Self-Learning Perfect Optical Chirality via a Deep Neural Network

Unidirectional Transmission Metasurfaces with Topological Continuity Generated from High-dimensional Design Space

With the growing demand for nanodevices, there is a concerted effort to improve the design flexibility of nanostructures, thereby expanding the capabilities of nanophotonic devices. In this work, a Laplacian-weighted binary search (LBS) algorithm is proposed to generate a unidirectional transmission metasurface from a high-dimensional design space, offering an increased degree of design freedom. The LBS algorithm incorporates topological continuity based on the Laplacian, effectively circumventing the common issue of high structural complexity in designing high-dimensional nanostructures. As a result, metasurfaces developed using the LBS algorithm in a high-dimensional design space exhibit reduced complexity, which is advantageous for experimental fabrication. An all-dielectric metasurface with unidirectional transmission, designed from the high-dimensional space using the LBS method, demonstrated the successful application of these design principles in experiments. The metasurface exhibits high optical performance on unidirectional transmission in measurements by a high-resolution angle-resolved micro-spectra system, achieving forward transmissivity above 90% (400-700 nm) and back transmissivity below 20% (400-500 nm) within the targeted wavelength range. This work provides a feasible approach for advancing high-dimensional metasurface applications, as the LBS design method takes into account topological continuity during experimental processing. Compared to traditional direct binary search (DBS) methods, the LBS method not only improves information processing efficiency but also maintains the topological continuity of structures. Beyond unidirectional transmission, the LBS-based design method has generality and flexibility to accommodate almost all physical scenarios in metasurface design, enabling a multitude of complex functions and applications.

Expanding the Horizons of Machine Learning in Nanomaterials to Chiral Nanostructures

Machine learning holds significant research potential in the field of nanotechnology, enabling nanomaterial structure and property predictions, facilitating materials design and discovery, and reducing the need for time-consuming and labor-intensive experiments and simulations. In contrast to their achiral counterparts, the application of machine learning for chiral nanomaterials is still in its infancy, with a limited number of publications to date. This is despite the great potential of machine learning to advance the development of new sustainable chiral materials with high values of optical activity, circularly polarized luminescence, and enantioselectivity, as well as for the analysis of structural chirality by electron microscopy. In this review, an analysis of machine learning methods used for studying achiral nanomaterials is provided, subsequently offering guidance on adapting and extending this work to chiral nanomaterials. An overview of chiral nanomaterials within the framework of synthesis-structure-property-application relationships is presented and insights on how to leverage machine learning for the study of these highly complex relationships are provided. Some key recent publications are reviewed and discussed on the application of machine learning for chiral nanomaterials. Finally, the review captures the key achievements, ongoing challenges, and the prospective outlook for this very important research field.

Chiral plasmonic sensing: From the perspective of light-matter interaction

Molecular chirality is represented as broken mirror symmetry in the structural orientation of constituent atoms and plays a pivotal role at every scale of nature. Since the discovery of the chiroptic property of chiral molecules, the characterization of molecular chirality is important in the fields of biology, physics, and chemistry. Over the centuries, the field of optical chiral sensing was based on chiral light-matter interactions between chiral molecules and polarized light. Starting from simple optics-based sensing, the utilization of plasmonic materials that could control local chiral light-matter interactions by squeezing light into molecules successfully facilitated chiral sensing into noninvasive, ultrasensitive, and accurate detection. In this Review, the importance of plasmonic materials and their engineering in chiral sensing are discussed based on the principle of chiral light-matter interactions and the theory of optical chirality and chiral perturbation; thus, this Review can serve as a milestone for the proper design and utilization of plasmonic nanostructures for improved chiral sensing.

Diverse ranking metamaterial inverse design based on contrastive and transfer learning

Metamaterials, thoughtfully designed, have demonstrated remarkable success in the manipulation of electromagnetic waves. More recently, deep learning can advance the performance in the field of metamaterial inverse design. However, existing inverse design methods based on deep learning often overlook potential trade-offs of optimal design and outcome diversity. To address this issue, in this work we introduce contrastive learning to implement a simple but effective global ranking inverse design framework. Viewing inverse design as spectrum-guided ranking of the candidate structures, our method creates a resemblance relationship of the optical response and metamaterials, enabling the prediction of diverse structures of metamaterials based on the global ranking. Furthermore, we have combined transfer learning to enrich our framework, not limited in prediction of single metamaterial representation. Our work can offer inverse design evaluation and diverse outcomes. The proposed method may shrink the gap between flexibility and accuracy of on-demand design.

Chirality in Light-Matter Interaction

The scientific effort to control the interaction between light and matter has grown exponentially in the last 2 decades. This growth has been aided by the development of scientific and technological tools enabling the manipulation of light at deeply sub-wavelength scales, unlocking a large variety of novel phenomena spanning traditionally distant research areas. Here, the role of chirality in light-matter interactions is reviewed by providing a broad overview of its properties, materials, and applications. A perspective on future developments is highlighted, including the growing role of machine learning in designing advanced chiroptical materials to enhance and control light-matter interactions across several scales.

Inverse design of photonic crystal filters with arbitrary correlation and size for accurate spectrum reconstruction

Spectroscopic technique based on nanophotonic filters can recover spectral information through compressive sensing theory. The spectral information is encoded by nanophotonic response functions and decoded by computational algorithms. They are generally ultracompact, low in cost, and offer single-shot operation with spectral resolution better than 1 nm. Thus, they could be ideally suited for emerging wearable and portable sensing and imaging applications. Previous work has revealed that successful spectral reconstruction relies on well-designed filter response functions with sufficient randomness and low mutual correlation, but no thorough discussion has been performed on the filter array design. Here, instead of blind selection of filter structures, inverse design algorithms are proposed to obtain a photonic crystal filter array with predefined correlation coefficients and array size. Such rational spectrometer design can perform accurate reconstruction for a complex spectrum and maintain the performance under noise perturbation. We also discuss the impact of correlation coefficient and array size on the spectrum reconstruction accuracy. Our filter design method can be extended to different filter structures and suggests a better encoding component for reconstructive spectrometer applications.

Neural-Network-Enabled Design of a Chiral Plasmonic Nanodimer for Target-Specific Chirality Sensing

Quantitative analysis of chiral molecules in various solvents is essential. However, there are still many challenges to enhancing the sensitivity in precisely determining both concentration and chirality. Here, we built an algorithmic methodology to predict and optimally design the chiroptical response of chiral plasmonic sensors for a specific target chiral analyte with the aid of deep learning. Based upon the analytic and intuitive understanding of the Born-Kuhn type plasmonic nanodimer, we designed and trained the neural networks that can successfully predict the chiroptical properties and further inversely design the plasmonic structure to achieve the intended circular dichroism. The developed algorithm could identify the optimum structure exhibiting the maximum sensitivity for the given specific analytes. Surprisingly, we discovered that sensitivity strongly depends on the various conditions of analytes and can be finely tuned with the structural parameters of plasmonic nanodimers. We envision that this study can provide a general platform to develop ultrasensitive chiral plasmonic sensors whose structure and sensitivity have been evolved algorithmically for adoption in specific applications.

Unsupervised Data-Driven Classification of Topological Gapped Systems with Symmetries

A remarkable breakthrough in topological phase classification is the establishment of the topological periodic table, which is mainly based on the classifying space analysis or K theory, but not based on concrete Hamiltonians that possess finite bands or arise in a lattice. As a result, it is still difficult to identify the topological phase of an arbitrary Hamiltonian; the common practice is, instead, to check the incomplete and still growing list of topological invariants one by one, very often by trial and error. Here, we develop unsupervised classifications of topological gapped systems with symmetries, and demonstrate the data-driven construction of the topological periodic table without a priori knowledge of topological invariants. This unsupervised data-driven strategy can take into account spatial symmetries, and further classify phases that were previously classified as trivial in the past. Our Letter introduces machine learning into topological phase classification and paves the way for intelligent explorations of new phases of topological matter.

Application of Image Super-Resolution Reconstruction in Gymnastics Training by Using Internet of Things Technology

Image super-resolution reconstruction, in short, is to restore some not too clear images, so that the image is more convenient to identify. It is generally used in intelligent surveillance systems and medical imaging systems in hospitals. This kind of technology is applied in many traditional algorithms. Today, the ultra-high-resolution algorithm has been revised. This paper analyzes in detail the convergence characteristics of two widely used pixel-by-pixel loss functions from theoretical and experimental perspectives, fully considers each convergence characteristic, and studies the combination of MAE and network. The MSE advantage learning method uses a single loss function to train the network. This training method can improve network performance. The level of Chinese gymnasts is relatively high, and it can even be said that they represent the most advanced level in the world. For many gymnasts, training for sharp turns is the focus of training, as well as training. Chinese gymnasts face similar problems. How to help Chinese gymnasts to improve their training quality has become a major issue in gymnastics training at this stage.

A nested U-shaped network for accurately predicting directional scattering of all-dielectric nanostructures

Forward prediction of directional scattering from all-dielectric nanostructures by a two-level nested U-shaped convolutional neural network (U²-Net) is investigated. Compared with the traditional U-Net method, the U²-Net model with lower model height outperforms for the case of a smaller image size. For the input image size of 40 × 40, the prediction performance of the U²-Net model with the height of three is enhanced by almost an order of magnitude, which can be attributed to the more excellent capacity in extracting richer multi-scale features. Since it is the common problem in nanophotonics that the model height is limited by the smaller image size, our findings can promote the nested U-shaped network as a powerful tool applied to various tasks concerning nanostructures.

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.

Inverse deep learning methods and benchmarks for artificial electromagnetic material design

In this work we investigate the use of deep inverse models (DIMs) for designing artificial electromagnetic materials (AEMs) - such as metamaterials, photonic crystals, and plasmonics - to achieve some desired scattering properties (e.g., transmission or reflection spectrum). DIMs are deep neural networks (i.e., deep learning models) that are specially-designed to solve ill-posed inverse problems. There has recently been tremendous growth in the use of DIMs for solving AEM design problems however there has been little comparison of these approaches to examine their absolute and relative performance capabilities. In this work we compare eight state-of-the-art DIMs on three unique AEM design problems, including two models that are novel to the AEM community. Our results indicate that DIMs can rapidly produce accurate designs to achieve a custom desired scattering on all three problems. Although no single model always performs best, the Neural-Adjoint approach achieves the best overall performance across all problem settings. As a final contribution we show that not all AEM design problems are ill-posed, and in such cases a conventional deep neural network can perform better than DIMs. We recommend that a deep neural network is always employed as a simple baseline approach when addressing AEM design problems. We publish python code for our AEM simulators and our DIMs to enable easy replication of our results, and benchmarking of new DIMs by the AEM community.

The fabrication of a highly electroactive chiral-interface self-assembled Cu(ii)-coordinated binary-polysaccharide composite for the differential pulse voltammetry (DPV) detection of tryptophan isomers

It is of significance to fabricate excellently performing chiral carbon nanocomposites for chiral electrochemical detection applications.

Light scattering of Laguerre-Gaussian vortex beams by arbitrarily shaped chiral particles

Laguerre-Gaussian (LG) beams with vortex phase possess a handedness, which would produce chiroptical interactions with chiral matter and may be used to probe structural chirality of matter. In this paper, we numerically investigate the light scattering of LG vortex beams by chiral particles. Using the vector potential method, the electric and magnetic field components of the incident LG vortex beams are derived. The method of moments (MoM) based on surface integral equations (SIEs) is applied to solve the scattering problems involving arbitrarily shaped chiral particles. The numerical results for the differential scattering cross sections (DSCSs) of several selected chiral particles illuminated by LG vortex beams are presented and analyzed. In particular, we show how the DSCSs depend on the chiral parameter of the particles and on the parameters describing the incident LG vortex beams, including the topological charge, the state of circular polarization, and the beam waist. This research may provide useful insights into the interaction of vortex beams with chiral particles and its further applications.

Graphic-processable deep neural network for the efficient prediction of 2D diffractive chiral metamaterials

We propose a novel, to the best of our knowledge, graphic-processable deep neural network (DNN) to automatically predict and elucidate the optical chirality of two-dimensional (2D) diffractive chiral metamaterials. Four classes of 2D chiral metamaterials are studied here, with material components changing among Au, Ag, Al, and Cu. The graphic-processable DNN algorithm can not only handle arbitrary 2D images representing any metamaterials that may even go beyond human intuition, but also capture the influence of other parameters such as thickness and material composition, which are rarely explored in the field of metamaterials, laying the groundwork for future research into more complicated nanostructures and nonlinear optical devices. Notably, the rigorous coupled wave analysis (RCWA) algorithm is first deployed to calculate circular dichroism (CD) in the higher-order diffraction beams and simultaneously promote the training of DNN. For the first time we creatively encode the material component and thickness of the metamaterials into the color images serving as input of the graphic-processable DNN, in addition to arbitrary graphical parameters. Especially, the smallest intensity is found in the third-order diffraction beams of E-like metamaterials, whose CD response turns out to be the largest. A comprehensive study is conducted to capture the influence of shape, unit period, thickness, and material component of arrays on chiroptical response. As expected, a satisfied precision and an accelerated computing speed that is 4 orders of magnitude quicker than RCWA are both achieved using DNN. This work belongs to one of the first attempts to thoroughly examine the generalization ability of the graphic-processable DNN for the study of arbitrary-shaped nanostructures and hypersensitive nanodevices.

Tackling Photonic Inverse Design with Machine Learning

Machine learning, as a study of algorithms that automate prediction and decision-making based on complex data, has become one of the most effective tools in the study of artificial intelligence. In recent years, scientific communities have been gradually merging data-driven approaches with research, enabling dramatic progress in revealing underlying mechanisms, predicting essential properties, and discovering unconventional phenomena. It is becoming an indispensable tool in the fields of, for instance, quantum physics, organic chemistry, and medical imaging. Very recently, machine learning has been adopted in the research of photonics and optics as an alternative approach to address the inverse design problem. In this report, the fast advances of machine-learning-enabled photonic design strategies in the past few years are summarized. In particular, deep learning methods, a subset of machine learning algorithms, dealing with intractable high degrees-of-freedom structure design are focused upon.

LIDAR and Beam Steering Tailored by Neuromorphic Metasurfaces Dipped in a Tunable Surrounding Medium

The control of amplitude, losses and deflection of light with elements of an optical array is of paramount importance for realizing dynamic beam steering for light detection and ranging applications (LIDAR). In this paper, we propose an optical beam steering device, operating at a wavelength of 1550 nm, based on high index material as molybdenum disulfide (MoS2) where the direction of the light is actively controlled by means of liquid crystal. The metasurface have been designed by a deep machine learning algorithm jointed with an optimizer in order to obtain univocal optical responses. The achieved numerical results represent a promising way for the realization of novel LIDAR for future applications with increase control and precision.

Building Multifunctional Metasystems via Algorithmic Construction

Flat optics foresees a promising route to ultracompact optical devices, where metasurfaces serve as the foundation. Conventional designs of metasurfaces start with a certain structure as the prototype, followed by extensive parametric sweeps to accommodate the requirements of phase and amplitude of the emerging light. Regardless of how computation consuming the process is, a predefined structure can hardly realize the independent control over polarization, frequency, and spatial channels, which hinders the potential of metasurfaces to be multifunctional. Besides, achieving complicated and multiple functions calls for designing metasystems with multiple cascading layers of metasurfaces, which introduces exponential complexity. In this work, we present a hybrid deep learning framework for designing multilayer metasystems with multifunctional capabilities. We demonstrate examples of a polarization-multiplexed dual-functional beam generator, a second-order differentiator for all-optical computing, and a space-polarization-wavelength multiplexed hologram. These examples are barely achievable by single-layer metasurfaces and unattainable by traditional design processes.

Decoding Optical Data with Machine Learning

Optical spectroscopy and imaging techniques play important roles in many fields such as disease diagnosis, biological study, information technology, optical science, and materials science. Over the past decade, machine learning (ML) has proved promising in decoding complex data, enabling rapid and accurate analysis of optical spectra and images. This review aims to shed light on various ML algorithms for optical data analysis with a focus on their applications in a wide range of fields. The goal of this work is to sketch the validity of ML-based optical data decoding. The review concludes with an outlook on unaddressed problems and opportunities in this emerging subject that interfaces optics, data science and ML.

Neural network enabled metasurface design for phase manipulation

The phase of electromagnetic waves can be manipulated and tailored by artificial metasurfaces, which can lead to ultra-compact, high-performance metalens, holographic and imaging devices etc. Usually, nanostructured metasurfaces are associated with a large number of geometric parameters, and the multi-parameter optimization for phase design cannot be possibly achieved by conventional time-consuming simulations. Deep learning tools capable of acquiring the relationship between complex nanostructure geometry and electromagnetic responses are best suited for such challenging task. In this work, by innovations in the training methods, we demonstrate that deep neural network can handle six geometric parameters for accurately predicting the phase value, and for the first time, perform direct inverse design of metasurfaces for on-demand phase requirement. In order to satisfy the achromatic metalens design requirements, we also demonstrate simultaneous phase and group delay prediction for near-zero group delay dispersion. Our results suggest significantly improved design capability of complex metasurfaces with the aid of deep learning tools.

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.

Phase transitions, percolation, fracture of materials, and deep learning

Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold p_{c} and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point p_{c} or the IFP and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold p_{c}, the elastic moduli, and the universal Poisson ratio at p_{c}. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly p_{c}, even though the training data were for the state of the systems far from p_{c}. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point.

Chiral Plasmons with Twisted Atomic Bilayers

van der Waals heterostructures of atomically thin layers with rotational misalignments, such as twisted bilayer graphene, feature interesting structural moiré superlattices. Because of the quantum coupling between the twisted atomic layers, light-matter interaction is inherently chiral; as such, they provide a promising platform for chiral plasmons in the extreme nanoscale. However, while the interlayer quantum coupling can be significant, its influence on chiral plasmons still remains elusive. Here we present the general solutions from full Maxwell equations of chiral plasmons in twisted atomic bilayers, with the consideration of interlayer quantum coupling. We find twisted atomic bilayers have a direct correspondence to the chiral metasurface, which simultaneously possesses chiral and magnetic surface conductivities, besides the common electric surface conductivity. In other words, the interlayer quantum coupling in twisted van der Waals heterostructures may facilitate the construction of various (e.g., bi-anisotropic) atomically-thin metasurfaces. Moreover, the chiral surface conductivity, determined by the interlayer quantum coupling, determines the existence of chiral plasmons and leads to a unique phase relationship (i.e., ±π/2 phase difference) between their transverse-electric (TE) and transverse-magnetic (TM) wave components. Importantly, such a unique phase relationship for chiral plasmons can be exploited to construct the missing longitudinal spin of plasmons, besides the common transverse spin of plasmons.

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.

Optical circular dichroism engineering in chiral metamaterials utilizing a deep learning network

Here, a deep learning (DL) algorithm based on deep neural networks is proposed and employed to predict the chiroptical response of two-dimensional (2D) chiral metamaterials. Specifically, these 2D metamaterials contain nine types of left-handed nanostructure arrays, including U-like, T-like, and I-like shapes. Both the traditional rigorous coupled wave analysis (RCWA) method and DL approach are utilized to study the circular dichroism (CD) in higher-order diffraction beams. One common feature of these chiral metamaterials is that they all exhibit the weakest intensity but the strongest CD response in the third-order diffracted beams. Our work suggests that the DL model can predict CD performance of a 2D chiral nanostructure with a computational speed that is four orders of magnitude faster than RCWA but preserves high accuracy. The DL model introduced in this work shows great potentials in exploring various chiroptical interactions in metamaterials and accelerating the design of hypersensitive photonic devices.

Chiral nanohole arrays

Chiral nanohole array (CNA) films are fabricated by a simple and efficient shadow sphere lithography (SSL) method and achieve label-free enantiodiscrimination of biomolecules and drug molecules at the picogram level. The intrinsic mirror symmetry of the structure is broken by three subsequent depositions onto non-close packed nanosphere monolayers with different polar and azimuthal angles. Giant chiro-optical responses with a transmission as high as 45%, a chirality of 21°μm^-1, and a g-factor of 0.17, respectively, are generated, which are among the largest values that have been reported in the literature. Such properties are due to the local rotating current density generated by a surface plasmon polariton as well as a strong local rotating field produced by localized surface plasmon resonance, which leads to the excitation of substantial local superchiral fields. The 70 nm-thick CNAs can achieve label-free enantiodiscrimination of biomolecules and drug molecules at the picogram level as demonstrated experimentally. All these advantages make the CNAs ready for low-cost, high-performance, and ultracompact polarization converters and label-free chiral sensors.