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

Image processing is central to applications such as augmented reality, driver assistance, and biomedical imaging, but is commonly performed digitally, which can suffer from limited speed and high energy consumption. Analog optical components can augment digital processors by performing specific computations with high speed and low power. Conventional analog image processing often uses 4F Fourier filtering with bulky optics and alignment sensitivities, limiting integration. Metasurfaces—ultra-thin planar devices—enable compact optical computation, including wavefront shaping and polarization control. Metasurface-based analog image processing can implement spatial differentiation and edge detection by angle-selective filtering of the plane-wave components of an image, encoding a desired Fourier-space transfer function. For two-dimensional, polarization-independent edge detection, the metasurface must suppress low-angle (low spatial frequency) components and transmit higher-angle components with an isotropic, polarization-independent transfer function up to a large numerical aperture. Practical performance requires: (i) high NA to process high-resolution images without distortion, (ii) large overall gain factor (|C| not too small) to ensure strong output signal (high throughput), and (iii) broadband operation because input light may be polychromatic or of unknown wavelength. Existing approaches face trade-offs and limitations in bandwidth, throughput, isotropy, polarization symmetry, or footprint. The authors propose and experimentally demonstrate dispersion engineering to realize compact metasurfaces that optimize these figures of merit simultaneously, showing isotropic, dual-polarization edge detection with NA > 0.35, ~35 nm bandwidth around 1500 nm, and introducing quantitative efficiency metrics to assess throughput and insertion loss.

Prior works realized edge detection using nonlocal metasurfaces that support a single optical mode producing a Fano lineshape. At a chosen frequency, normal-incidence transmission is near zero, and increasing angle shifts the resonance to increase transmission. However, the bandwidth of near-zero normal-incidence transmission is much smaller than the resonance linewidth, so using lower-Q modes to widen bandwidth reduces the slope and thus the transmission of high spatial frequencies, creating a bandwidth–throughput trade-off. Moreover, many demonstrated nonlocal metasurfaces have C2 or C4 symmetry, inducing azimuthal anisotropy and polarization asymmetry. Topological photonics approaches can improve bandwidth and isotropy but typically require cross-polarized reflection at large, fixed incidence angles, constraining numerical aperture and device footprint. PB-phase metasurfaces placed in the Fourier plane of a 4F system can be broadband because spectral and angular responses are decoupled, but the 4F arrangement and polarizers limit miniaturization. Analog optical filtering generally requires spatial coherence; recent methods address incoherent illumination at the cost of larger footprint and digital postprocessing. Overall, a compact metasurface achieving isotropic, broadband, polarization-independent, high-NA, and high-efficiency edge detection without a 4F system had not been demonstrated, and efficiency metrics have been underexplored.

Concept: Engineer the angular dispersion of two distinct optical modes in a periodic nonlocal metasurface so that (i) their normal-incidence frequencies are close (detuning Δω > 0), (ii) each mode’s radiative linewidth is comparable to or slightly larger than Δω, and (iii) their frequencies shift in opposite directions with increasing in-plane wavevector |k|| | (one increases, one decreases). This creates, at normal incidence, a broad spectral band B of near-zero transmission (suppressing low spatial frequencies), and as angle increases, both modes move away from the central band, raising transmission toward unity across B, enabling a Laplacian-like, high-pass response with high throughput over large angles. Using a C6-symmetric lattice maximizes isotropy and polarization independence at normal incidence; off-normal polarization independence is ensured by designing modes with similar coupling to s and p polarizations. Design and simulation: A photonic-crystal-slab metasurface is implemented as a triangular lattice of air holes in an amorphous silicon slab (εs = 11.90) on a glass substrate (εg = 2.31). Parameters: lattice constant a = 924 nm (targeting ~1500 nm operation), slab thickness H, and hole radius R. Simulations (Ansys HFSS) scan H at fixed R = 265 nm; H = 270 nm is selected so the two dominant modes at normal incidence have detuning comparable to their linewidths. Angle- and wavelength-dependent transmission amplitudes tpp and tss are computed versus polar angle θ. The two modes exhibit opposite dispersions up to θmax ≈ 26° (NA ≈ 0.44), yielding an operational bandwidth ~35 nm (~5 THz) around 1500 nm with Laplacian-like response. Vertical cuts show |tpp(θ)| increases nearly monotonically with θ, approaching >0.9 by ~30°. For s polarization, one mode is weakly dispersive at small angles and crosses the band, yielding a transmission zero at intermediate θ (10°–20°) for certain wavelengths; nevertheless, the overall high-pass behavior and high transmission at larger angles are maintained. Transfer functions tpp(kx,ky) and tss(kx,ky) are computed, showing isotropy up to NA ≈ 0.35 with angle- and azimuth-independent phase; cross-polarized terms tsp and tps are negligible up to NA = 0.35. Efficiency metrics: Two image-based metrics are defined to quantify throughput: peak efficiency ηpeak = max(Jout)/max(Jin), and average efficiency ηavg = avg(Jout around edges)/max(Jin). Numerical image-processing simulations use an unpolarized input image (CUNY logo, lateral extent ~80λ), include full polarization-dependent plane-wave expansions and both co- and cross-polarized transfer functions, and set max(Jin) = 1 for direct estimation. Fabrication: Glass coverslips are cleaned (acetone ultrasonic bath, oxygen plasma), coated with 270 nm PECVD a-Si, spin-coated with ZEP 520-A e-beam resist and anti-charging polymer. Patterning uses 50 keV e-beam lithography (photonic-crystal triangular hole lattice), transferred via ICP dry etch (Oxford PlasmaPro System 100). Resist is removed (Remover PG). SEMs provided in Supplementary. Optical characterization of transfer functions: A custom setup mounts samples on rotation stages to control polar (θ) and azimuthal (φ) angles. A supercontinuum laser filtered by a narrowband tunable filter provides illumination. The beam is weakly focused (f = 20 cm lenses) and transmitted light is re-collimated and detected by germanium powermeters. A linear polarizer sets x or y polarization (mapping to p or s for any θ, φ). Transmission amplitudes versus θ and wavelength are recorded; data for φ = 0° shown, with φ = 30° in Supplementary. Imaging experiments: A chromium-on-glass target (institution logo) is illuminated by a collimated beam (wide-field). The scattered image is collected by a NIR objective (Mitutoyo 50X, NA = 0.42) and relayed to a NIR camera via a tube lens (f = 15 cm). The metasurface is placed a few hundred microns in front of the target. For narrowband tests, a 5 nm FWHM filter selects wavelengths across the operational band; illumination is nearly unpolarized (degree of polarization ~10%). For broadband tests, a custom pulse shaper produces spectra spanning 1450–1485 nm. Camera counts are normalized by integration time and impinging power for consistent efficiency estimation across conditions.

- The proposed dispersion-engineered metasurface achieves isotropic, dual-polarization edge detection with large numerical aperture: isotropy verified up to NA ≈ 0.35, with negligible cross-polarization and near angle-independent phase in the transfer function. - Operational spectral bandwidth: ~35 nm (~5 THz) centered near 1500 nm, with near-zero normal-incidence transmission and increasing transmission with angle, approaching |t| ≈ 0.9–1.0 at large θ. - Simulations show robust Laplacian-like, high-pass behavior for both p and s polarizations; s polarization exhibits a transmission zero at intermediate θ for certain wavelengths but maintains high-pass response and high transmission at larger angles. - Numerical image processing with an unpolarized input (logo of lateral extent ~80λ) produces sharp, uniform edges largely independent of edge direction; simulated ηpeak ≈ 7–9% and ηavg ≈ 1.5–3% across the band, close to the theoretical maximum for an ideal k-space Laplacian filter with NA = 0.35. - Experimental angle–wavelength transmission maps (p and s) agree closely with simulations, including the two normal-incidence zeros and opposite dispersions with θ. - Experimental narrowband imaging (1452–1485 nm): high-quality edge detection across the band; measured ηpeak > 5% and ηavg > 1% across wavelengths, approaching the ideal filter bound (ηideal ≈ 8–9% for NA = 0.35). - Experimental broadband imaging (1450–1485 nm) for six input polarizations (linear x, y, diagonal, anti-diagonal, right/left circular): consistently sharp, high-contrast edges with polarization-insensitive performance; efficiencies remain high with ηpeak ≥ 3.5% and ηavg ≥ 1%. - Additional observed peaks in output images correspond to differentiation of weak input intensity fluctuations due to diffraction at the target aperture, consistent with the device’s differentiation action; main-edge peaks are ~4x higher than those from weak fluctuations. - Bandwidth can be further increased via dispersion engineering; a numerically optimized variant achieves ~10 THz bandwidth (twice the demonstrated) with a modest background increase.

The study demonstrates that engineering the angular dispersion of two optical modes in a nonlocal metasurface provides sufficient design freedom to simultaneously optimize key performance metrics—bandwidth, throughput efficiency, isotropy, polarization independence, and numerical aperture—over realistic operating conditions. Implemented in a simple silicon-on-glass photonic-crystal-slab platform, the device exhibits isotropic transfer functions up to NA > 0.35 and broad operational bandwidth around 1500 nm, achieving high-quality, high-efficiency second-order differentiation for arbitrary polarizations and both narrowband and broadband inputs. The introduced efficiency metrics (peak and average) rigorously quantify throughput, showing experimental values close to the theoretical maximum for an ideal passive k-space filter at the same NA, and within about a factor of two of the exact Laplacian operation. The approach is versatile and manufacturable, and the dispersion-engineering framework can be extended to increase bandwidth (e.g., larger mode detuning with correspondingly adjusted Q factors) and to include more than two modes to further shape angle-dependent responses and enable advanced transfer functions.

This work presents and validates a dispersion-engineering strategy for metasurfaces that perform analog edge detection with simultaneous optimization of bandwidth, efficiency, isotropy, polarization independence, and NA, without a 4F configuration. A single-layer silicon photonic-crystal-slab metasurface realizes isotropic, dual-polarization Laplacian-like filtering over a ~35 nm band near 1500 nm and NA > 0.35, delivering experimentally measured edge intensities close to ideal k-space filter limits. The method is compatible with scalable fabrication and practical imaging setups. Future directions include expanding bandwidth by adjusting mode detuning and Q factors, leveraging additional optical modes for greater control of zeros and poles in the transfer function, and pursuing designs with even higher efficiencies and more sophisticated analog operations.

- Demonstrated NA is > 0.35 (θ ≈ 21°–26° depending on metric); larger NA operation would require further dispersion engineering and may introduce additional design complexity. - s-polarized response exhibits a sub-ideal feature: a transmission zero at intermediate angles for certain wavelengths, though it does not significantly impact overall edge-detection performance. - Current bandwidth is ~35 nm (~5 THz) for the fabricated device; larger bandwidths are possible but may increase background transmission at the central frequency unless carefully optimized. - Efficiencies, while close to ideal k-space filter limits for the given NA, remain about a factor of two below what would be achieved by an exact Laplacian operation on the image. - As with most analog optical filtering approaches, operation assumes some spatial coherence in the illumination; fully incoherent scenarios generally require additional system complexity or postprocessing. - Output images can show additional weaker peaks due to differentiation of small intensity fluctuations in the input image (e.g., from diffraction by the target aperture), though main edges remain clearly identifiable.