical results suggest that machine learning techniques could address these issues as they are capable of modeling the response of nanophotonic structures at orders of magnitude lower time per result. In this work, we explore the utilization of artificial neural network (ANN) techniques to improve the algorithmic design of simple absorbing nanophotonic structures. We show that different approaches show various aptitudes in interpolation versus extrapolation, as well as peak performances versus consistency. Combining ANNs with classical machine learning techniques can outperform some standard ANN techniques for forward design, both in terms of training speed and accuracy in interpolation, but extrapolative performance can suffer. Networks pretrained on general image classification perform well in predicting optical responses of both interpolative and extrapolative structures, with very little additional training time required. Furthermore, we show that traditional deep neural networks are able to perform significantly better in extrapolation than more complicated architectures using convolutional or autoencoder layers. Finally, we show that such networks are able to perform extrapolation tasks in structure generation to produce structures with spectral responses significantly outside those of the structures on which they are trained.

Machine learning-assisted design of polarization-controlled dynamically switchable full-color metasurfaces

Dynamic color tuning has significant application prospects in the fields of color display, steganography, and information encryption. However, most methods for color switching require external stimuli, which increases the structural complexity and hinders the applicability of front-end dynamic display technology. In this study, we propose polarization-controlled hybrid metal-dielectric metasurfaces to realize full-color display and dynamic color tuning by altering the polarization angle of incident light without changing the structure and properties of the material. A bidirectional neural network is trained to predict the colors of mixed metasurfaces and inversely design the geometric parameters for the desired colors, which is less dependent on design experience and reduces the computational cost. According to the color recognition ability of human eyes, the accuracy of color prediction realized in our study is 93.18% and that of inverse parameter design is 92.37%. This study presents a simple method for dynamic structural color tuning and accelerating the design of full-color metasurfaces, which can offer further insight into the design of color filters and promote photonics research.

NEUTRON: Neural particle swarm optimization for material-aware inverse design of structural color

Designing optical structures for generating structural colors is challenging because of the complex relationship between the optical structures and the color perceived by human eyes. Machine learning-based approaches have been developed to expedite this design process. However, existing methods solely focus on structural parameters of the optical design, which could lead to suboptimal color generation because of the inability to optimize the selection of materials. To address this issue, an approach known as Neural Particle Swarm Optimization is proposed in this paper. The proposed method achieves high design accuracy and efficiency on two structural color design tasks; the first task is designing environment-friendly alternatives to chrome coatings, and the second task concerns reconstructing pictures with multilayer optical thin films. Several designs that could replace chrome coatings have been discovered; pictures with more than 200,000 pixels and thousands of unique colors can be accurately reconstructed in a few hours.

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NEUTRON combines machine learning and optimization for structural color designs

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On two benchmark tasks, NEUTRON demonstrates high design accuracy and efficiency

Liquid crystal-powered Mie resonators for electrically tunable photorealistic color gradients and dark blacks

Taking inspiration from beautiful colors in nature, structural colors produced from nanostructured metasurfaces have shown great promise as a platform for bright, highly saturated, and high-resolution colors. Both plasmonic and dielectric materials have been employed to produce static colors that fulfil the required criteria for high-performance color printing, however, for practical applications in dynamic situations, a form of tunability is desirable. Combinations of the additive color palette of red, green, and blue enable the expression of further colors beyond the three primary colors, while the simultaneous intensity modulation allows access to the full color gamut. Here, we demonstrate an electrically tunable metasurface that can represent saturated red, green, and blue pixels that can be dynamically and continuously controlled between on and off states using liquid crystals. We use this to experimentally realize ultrahigh-resolution color printing, active multicolor cryptographic applications, and tunable pixels toward high-performance full-color reflective displays.

Machine-learning reinforcement for optimizing multilayered thin films: applications in designing broadband antireflection coatings

The design and fabrication of nanoscale multilayered thin films play an essential role in regulating the operation efficiency of sensitive optical sensors and filters. In this paper, we introduce a packaged tool that employs flexible electromagnetic calculation software with machine learning in order to find the optimized double-band antireflection coatings in intervals of wavelength from 3 to 5 µm and 8 to 12 µm. Instead of computing or modeling an extremely enormous set of thin film structures, this tool enhanced with machine learning can swiftly predict the optical properties of a given structure with >99.7% accuracy and a substantial reduction in computation costs. Furthermore, the tool includes two learning methods that can infer a global optimal structure or suitable local optimal ones. Specifically, these well-trained models provide the highest accurate double-band average transmission coefficient combined with the lowest number of layers or the thinnest total thickness starting from a reference multilayered structure. Finally, the more sophisticated enhancement method, called the double deep Q-learning network, exhibited the best performance in finding optimal antireflective multilayered structures with the highest double-band average transmission coefficient of about 98.95%.

Smart and Rapid Design of Nanophotonic Structures by an Adaptive and Regularized Deep Neural Network

The design of nanophotonic structures based on deep learning is emerging rapidly in the research community. Design methods using Deep Neural Networks (DNN) are outperforming conventional physics-based simulations performed iteratively by human experts. Here, a self-adaptive and regularized DNN based on Convolutional Neural Networks (CNNs) for the smart and fast characterization of nanophotonic structures in high-dimensional design parameter space is presented. This proposed CNN model, named LRS-RCNN, utilizes dynamic learning rate scheduling and L2 regularization techniques to overcome overfitting and speed up training convergence and is shown to surpass the performance of all previous algorithms, with the exception of two metrics where it achieves a comparable level relative to prior works. We applied the model to two challenging types of photonic structures: 2D photonic crystals (e.g., L3 nanocavity) and 1D photonic crystals (e.g., nanobeam) and results show that LRS-RCNN achieves record-high prediction accuracies, strong generalizibility, and substantially faster convergence speed compared to prior works. Although still a proof-of-concept model, the proposed smart LRS-RCNN has been proven to greatly accelerate the design of photonic crystal structures as a state-of-the-art predictor for both Q-factor and V. It can also be modified and generalized to predict any type of optical properties for designing a wide range of different nanophotonic structures. The complete dataset and code will be released to aid the development of related research endeavors.

Designing high efficiency asymmetric polarization converter for blue light: a deep reinforcement learning approach

Conventional polarization converters selectively preserve the required polarization state by absorbing, reflecting or refracting light with unwanted polarization state, leading to a theoretical transmittance limit of 0.5 for linearly polarized light with unpolarized light incidence. In the meanwhile, due to the high-dimensional structure parameters and time-consuming numerical simulations, designing a converter with satisfactory performance is extremely difficult and closely relies on human experts' experiences and manual intervention. To address these open issues, in this paper, we first propose an asymmetric polarization converter which shows both high transmittance for one linearly polarized light and high transmittance for the orthogonal linearly polarized light with 90° rotation in blue wavelength region. To maximize the performance of the proposed structure, a deep reinforcement learning approach is further proposed to search for the optimal set of structure parameters. To avoid overly long training time by using the numerical simulations as environment, a deep neural network is proposed to serve as the surrogate model, where a prediction accuracy of 96.6% and 95.5% in two orthogonal polarization directions is achieved with micro-second grade simulation time respectively. With the optimized structure, the average transmittance is larger than 0.5 for the wavelength range from 444 to 466 nm with a maximum of 0.605 at 455 nm, which is 21% higher than the theoretical limit of 0.5 of conventional polarization converters.

Active optical metasurfaces: comprehensive review on physics, mechanisms, and prospective applications

Optical metasurfaces with subwavelength thickness hold considerable promise for future advances in fundamental optics and novel optical applications due to their unprecedented ability to control the phase, amplitude, and polarization of transmitted, reflected, and diffracted light. Introducing active functionalities to optical metasurfaces is an essential step to the development of next-generation flat optical components and devices. During the last few years, many attempts have been made to develop tunable optical metasurfaces with dynamic control of optical properties (e.g., amplitude, phase, polarization, spatial/spectral/temporal responses) and early-stage device functions (e.g., beam steering, tunable focusing, tunable color filters/absorber, dynamic hologram, etc) based on a variety of novel active materials and tunable mechanisms. These recently-developed active metasurfaces show significant promise for practical applications, but significant challenges still remain. In this review, a comprehensive overview of recently-reported tunable metasurfaces is provided which focuses on the ten major tunable metasurface mechanisms. For each type of mechanism, the performance metrics on the reported tunable metasurface are outlined, and the capabilities/limitations of each mechanism and its potential for various photonic applications are compared and summarized. This review concludes with discussion of several prospective applications, emerging technologies, and research directions based on the use of tunable optical metasurfaces. We anticipate significant new advances when the tunable mechanisms are further developed in the coming years.

Instantaneous Property Prediction and Inverse Design of Plasmonic Nanostructures Using Machine Learning: Current Applications and Future Directions

Advances in plasmonic materials and devices have given rise to a variety of applications in photocatalysis, microscopy, nanophotonics, and metastructures. With the advent of computing power and artificial neural networks, the characterization and design process of plasmonic nanostructures can be significantly accelerated using machine learning as opposed to conventional FDTD simulations. The machine learning (ML) based methods can not only perform with high accuracy and return optical spectra and optimal design parameters, but also maintain a stable high computing efficiency without being affected by the structural complexity. This work reviews the prominent ML methods involved in forward simulation and inverse design of plasmonic nanomaterials, such as Convolutional Neural Networks, Generative Adversarial Networks, Genetic Algorithms and Encoder–Decoder Networks. Moreover, we acknowledge the current limitations of ML methods in the context of plasmonics and provide perspectives on future research directions.

Artificial intelligence: A powerful paradigm for scientific research

Artificial intelligence (AI) coupled with promising machine learning (ML) techniques well known from computer science is broadly affecting many aspects of various fields including science and technology, industry, and even our day-to-day life. The ML techniques have been developed to analyze high-throughput data with a view to obtaining useful insights, categorizing, predicting, and making evidence-based decisions in novel ways, which will promote the growth of novel applications and fuel the sustainable booming of AI. This paper undertakes a comprehensive survey on the development and application of AI in different aspects of fundamental sciences, including information science, mathematics, medical science, materials science, geoscience, life science, physics, and chemistry. The challenges that each discipline of science meets, and the potentials of AI techniques to handle these challenges, are discussed in detail. Moreover, we shed light on new research trends entailing the integration of AI into each scientific discipline. The aim of this paper is to provide a broad research guideline on fundamental sciences with potential infusion of AI, to help motivate researchers to deeply understand the state-of-the-art applications of AI-based fundamental sciences, and thereby to help promote the continuous development of these fundamental sciences.

Optical meta-waveguides for integrated photonics and beyond

The growing maturity of nanofabrication has ushered massive sophisticated optical structures available on a photonic chip. The integration of subwavelength-structured metasurfaces and metamaterials on the canonical building block of optical waveguides is gradually reshaping the landscape of photonic integrated circuits, giving rise to numerous meta-waveguides with unprecedented strength in controlling guided electromagnetic waves. Here, we review recent advances in meta-structured waveguides that synergize various functional subwavelength photonic architectures with diverse waveguide platforms, such as dielectric or plasmonic waveguides and optical fibers. Foundational results and representative applications are comprehensively summarized. Brief physical models with explicit design tutorials, either physical intuition-based design methods or computer algorithms-based inverse designs, are cataloged as well. We highlight how meta-optics can infuse new degrees of freedom to waveguide-based devices and systems, by enhancing light-matter interaction strength to drastically boost device performance, or offering a versatile designer media for manipulating light in nanoscale to enable novel functionalities. We further discuss current challenges and outline emerging opportunities of this vibrant field for various applications in photonic integrated circuits, biomedical sensing, artificial intelligence and beyond.

Inverse design of the MMI power splitter by asynchronous double deep Q-learning

The asynchronous double deep Q-learning (A-DDQN) method is proposed to design the multi-mode interference (MMI) power splitters for low insertion loss and wide bandwidth from 1200 to 1650 nm wavelength range. By using A-DDQN to guide hole etchings in the interference region of MMI, the target splitting ratio (SR) can be obtained with much less CPU time (about 10 hours for one design) and more effective utilization of the computational resources in asynchronous/parallel manner. Also, this method can simplify the design by using relatively few holes to obtain the same SR with small return loss.

Reinforcement learning applied to metamaterial design

This paper presents a semi-analytical method of suppressing acoustic scattering using reinforcement learning (RL) algorithms. We give a RL agent control over design parameters of a planar configuration of cylindrical scatterers in water. These design parameters control the position and radius of the scatterers. As these cylinders encounter an incident acoustic wave, the scattering pattern is described by a function called total scattering cross section (TSCS). Through evaluating the gradients of TSCS and other information about the state of the configuration, the RL agent perturbatively adjusts design parameters, considering multiple scattering between the scatterers. As each adjustment is made, the RL agent receives a reward negatively proportional to the root mean square of the TSCS across a range of wavenumbers. Through maximizing its reward per episode, the agent discovers designs with low scattering. Specifically, the double deep Q-learning network and the deep deterministic policy gradient algorithms are employed in our models. Designs discovered by the RL algorithms performed well when compared to a state-of-the-art optimization algorithm using fmincon.

Multiple-patterning colloidal lithography-implemented scalable manufacturing of heat-tolerant titanium nitride broadband absorbers in the visible to near-infrared

Broadband perfect absorbers have been intensively researched for decades because of their near-perfect absorption optical property that can be applied to diverse applications. Unfortunately, achieving large-scale and heat-tolerant absorbers has been remained challenging work because of costly and time-consuming lithography methods and thermolability of materials, respectively. Here, we demonstrate a thermally robust titanium nitride broadband absorber with >95% absorption efficiency in the visible and near-infrared region (400-900 nm). A relatively large-scale (2.5 cm × 2.5 cm) absorber device is fabricated by using a fabrication technique of multiple-patterning colloidal lithography. The optical properties of the absorber are still maintained even after heating at the temperatures >600 ^∘C. Such a large-scale, heat-tolerant, and broadband near-perfect absorber will provide further useful applications in solar thermophotovoltaics, stealth, and absorption controlling in high-temperature conditions.

Spectral Modulation through the Hybridization of Mie-Scatterers and Quasi-Guided Mode Resonances: Realizing Full and Gradients of Structural Color

Metasurfaces made up of subwavelength arrays of Mie scatterers can be engineered to control the optical properties of incident light. The hybridization of the fundamental Mie resonances with lattice resonances greatly enhances the scattering cross-section of individual Mie scatterers. Through careful design of the locations of these hybridized modes using two differently engineered hydrogenated amorphous silicon nanorods, we numerically calculate and experimentally fabricate two examples of full color printing; one with spectral colors comparable to the Adobe RGB gamut, and another with gradients of color. We identify and characterize the mechanisms behind each and provide a framework that can be used to design any all-dielectric metasurfaces of subwavelength Mie scatterers for spectral modulation.

Deep Convolutional Mixture Density Network for Inverse Design of Layered Photonic Structures

Machine learning (ML) techniques, such as neural networks, have emerged as powerful tools for the inverse design of nanophotonic structures. However, this innovative approach suffers some limitations. A primary one is the nonuniqueness problem, which can prevent ML algorithms from properly converging because vastly different designs produce nearly identical spectra. Here, we introduce a mixture density network (MDN) approach, which models the design parameters as multimodal probability distributions instead of discrete values, allowing the algorithms to converge in cases of nonuniqueness without sacrificing degenerate solutions. We apply our MDN technique to inversely design two types of multilayer photonic structures consisting of thin films of oxides, which present a significant challenge for conventional ML algorithms due to a high degree of nonuniqueness in their optical properties. In the 10-layer case, the MDN can handle transmission spectra with high complexity and under varying illumination conditions. The 4-layer case tends to show a stronger multimodal character, with secondary modes indicating alternative solutions for a target spectrum. The shape of the distributions gives valuable information for postprocessing and about the uncertainty in the predictions, which is not available with deterministic networks. Our approach provides an effective solution to the inverse design of photonic structures and yields more optimal searches for the structures with high degeneracy and spectral complexity.

Machine learning identifies scale-free properties in disordered materials

The vast amount of design freedom in disordered systems expands the parameter space for signal processing. However, this large degree of freedom has hindered the deterministic design of disordered systems for target functionalities. Here, we employ a machine learning approach for predicting and designing wave-matter interactions in disordered structures, thereby identifying scale-free properties for waves. To abstract and map the features of wave behaviors and disordered structures, we develop disorder-to-localization and localization-to-disorder convolutional neural networks, each of which enables the instantaneous prediction of wave localization in disordered structures and the instantaneous generation of disordered structures from given localizations. We demonstrate that the structural properties of the network architectures lead to the identification of scale-free disordered structures having heavy-tailed distributions, thus achieving multiple orders of magnitude improvement in robustness to accidental defects. Our results verify the critical role of neural network structures in determining machine-learning-generated real-space structures and their defect immunity.

Deep Q-network to produce polarization-independent perfect solar absorbers: a statistical report

Using reinforcement learning, a deep Q-network was used to design polarization-independent, perfect solar absorbers. The deep Q-network selected the geometrical properties and materials of a symmetric three-layer metamaterial made up of circular rods on top of two films. The combination of all the possible permutations gives around 500 billion possible designs. In around 30,000 steps, the deep Q-network was able to produce 1250 structures that have an integrated absorption of higher than 90% in the visible region, with a maximum of 97.6% and an integrated absorption of less than 10% in the 8-13 µm wavelength region, with a minimum of 1.37%. A statistical analysis of the distribution of materials and geometrical parameters that make up the solar absorbers is presented.

Multilayer optical thin film design with deep Q learning

Multilayer optical film plays a significant role in broad fields of optical application. Due to the nonlinear relationship between the dispersion characteristics of optical materials and the actual performance parameters of optical thin films, it is challenging to optimize optical thin film structure with the traditional models. In this paper, we present an implementation of Deep Q-learning, which suited for the most part for optical thin film. As a set of concrete demonstrations, we optimize solar absorber. The optimal program could optimal this solar absorber in 500 epoch (about 200 steps per-epoch) without any human intervention. Search results perform better than researchers’ manual searches.

Scalable and High-Throughput Top-Down Manufacturing of Optical Metasurfaces

Metasurfaces have shown promising potential to miniaturize existing bulk optical components thanks to their extraordinary optical properties and ultra-thin, small, and lightweight footprints. However, the absence of proper manufacturing methods has been one of the main obstacles preventing the practical application of metasurfaces and commercialization. Although a variety of fabrication techniques have been used to produce optical metasurfaces, there are still no universal scalable and high-throughput manufacturing methods that meet the criteria for large-scale metasurfaces for device/product-level applications. The fundamentals and recent progress of the large area and high-throughput manufacturing methods are discussed with practical device applications. We systematically classify various top-down scalable patterning techniques for optical metasurfaces: firstly, optical and printing methods are categorized and then their conventional and unconventional (emerging/new) techniques are discussed in detail, respectively. In the end of each section, we also introduce the recent developments of metasurfaces realized by the corresponding fabrication methods.

Machine learning and evolutionary algorithm studies of graphene metamaterials for optimized plasmon-induced transparency

Machine learning and optimization algorithms have been widely applied in the design and optimization for photonics devices. We briefly review recent progress of this field of research and show data-driven applications, including spectrum prediction, inverse design and performance optimization, for novel graphene metamaterials (GMs). The structure of the GMs is well-designed to achieve the wideband plasmon induced transparency (PIT) effect, which can be theoretically demonstrated by using the transfer matrix method. Some traditional machine learning algorithms, including k nearest neighbour, decision tree, random forest and artificial neural networks, are utilized to equivalently substitute the numerical simulation in the forward spectrum prediction and complete the inverse design for the GMs. The calculated results demonstrate that all algorithms are effective and the random forest has advantages in terms of accuracy and training speed. Moreover, evolutionary algorithms, including single-objective (genetic algorithm) and multi-objective optimization (NSGA-II), are used to achieve the steep transmission characteristics of PIT effect by synthetically taking many different performance metrics into consideration. The maximum difference between the transmission peaks and dips in the optimized transmission spectrum reaches 0.97. In comparison to previous works, we provide a guidance for intelligent design of photonics devices based on machine learning and evolutionary algorithms and a reference for the selection of machine learning algorithms for simple inverse design problems.

Deep learning: a new tool for photonic nanostructure design

Early results have shown the potential of Deep Learning (DL) to disrupt the fields of optical inverse-design, particularly, the inverse design of nanostructures. In the last three years, the complexity of the optical nanostructure being designed and the sophistication of the employed DL methodology have steadily increased. This topical review comprehensively surveys DL based design examples from the nanophotonics literature. Notwithstanding the early success of this approach, its limitations, range of validity and its place among established design techniques remain to be assessed. The review also provides a perspective on the limitations of this approach and emerging research directions. It is hoped that this topical review may help readers to identify unaddressed problems, to choose an initial setup for a specific problem, and, to identify means to improve the performance of existing DL based workflows.

Topological encoding method for data-driven photonics inverse design

Data-driven approaches have been proposed as effective strategies for the inverse design and optimization of photonic structures in recent years. In order to assist data-driven methods for the design of topology of photonic devices, we propose a topological encoding method that transforms photonic structures represented by binary images to a continuous sparse representation. This sparse representation can be utilized for dimensionality reduction and dataset generation, enabling effective analysis and optimization of photonic topologies with data-driven approaches. As a proof of principle, we leverage our encoding method for the design of two dimensional non-paraxial diffractive optical elements with various diffraction intensity distributions. We proved that our encoding method is able to assist machine-learning-based inverse design approaches for accurate and global optimization.

Meta-model-based multi-objective optimization for robust color reproduction using hybrid diffraction gratings

We propose an efficient and versatile optimization scheme, based on the combination of multi-objective genetic algorithms and neural-networks, to reproduce specific colors through the optimization of the geometrical parameters of metal-dielectric diffraction gratings. To illustrate and assess the performance of this approach, we tailor the chromatic response of a structure composed of three adjacent hybrid V-groove diffraction gratings. To be close to the experimental situation, we include the feasibility constraints imposed by the fabrication process. The strength of our approach lies in the possibility to simultaneously optimize different contradictory objectives, avoiding time-consuming electromagnetic calculations.

Biomimetic ultra-broadband perfect absorbers optimised with reinforcement learning

By learning the optimal policy with a double deep Q-learning network (DDQN), we design ultra-broadband, biomimetic, perfect absorbers with various materials, based the structure of a moth's eye. All absorbers achieve over 90% average absorption from 400 to 1600 nm. By training a DDQN with moth-eye structures made up of chromium, we transfer the learned knowledge to other, similar materials to quickly and efficiently find the optimal parameters from the ∼1 billion possible options. The knowledge learned from previous optimisations helps the network to find the best solution for a new material in fewer steps, dramatically increasing the efficiency of finding designs with ultra-broadband absorption.

Accurate and instant frequency estimation from noisy sinusoidal waves by deep learning

We used a deep learning network to find the frequency of a noisy sinusoidal wave. A three-layer neural network was designed to extract the frequency of sinusoidal waves that had been combined with white noise at a signal-to-noise ratio of 25 dB. One hundred thousand waves were prepared for training and testing the model. We designed a neural network that could achieve a mean squared error of 4 × 10^-5 for normalized frequencies. This model was written for the range 1 kHz ≤ f ≤ 10 kHz but also shown how to easily be generalized to other ranges. The algorithm is easy to rewrite and the final results are highly accurate. The trained model can find frequency of any previously-unseen noisy wave in less than a second.

Double-deep Q-learning to increase the efficiency of metasurface holograms

We use a double deep Q-learning network (DDQN) to find the right material type and the optimal geometrical design for metasurface holograms to reach high efficiency. The DDQN acts like an intelligent sweep and could identify the optimal results in ~5.7 billion states after only 2169 steps. The optimal results were found between 23 different material types and various geometrical properties for a three-layer structure. The computed transmission efficiency was 32% for high-quality metasurface holograms; this is two times bigger than the previously reported results under the same conditions. The found structure is transmission-type and polarization-independent and works in the visible region.

Finding the optical properties of plasmonic structures by image processing using a combination of convolutional neural networks and recurrent neural networks

Image processing can be used to extract meaningful optical results from images. Here, from images of plasmonic structures, we combined convolutional neural networks with recurrent neural networks to extract the absorption spectra of structures. To provide the data required for the model, we performed 100,000 simulations with similar setups and random structures. In designing this deep network, we created a model that can predict the absorption response of any structure with a similar setup. We used convolutional neural networks to collect spatial information from the images, and then, we used that data and recurrent neural networks to teach the model to predict the relationship between the spatial information and the absorption spectrum. Our results show that this image processing method is accurate and can be used to replace time- and computationally-intensive numerical simulations. The trained model can predict the optical results in less than a second without the need for a strong computing system. This technique can be easily extended to cover different structures and extract any other optical properties.