Neural network assisted high-spatial-resolution polarimetry with non-interleaved chiral metasurfaces

Amplitude, phase, polarization, and wavelength are fundamental properties of light. Among them, the state of polarization (SoP) characterizes the direction in which the electric component of the field oscillates. The analysis and measurement of the SoP plays a key role in wide applications from remote sensing and astronomy to biology and microscopy since the light-matter interactions have strong dependences on the SoP. Hence, various types of polarization detection (i.e., polarimetry) systems have been developed over the past decades. In general, traditional polarimetry systems can be categorized into division of time and division of space. The former requires rotating polarization elements resulting in long detection time. The latter can be further grouped into division of amplitude, aperture, and focal plane. All of these techniques are equipped with a set of polarizers, waveplates, beam-splitters or filters, making the systems bulky and complex, therefore hinders the future development for miniature and compact optical devices. Metasurface, a new emerging flat optical device, enables thin and lightweight optical elements with precisely engineered wavefronts. Many innovative methods based on metasurfaces for polarimetry have been proposed. Constructing a subwavelength scatterer or antenna array, on-chip polarimeter can be realized, however, the propagation waveguide for polarization-selective coupling or the free space for directional scattering restricts the application in full local mapping of the inhomogeneous SoP. Based on polarization filters and spatial multiplexing scheme, full-Stokes polarimetric measurements can be obtained with complex fabrication due to the dual-layer configuration. Polarimetry can also be demonstrated with the design of plasmonic meta-gratings, yet the reflection/diffraction mode makes it challenging for direct integration on sensors. Similar to the division of focal plane, researchers design a metalens array (usually consisting three to six metalenses) to split and focus light in different polarization bases for estimating the full Stokes vectors. However, this spatial interleaved design method still suffers from the trade-off between the detection pixel size (i.e., 3–6 metalenses) and measurement crosstalk, prohibiting them to access high-spatial resolution in polarization analyses. Matrix Fourier optics has also been introduced and applied to the realization of polarimetry, whereas the design needs to be fed into an optimization and the polarization-dependent propagation with different diffraction orders would occupy a substantial volume of space. Most of the relevant works focused on the intensity measurement of different polarization bases (at least four) to calculate the Stokes vector. Actually, for an arbitrary SoP, it can be decomposed into a pair of orthogonal polarization states (e.g., right-hand and left-hand circular polarizations, termed as RCP and LCP) with different amplitudes and phase shifts. If the amplitude contrast and the phase difference can be detected simultaneously, then the SoP can be obtained one time without spatial multiplexing. Here, we propose a new strategy based on a non-interleaved chiral metasurface and neural network assistance to analyze the SoP in high spatial resolution. This single chiral metasurface can modulate the co-polarization and two cross-polarizations independently to present the amplitude and phase information. Both spatially uniform and non-uniform polarization states are detected in simulations and experiments, showing very good fidelity. Note that in the spatially nonuniform polarization detection, an inhomogeneous SoP beam is generated by a specially designed metasurface, and a neural network is employed to strengthen the detection of SoPs. Finally, we demonstrate its applications in daily life for picking out different functional glasses with similar morphology features.

The authors review conventional polarimetry approaches: division of time (requiring rotating polarization elements and leading to long detection times) and division of space (division of amplitude, aperture, and focal plane), which require multiple bulk components (polarizers, waveplates, beam-splitters, filters) and hinder miniaturization. They summarize metasurface-based polarimetry: on-chip polarimeters using subwavelength scatterers or antenna arrays enable polarization-selective coupling or directional scattering but are limited for full local mapping of inhomogeneous SoP; dual-layer polarization filters with spatial multiplexing can achieve full-Stokes measurements but involve complex fabrication; plasmonic meta-gratings work in reflection/diffraction modes that complicate direct sensor integration; metalens arrays (3–6 metalenses) emulate division of focal plane for full Stokes retrieval but suffer a trade-off between pixel size and crosstalk, limiting high spatial resolution; matrix Fourier optics can perform polarimetry but requires optimization and occupies substantial space due to polarization-dependent diffraction orders. The authors conclude that most prior methods rely on measuring multiple polarization bases, whereas simultaneous retrieval of amplitude contrast and phase difference between RCP and LCP could enable single-shot SoP estimation without spatial multiplexing.

Concept: The method uses a single, non-interleaved chiral metasurface that independently modulates three polarization channels—co-circular polarization (co-CP) and the two cross-circular polarization (cross-CP) conversions (RCP→LCP and LCP→RCP). By forming three off-axis focal lines that interfere at designated points, the device enables simultaneous extraction of amplitude contrast and relative phase between RCP and LCP components, allowing full SoP determination in a single shot without spatial multiplexing. Interferometric readout: Under RCP incidence, two focal lines form: n (cross-CP, RCP→LCP) and m (co-CP), intersecting at point A. Under LCP incidence, the co-CP focal line m reappears and another cross-CP line l (LCP→RCP) forms, intersecting at point B. For general linear/elliptical SoP, all three lines appear with an additional intersection C. The average intensity distributions along AC and BC yield the amplitude contrast of RCP and LCP components. The intensities at A and B include interference terms that encode the RCP–LCP phase difference δrl = φr − φl, enabling phase retrieval. Formalism: The SoP is represented via Stokes parameters S0, S1, S2, S3 with Ex, Ey and their phase difference δxy. In the circular basis, ellipticity χ and azimuth ψ are given by χ = ½arcsin((|Er|²−|El|²)/(|Er|²+|El|²)) and ψ = δrl. Field expressions at the interference points are modeled as Ea = a0(|Er|e^{iφr}|R⟩ + |El|e^{iφl}|L⟩) + a1|Er|e^{iφr}|L⟩ and Eb = a0(|Er|e^{iφr}|R⟩ + |El|e^{iφl}|L⟩) + a2|El|e^{iφl}|R⟩, where a0, a1, a2 depend on design, enabling derivation of δrl from measured intensities. Meta-atom design and phase decoupling: A single planar anisotropic, planar-chiral meta-atom is used. The Cartesian-basis Jones matrix is J = R(−θ) diag(√(εx/εz) e^{iφx}, √(εy/εz) e^{iφy}) R(θ). Transformed to the circular basis, J_CP shows that a nonzero cross term (related to εxy and φx−φy) allows independent phase control of the co-CP (diagonal) and cross-CP (off-diagonal) channels. To achieve independent control, the meta-atom must break mirror symmetry and n-fold (n>2) rotational symmetry. Phases are decomposed as φCO = φa (propagation phase), φRL = φXRL + φPB, and φLR = φXLR + φPB, where φPB is the Pancharatnam–Berry phase and φXRL ≠ φXLR are chiral phase delays for opposite CP conversions. Device phase profiles: The three channels are assigned uncorrelated focusing phase profiles to generate three off-axis focal lines at prescribed orientations and offsets. For a device with diameter D = 20 μm, offset δ0 = 3 μm, and focal length f = 25 μm, the co-CP phase implements an off-axis cylindrical lens; the two cross-CP phases are rotated versions (angles θ0 = 120°, θ1 = −120°) to form lines l and n. Meta-atom library and selection: Full-wave FDTD (Lumerical) simulations at 470 nm are used to build a library of planar-chiral SiNx meta-atoms (n = 2.032 + 0.0013i). A hexagonal lattice with period a = 360 nm suppresses higher orders; meta-atom height is 1.2 μm to span 0–2π. Varying chiral geometries (including nanorods as special cases) yields a data cube of φCO, φRL, φLR. Parameter space of φCO and (φRL + φLR) is explored with an eight-level phase approximation; atoms simultaneously satisfying target φCO and φRL + φLR with high transmission are chosen. The final set averages ~71% efficiency (simulation). Array and fabrication: To cover both uniform and nonuniform SoP detections, an array (25×25) of the designed chiral metasurface elements is fabricated as a detection pixel. Optical microscopy and SEM confirm morphology; an example image shows 2×2 supercells within a 40 μm × 40 μm region. The metasurface operates in transmission using SiNx, compatible with CMOS integration. Optical setup and measurement: A white-light laser (Fianium Super-continuum, 4 W) with a 470 nm bandpass filter (10 nm bandwidth) illuminates the metasurface. A linear polarizer (Thorlabs WP25L-VIS) and quarter-wave plate (Thorlabs AQWP05M-600) generate desired input SoPs. The focal plane is imaged onto a sensor via a microscope objective (NA = 0.5). In both simulations and experiments, additional circular polarization analysis (using CP filters experimentally; extracting CP components in simulations) is applied to improve accuracy. A deep convolutional neural network is incorporated to robustly locate interference points (A, B, C) and extract line intensities across varying imaging conditions, improving speed and resilience to setup changes and positional variations. SoP reconstruction: From measured intensity contrasts along AC and BC and the interferometric signals at A and B under CP analysis, the amplitudes |Er|, |El| and phase difference δrl are retrieved. Ellipticity angle χ and azimuth ψ are computed, and full Stokes parameters S are derived. Performance is validated for multiple uniform SoPs and extended to spatially nonuniform polarization fields generated by a specially designed metasurface.

- The non-interleaved chiral metasurface produces three independent focal lines (two cross-CP, one co-CP) whose interferometric intersections encode both amplitude contrast and phase difference between RCP and LCP components, enabling single-shot SoP retrieval without spatial multiplexing. - Simulation and experimental validation on six representative uniform SoPs (x, y linear; LCP; RCP; and two ellipticals S = (0.64,0,±0.77)) show expected line patterns and interference behavior, allowing accurate reconstruction of ellipticity χ and azimuth ψ and derivation of Stokes parameters. Experimental results closely match simulations despite fabrication-related intensity differences. - Efficiency metrics: average transmission ~80%; average diffraction efficiency (power within 3×FWHM of focal line relative to transmitted co-polarized light) ~70%; total efficiency ~56% (product of the two), indicating practical viability. - Adding circular polarization analysis (CP bias/filters) improves accuracy in the presence of background noise and nonideal local periodic approximation. - The approach works for both spatially uniform and nonuniform polarization fields; a neural network strengthens detection by automating feature localization and enhancing robustness to setup variations. - A proof-of-concept application distinguishes two similar-looking functional glasses, demonstrating sensing utility.

The work addresses long-standing limitations of polarimetry systems that rely on bulky, multi-element optics or spatial multiplexing across multiple pixels/metalenses. By independently controlling the phases of co-CP and two cross-CP channels within a single planar chiral metasurface, the device creates interferometric signatures that encode both amplitude contrast and phase between CP components. This eliminates the need for multiple polarization bases or interleaved metalens arrays, mitigating crosstalk and preserving high spatial resolution at the pixel level. The use of SiNx in transmission mode enhances compatibility with CMOS sensors, facilitating compact integration. Interferometric readout combined with CP analysis counters background and nonidealities, while a deep CNN automates the localization of key features (intersections and line intensities), improving robustness to alignment shifts and enabling fast, accurate SoP retrieval. The demonstrated total efficiency (~56%) and accurate reconstruction across multiple SoPs suggest the method’s practicality for real-world applications, including spatially varying polarization mapping and material discrimination (e.g., glasses with similar morphology).

The authors demonstrate a compact, non-interleaved, interferometric polarimetry method using a single chiral metasurface that independently controls three polarization channels to retrieve both amplitude and phase information of the incident SoP in one shot. With the assistance of a deep convolutional neural network, the system achieves fast, robust, and accurate measurements for both uniform and nonuniform polarization fields and shows a sensing application distinguishing similar glasses. The device operates efficiently in transmission (total efficiency ~56%) and is compatible with CMOS integration, promising high-spatial-resolution polarimetry in miniature platforms. The approach is expected to inspire further designs for detection and sensing; future work may explore broader bandwidths, improved efficiency, fully on-chip integration, and expanded machine-learning-assisted reconstruction for complex scenes.

- Background noise and nonuniform focal-line intensity arise from the breakdown of the local periodic approximation, affecting ideality of focal patterns. - Experimental intensity ratios differ from simulations due to fabrication errors, impacting quantitative accuracy. - Precise localization of interference points (A, B, C) is required; although mitigated by the neural network, performance can be sensitive to imaging setup changes and feature positioning. - The demonstrated operation is centered at 470 nm with a narrowband filter (10 nm), suggesting potential spectral bandwidth limitations for the current design. - Additional circular polarization analysis (filters/bias) was employed to improve accuracy, adding components to the measurement pipeline.