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The manipulation of vector optical fields in three-dimensional (3D) space plays a vital role in both fundamental research and practical implementations of polarization optics. However, existing studies mostly focus on 3D vector optical fields with limited modes. Here, an approach of spin-decoupled spatial partitioning is proposed to generate complex 3D vector optical fields with a customizable number of modes on demand. The crosstalk among different modes is effectively suppressed by the decoupling capability of asymmetric photonic spin–orbit interactions (PSOIs) and the design of region displacement for opposite spin states. As a proof-of-concept demonstration, a metasurface is designed to generate longitudinally varying high-order cylindrical vector fields, ranging from the 2nd to the 10th order in even sequences along the propagation direction. The experimental results demonstrate the effectiveness and potential of our approach to enabling precise control of 3D vector optical fields with arbitrary mode combinations. This work holds promising applications in biophotonics, quantum optics, and communications.

Non-line-of-sight (NLOS) imaging aims at recovering hidden objects located beyond the traditional line of sight, with potential applications in areas such as security monitoring, search and rescue, and autonomous driving. Conventionally, NLOS imaging requires raster scanning of laser pulses and collecting the reflected photons from a relay wall. High-time-resolution detectors obtain the flight time of photons undergoing multiple scattering for image reconstruction. Expanding the scanning area while maintaining the sampling rate is an effective method to enhance the resolution of NLOS imaging, where an angle magnification system is commonly adopted. Compared to traditional optical components, planar optical elements such as liquid crystal, offer the advantages of high efficiency, lightweight, low cost, and ease of processing. By introducing liquid crystal with angle magnification capabilities into the NLOS imaging system, we successfully designed a large field-of-view high-resolution system for a wide scanning area and high-quality image reconstruction. Furthermore, in order to reduce the long data acquisition time, a sparse scanning method capitalizing on the correlation between measurement data to reduce the number of sampling points is thus proposed. Both the simulation and experiment results demonstrate a >20 % reduction in data acquisition time while maintaining the exact resolution.

Longitudinal optical field modulation is of critical importance in a wide range of applications, including optical imaging, spectroscopy, and optical manipulation. However, it remains a considerable challenge to realize a uniformly distributed light field with extended depth-of-focus. Here, a high-efficiency extended depth-of-focus metalens is proposed by adjoint-based topology-shape optimization approach, wherein the theoretical electric field intensity corresponding to a variable focal-length phase is utilized as the figure of merit. Using a dozen of metalens with random structure parameters as initial structures, the average focal depth of topology-shape optimized metalens is greatly improved up to 18.80 μm (about 29.7λ), which is 1.54 times higher than the diffraction-limited focal depth. Moreover, all the topology-shape optimized metalens exhibit high diffraction efficiency exceeding 0.7 over the whole focal depth range, which is approximately three times greater than that of the forward design. Our results offer a new insight into the design of extended depth-of-focus metalens and may find potential applications in imaging, holography, and optical fabrication.

Metasurfaces based on the Pancharatnam–Berry (PB) phase have attracted significant attention in the domains of subwavelength optics and electromagnetics. Conventional theory predicts that the PB phase is exactly twice the rotation angle of the anisotropic meta-atoms. Differently, a recent advance has demonstrated that the generalized PB phase representing multiple times of the rotation angle could be obtained with high-fold rotational symmetry meta-atoms, but it suffers from the low cross-polarization conversion efficiency (the theoretical upper limit of 25%) that impedes its further applications, especially for meta-atoms with rotational symmetry ≥3. Here, we verify that the chiral meta-atoms with high-fold rotational symmetries could produce the generalized PB phase. Besides, the all-metallic configuration is utilized to design C2, C3, and C5 chiral catenary meta-atoms to improve their efficiency and bandwidth. The equivalent air waveguide with low loss between two adjacent meta-atoms is formed to analyse the higher performances of the all-metallic scheme for the realization of the generalized PB phase compared with the metal–insulator–metal and all-dielectric C3 meta-atoms. As a proof of concept, four metadevices including two spin-Hall metadevices and two holograms are experimentally demonstrated and their maximum efficiency could exceed 83% in simulation. This work could provide a high-efficiency platform for the study of the generalized PB phase in linear and nonlinear optics.

During the past few years, metasurface polarization optics has experienced remarkable advances, resulting in revolutionary applications in imaging, sensing, computing, etc. The realization of complex optical operations requires the consideration of both the individual meta‐atoms as well as their intricate couplings. However, conventional design methods face challenges as design degrees of freedom and functionality complexity. Additionally, previous studies are restricted to the local design of single meta‐atoms based on explicit mapping relationships while ignoring interactions, resulting in an inability to meet the on‐demand requirements of complex light‐field operations. Here, a global design strategy based on field‐driven polygon evolution to achieve the inverse design of large‐scale coupled meta‐atoms is proposed. Through two global simulations, it can effectively reshape any given target optical field into an optimal structural distribution of devices without knowing mapping relationship. Near‐perfect spin‐decoupled beam‐splitting and high‐performance focusing, as well as the generation of arbitrary vector optical fields on the Poincaré sphere with a maximal diffraction efficiency closely approaching 100%, are experimentally demonstrated. This strategy opens up a new avenue for a rapid inverse design of large‐scale, high‐performance multifunctional meta‐devices, which can hold significant implications for both classical and quantum information processing domains. [ABSTRACT FROM AUTHOR]

Reconfigurable metasurfaces have exhibited significant potential in wireless communication owing to their capacity to transmit information without relying on traditional complex radio frequency (RF) chain transmitters. Nonetheless, the majority of metasurface‐based wireless communication systems modulate signals only in the time domain. Here, an amplitude‐phase reconfigurable metasurface is proposed to establish a wireless communication system that can simultaneously transmit different messages to users by encoding digital signals within the spatial domain. By changing the bias voltages of varactors integrated in the meta‐atom, the reconfigurable metasurface can achieve independent 3‐bit phase and 1‐bit amplitude coding. Through a beamforming methodology, the proposed metasurface generates diverse scattering beams with suppressed sidelobe levels, which not only enables multiple channels through space coding but also reduces signal leakage in undesired directions. Numerical simulations and experiments are carried out to verify the beamforming scheme, and a dual‐channel wireless communication system is established. The results show that two distinct images can be simultaneously retrieved by two separate users, which demonstrates the dual‐channel transmission capability of the wireless communication system. The proposed strategy opens up an avenue for implementing multi‐channel wireless communication systems, which indicates its great potential in multiple‐user collaborative wireless communication and radar systems. [ABSTRACT FROM AUTHOR]

Optical imaging systems, like microscopes, cameras, and telescopes, continue to expand the scope of human observation of the world. As one of the key indicators of imaging systems, the field-of-view (FOV) is often limited by coma aberration. Expanding it generally relies on a combination of complex lenses, leading to a bulky and cumbersome system. Recently, the emergency of meta-optics provides an alternative to constructing compact and lightweight large-FOV metalens through elaborated phase modulation within a flat surface, showing great potential in surveillance, unmanned vehicles, onboard planes or satellites, medical science, and other new applications. In this article, we review recent advances of wide-angle metalenses, including operation principles, design strategies, and application demos. Firstly, basic principles of wide-angle imaging using a single metalens are interpreted. Secondly, some advanced methods for designing subwavelength structures with high angle robustness and high efficiency are discussed. Thirdly, some representative functional devices and applications are surveyed. Finally, we conclude with an outlook on future potentials and challenges that need to be overcome.

Recently, full Poincaré beams (FPBs) with spatially variant polarization states spanning the entire surface of the Poincaré sphere have attracted considerable interests. Expanding the FPBs into an array way has the promising applications from multiparticle manipulation to optical communication. However, how to efficiently generate a high‐purity FPB array with intracavity method remains elusive. Here, a metasurface‐integrated degenerate cavity laser is proposed for efficient generation of 10 × 10 FPB array, where a pair of metasurfaces are adopted to independently modulate the circular polarization state while compensating the mode discrepancies within the cavity. Such a design strategy enables a self‐reproducing intracavity optical field, concurrently ensuring the stabilization of intracavity oscillation. It is numerically demonstrated that the purity of orbital angular momentum (OAM) in the first‐order FPB array can approach to 92.89%, with a root‐mean‐square error (RMSE) of polarization ellipse parameters below 8.17%. This work provides a compact and efficient design platform for the generation of a variety of vector beam arrays and may find promising applications in free space communication and multiple particle manipulation. [ABSTRACT FROM AUTHOR]

Quasi-continuous-phase metasurfaces overcome the side effects imposed by high-order diffraction on imaging and can impart optical parameters such as amplitude, phase, polarization, and frequency to incident light at sub-wavelength scales with high efficiency. Structured-light three-dimensional (3D) imaging is a hot topic in the field of 3D imaging because of its advantages of low computation cost, high imaging accuracy, fast imaging speed, and cost-effectiveness. Structured-light 3D imaging requires uniform diffractive optical elements (DOEs), which could be realized by quasi-continuous-phase metasurfaces. In this paper, we design a quasi-continuous-phase metasurface beam splitter through a vector iterative Fourier transform algorithm and utilize this device to realize structured-light 3D imaging of a target object with subsequent target reconstruction. A structured-light 3D imaging system is then experimentally implemented by combining the fabricated quasi-continuous-phase metasurface illuminated by the vertical-cavity surface-emitting laser and a binocular recognition system, which eventually provides a new technological path for the 3D imaging field. [ABSTRACT FROM AUTHOR]

Non‐line‐of‐sight (NLOS) imaging enables the reconstruction of targets beyond the direct line of sight, which has extensive applications across various fields. However, it remains unclear how and to what extent the vectorial nature of light, which plays a critical role in optical imaging and object recognition, can enhance the imaging performance of active NLOS imaging. Here, this work proposes a method that utilizes vector optical fields (VOFs) with arbitrarily designed polarization distributions to realize NLOS imaging in challenging conditions with low signal‐to‐noise ratio (SNR). A generalized VOF reflection model is established at the relay surface for active NLOS imaging to determine the optimal illumination angle and polarization as well as the received polarization. Based on this model, the feasibility of multi‐view NLOS imaging is demonstrated with enhanced SNR of echo signals under proper VOF modulation, surpassing the limitations of conventional single‐view NLOS imaging. Simulations and experiments validate the superior performance of the proposed approach to realize accurate reconstruction and recognition of hidden objects. [ABSTRACT FROM AUTHOR]

On‐chip metasurfaces integrated atop optical waveguides have demonstrated the capability of efficiently radiating guided‐waves into arbitrarily prescribed spatial modes by properly tailoring the phase distribution in the metasurface interface. To date, most on‐chip holographic metasurfaces, typically relying on path multiplexing or wavelength multiplexing to multiply the produced images, encounter certain limitations in further enhancing the image storage capacity due to the limited degrees of freedom available for on‐chip devices. This work introduces an on‐chip metasurface composed of polarization‐sensitive cross meta‐atoms allowing independent control of the propagation phase of diffracted waves from waveguided TE and TM modes. Meanwhile, incorporating the guided‐wave generated in‐plane detour phases into the metasurface yields another two degrees of freedom. Thus, four independent holographic images can be readily switched by simply selecting the excitation modes and waveguide ports. As a proof‐of‐concept, a dual‐port four‐channel multiplexed metasurface, whose optical functionalities are validated by performing full‐wave simulations, is successfully realized. Moreover, the application to the creation of 3D holograms is also extended. Thus, the presented method provides a new approach for multifunctional multiplexing of on‐chip metasurfaces, which could hold great potential for applications in next‐generation wearable AR devices, 3D vision, multifunctional micro‐photonic integrated circuits, etc. [ABSTRACT FROM AUTHOR]

Accurately predicting the price of carbon is an effective way of ensuring the stability of the carbon trading market and reducing carbon emissions. Aiming at the non-smooth and non-linear characteristics of carbon price, this paper proposes a novel hybrid prediction model based on improved feature extraction and non-linear integration, which is built on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), fuzzy entropy (FuzzyEn), improved random forest using particle swarm optimisation (PSORF), extreme learning machine (ELM), long short-term memory (LSTM), non-linear integration based on multiple linear regression (MLR) and random forest (MLRRF), and error correction with the autoregressive integrated moving average model (ARIMA), named CEEMDAN-FuzzyEn-PSORF-ELM-LSTM-MLRRF-ARIMA. Firstly, CEEMDAN is combined with FuzzyEn in the feature selection process to improve extraction efficiency and reliability. Secondly, at the critical prediction stage, PSORF, ELM, and LSTM are selected to predict high, medium, and low complexity sequences, respectively. Thirdly, the reconstructed sequences are assembled by applying MLRRF, which can effectively improve the prediction accuracy and generalisation ability. Finally, error correction is conducted using ARIMA to obtain the final forecasting results, and the Diebold–Mariano test (DM test) is introduced for a comprehensive evaluation of the models. With respect to carbon prices in the pilot regions of Shenzhen and Hubei, the results indicate that the proposed model has higher prediction accuracy and robustness. The main contributions of this paper are the improved feature extraction and the innovative combination of multiple linear regression and random forests into a non-linear integrated framework for carbon price forecasting. However, further optimisation is still a work in progress. [ABSTRACT FROM AUTHOR]

Polarization is the nature of optics. Exploiting metasurface's polarizations can enhance the multiplexing capacity but face a limited number of channels. For example, a single‐layer metasurface can offer three independent channels with six degrees of freedom (DoFs) including the amplitude and phase of Ex, Exy(yx), and Ey of the Jones matrix. In this work, it is theoretically demonstrated that the degrees of freedom of dual‐layer metasurfaces can reach eight, overcoming the polarization multiplexing constraints of single‐layer metasurfaces and that the cross‐talk can be largely reduced as compared with single‐layer metasurfaces when the channel number is larger than three. Numerical calculations manifest a decrease of 100%, 63%, and 50% for the cross‐talk of channels 4, 5, and 6, respectively. As a proof‐of‐concept demonstration of high‐capacity polarization multiplexing, an arbitrary‐polarization‐controlled 5‐channel dual‐layer metasurface exhibiting five nanoprintings and five holographic images with reduced cross‐talk under different incident and output polarizations is successfully designed. Thus, the research highlighting the high‐multiplexing‐capacity of dual‐layer metasurfaces can significantly advance multifunctional optical devices with high efficiency, simple integration, and ease of manipulation. [ABSTRACT FROM AUTHOR]

Spatial differentiator is the key element for edge detection, which is indispensable in image processing, computer vision involving image recognition, image restoration, image compression, and so on. Spatial differentiators based on metasurfaces are simpler and more compact compared with traditional bulky optical analog differentiators. However, most of them still rely on complex optical systems, leading to the degraded compactness and efficiency of the edge detection systems. To further reduce the complexity of the edge detection system, a monolithic metasurface spatial differentiator is demonstrated based on asymmetric photonic spin-orbit interactions. Edge detection can be accomplished via such a monolithic metasurface using the polarization degree. Experimental results show that the designed monolithic spatial differentiator works in a broadband range. Moreover, 2D edge detection is experimentally demonstrated by the proposed monolithic metasurface. The proposed design can be applied at visible and near-infrared wavelengths by proper dielectric materials and designs. We envision this approach may find potential applications in optical analog computing on compact optical platforms.

Self-accelerating beams show considerable captivating phenomena and applications owing to their transverse acceleration, diffraction-free and self-healing properties in free space. Metasurfaces consisting of dielectric or metallic subwavelength structures attract enormous attention to acquire self-accelerating beams, owing to their extraordinary capabilities in the arbitrary control of electromagnetic waves. However, because the self-accelerating beam generator possesses a large phase gradient, traditional discrete metasurfaces suffer from insufficient phase sampling, leading to a low efficiency and narrow spectral band. To overcome this limitation, a versatile platform of catenary-inspired dielectric metasurfaces is proposed to endow arbitrary continuous wavefronts. A high diffraction efficiency approaching 100% is obtained in a wide spectral range from 9 to 13 μm. As a proof-of-concept demonstration, the broadband, high-efficiency and high-quality self-accelerating beam generation is experimentally verified in the infrared band. Furthermore, the chiral response of the proposed metasurfaces enables the spin-controlled beam acceleration. Considering these superior performances, this design methodology may find wide applications in particle manipulation, high-resolution imaging, optical vortex generation, and so forth.

Geometric metasurfaces have shown superior phase control capacity owing to the geometric nature of their phase profile. The existing geometric metasurfaces are generally composed of metal-dielectric composites or all-dielectric subwavelength structures. Here, a novel configuration, all-metallic structure, is proposed to achieve broadband and high-performance electromagnetic wavefront manipulation based on the geometric phase. A catenary model is built to describe the optical dispersion and guide the design of metasurfaces. Two metadevices including a beam deflector and a hologram are designed and experimentally demonstrated in the infrared regime, with the measured optical efficiency up to 84% (the simulated efficiency reaches 93%). Compared to previous metal-insulator-metal structures, this approach can realize higher efficiency and broader operating bandwidth owing to its lower ohmic loss. This design strategy is universal and can be easily scaled to any other spectra without complex optimization. Moreover, since metals have excellent mechanical and physical properties, such as good thermal and electrical conductivity, this all-metallic structure may provide a new thinking on interdisciplinary research.

In the field of optical communications and quantum informatics, polarization and orbital angular momentum (OAM) offer a promising way to expand the dimension of information. However, detecting the polarization state and topological charge of the OAM beam on‐chip way can be challenging. To address this, an ultracompact metasurface is proposed and demonstrated. The metasurface is composed of six polarization‐sensitive metalenses that occupy 60°annular sectors each and are capable of simultaneous polarization state and orbital angular momentum detection. The metasurface focuses the coaxial polarized vortex beam into six locations, and the foci displacement is related to the value of the topological charge. The corresponding polarization state can be obtained through the reconstructed Stokes parameter using the six focus light intensities. For proof‐of‐concept, an ultracompact metasurface operating at a wavelength of 1064 nm is fabricated, which exhibits exceptional polarization and orbital angular momentum recognition ability. The proposed metasurface possesses the merits of ultra‐compact size and simultaneously entire polarization state and orbital angular momentum identification capability, which may encourage the development of on‐chip optical communication systems. [ABSTRACT FROM AUTHOR]

The electro‐optic (EO) modulator is a crucial device for achieving high‐speed optical communication and optical interconnection by loading the high‐frequency electrical signals onto the optical carrier. To date, modern communication technique demands for a low energy consumption for green data center establishment. In this work, a thin‐film BaTiO3 crystal waveguide Mach–Zehnder interferometer (MZI) type EO intensity modulator is experimentally implemented and its dynamic‐polarization interference process involving a phase‐polarization modulation (PPM) scheme other than conventional optical phase modulation (OPM) is carefully analyzed. Its findings show that the PPM scheme can efficiently reduce the half‐wave voltage (Vπ${V}_\pi$) and the equivalent half‐wave voltage (Veπ${V}_{e\pi }$) of the modulator. Then, a new theory of deriving the bit energy (BE) from Veπ${V}_{e\pi }$ is put forward, which has proven that the BE value under PPM is lower than the OPM counterpart. The EO modulator prototype featuring a length of 1.4 mm, Veπ${V}_{e\pi }$= 3.0 V and BE = 1.2 pJ/bit match well with the numerical calculations, thus validating the feasibility to achieve a BE<0.2 pJ/bit for an EO modulator through optimization of the electrode gap and state‐of‐the‐art fabrication techniques in the near future. [ABSTRACT FROM AUTHOR]

Distinct from conventional optical lenses suffering from the diffraction limit, the superoscillatory lens offers an alternative approach to realize far‐field sub‐diffraction focusing and find significant applications in both microscopy and telescopy. During the past few years, planar micro/nanostructures are unitized to precisely manipulate the optical fields through a standard lens to realize a superoscillatory field along the radial direction of the pupil. Here, an angular superoscillatory metalens (ASOM) is demonstrated by combining the superoscillatory phase and angular metalens phase in a single metasurface. To the best of the authors' knowledge, this is the first work that focuses on the angular superoscillatory phenomenon. As a proof‐of‐concept application demo, this study shows the ASOM can map the received orbital angular modes (OAMs) into focusing patterns at the focal plane with different azimuth angles. Therefore, the OAM spectrum incorporating multiple modes can be determined with a single‐shot measurement according to the precalibrated mapping relationship. This study shows that the OAM resolution is scaled up about 3.2 times compared with a normal angular metalens, thanks to the shrinkage of the focal patterns. This approach may push the development of integrated and high‐dimensional optical and quantum systems. [ABSTRACT FROM AUTHOR]

Sorting orbital angular momentum (OAM) and spin angular momentum (SAM) of photons is crucial for optical communications, optical storage, and quantum information processing, wherein complicated optical setups or bulky devices are conventionally utilized to determine the angular momentum via repetitive interference or diffractive projection measurements. Recently, advancements in compact and single‐shot OAM detection have been made via coordinate transformation metasurfaces. Nevertheless, most of these strategies require precise separation and alignment between multiple components and cannot simultaneously distinguish full angular momentum states. Besides, the single‐shot maximum identifiable OAM mode numbers are generally limited to 60 due to the tradeoff between the mode space and reduced‐cross‐talk mode interval. Here, this work puts forward and experimentally demonstrates a monolithic spiral metalens (SML) for ultrahigh‐capacity sorting full angular momentum states. The SML focus the incident vortex beam into multiple‐turn spiral ring rather than a circle ring on the focal plane according to its topological charge, with the mode order ranging from −250 to 250. Consequently, the maximum identifiable OAM mode number is up to 168 under a single‐shot measurement, which largely surpass the best results reported hitherto. The experimental results obtained in the telecom band underpin the design approach, which may find great potential in high‐capacity communication and storage applications. [ABSTRACT FROM AUTHOR]

Light beam carrying spin angular momentum (SAM) and orbital angular momentum (OAM) have attracted great interest due to their great potential for high‐capacity optical communication, optical tweezers, and quantum information. However, the current detection methods suffer from the lack of robustness to misalignments in the optical system, which limits the detection accuracy and the application for off‐axis vortex array detection. Here, a high‐efficiency, broadband, and single‐layer metasurface design is proposed for alignment‐free angular momentum detection via spin‐independent astigmatic transformation (SIAT). The SAM and OAM states can be recognized from the diffraction direction and patterns, respectively. Proof‐of‐concept demonstrations are experimentally carried out on different incident beams including circular‐polarization, linear‐polarization, and vector vortex beams, as well as vortex beam arrays, showing a high diffraction efficiency of ≈81% at 1064 nm while operating within the broadband region of 900–1300 nm. The alignment‐free merit for the incident position, incident angle, and detector distance grants the device great potential for integrated quantum systems and multiparticle micromanipulation with optical tweezers. [ABSTRACT FROM AUTHOR]

Vector optical field (VOF) manipulation greatly extended the boundaries of traditional scalar optics over the past decades. Meanwhile, the newly emerging techniques enabled by structural functional optical materials have driven the research domain into the subwavelength regime, where abundant new physical phenomena and technologies have been discovered and exploited for practical applications. In this Tutorial, we outline the basic principles, methodologies, and applications of VOF via structural functional materials. Among various technical routes, we focus on the metasurface-based approaches, which show obvious advantages regarding the design flexibility, the compactness of systems, and the overall performances. Both forward and inverse design methods based on the rigorous solution of Maxwell's equations are presented, which provide a valuable basis for future researchers. Finally, we discuss the generalized optical laws and conventions based on VOF manipulation. The applications in optical imaging, communications, precision measurement, laser fabrication, etc. are highlighted. [ABSTRACT FROM AUTHOR]