Analog image processing using optical metasurfaces offers the potential for faster processing speeds and lower power consumption compared to digital methods. Traditional analog image processing often involves bulky 4F lens systems for Fourier filtering. Metasurfaces, being planar and ultra-thin, provide a compact alternative. This research focuses on overcoming the limitations of existing metasurface designs for analog image processing, specifically edge detection, which involves applying a spatial differential operator like the Laplacian to enhance edges in an image. Current approaches, often relying on single optical modes and Fano lineshapes, struggle to achieve optimal performance across several key metrics simultaneously: spatial resolution (linked to the numerical aperture, NA), spectral bandwidth, polarization independence (isotropy and dual-polarization operation), and efficiency (throughput and low insertion losses). These factors are critical for practical applications in fields like augmented reality, advanced driver-assistance systems, and biomedical imaging, driving the need for improved metasurface designs that can perform high-quality analog image processing.

Several studies have explored metasurface-based analog image processing, particularly edge detection. Methods based on single optical modes with Fano lineshapes have demonstrated edge detection but suffer from limited bandwidth. Increasing bandwidth typically comes at the cost of reduced throughput. Furthermore, many designs exhibit polarization asymmetry and azimuthal anisotropy. Topological photonics approaches offer improved bandwidth and isotropy but often require cross-polarized reflection and specific incident angles, impacting device footprint and NA. Alternatively, using Pancharatnam–Berry phase metasurfaces in a 4F system with crossed polarizers achieves large bandwidth but lacks compactness. While some approaches address incoherent illumination, they often require digital postprocessing and increased footprint. The common thread among these methods is a compromise between bandwidth, throughput, polarization independence, and compactness. This research aims to address these limitations by introducing a dispersion engineering approach.

This study proposes and experimentally demonstrates a dispersion engineering approach for designing metasurfaces that overcome existing limitations in analog edge detection. The core concept involves engineering the band structure dispersion of a periodic nonlocal metasurface to create two dispersive modes, ω+(k||) and ω−(k||). These modes are designed such that their frequencies are similar at normal incidence (k||=0) but shift in opposite directions as the in-plane wave vector (k||) increases. The spectral detuning between the modes and their linewidths are carefully controlled to achieve a broad bandwidth of near-zero transmission at normal incidence while simultaneously ensuring high transmission at larger angles, achieving the desired high-pass filter behavior for edge enhancement. A silicon-on-glass platform with a triangular lattice of air holes etched into a silicon slab was chosen for implementation, with the lattice constant, slab thickness, and hole radius optimized to meet the dispersion requirements. Numerical simulations, using Ansys HFSS, were conducted to design and optimize the metasurface. The simulations involved calculating the transmission coefficients (tpp and tss) as functions of wavelength and incident angle for both p- and s-polarizations. The metasurface was fabricated using standard top-down lithography: PECVD for silicon deposition, E-beam lithography for patterning, and dry etching to transfer the pattern to the silicon. A custom-built setup was used for optical characterization, measuring transmission amplitudes as a function of wavelength and incident angle using a broadband supercontinuum laser and powermeters. Imaging experiments were performed using a target with the desired shape (the CUNY logo), illuminated with collimated light. The scattered light was collected and imaged with a near-infrared camera. The metasurface was placed between the target and the objective lens. Two efficiency metrics were defined to quantitatively assess edge detection performance: peak efficiency (ηpeak) and average efficiency (ηavg). These metrics are compared to theoretical limits for ideal k-space filters.

The research successfully demonstrates a dispersion engineered silicon metasurface for high-performance edge detection. The key findings are: 1. **Broadband Operation:** The fabricated metasurface exhibits an operational bandwidth of 35 nm (approximately 5 THz) centered around 1500 nm, significantly wider than previous approaches. This bandwidth was achieved experimentally. 2. **High Numerical Aperture:** The metasurface achieves a numerical aperture (NA) greater than 0.35, enabling high-resolution image processing. 3. **Dual-Polarization and Isotropy:** The device shows isotropic and polarization-independent responses, effectively processing images with any input polarization state. This isotropy was verified both numerically and experimentally up to NA=0.35. 4. **High Efficiency:** The metasurface demonstrates high throughput efficiencies, approaching the theoretical maximum for the given NA. Peak efficiencies (ηpeak) of 7-9% and average efficiencies (ηavg) of 1.5-3% were observed in numerical simulations for monochromatic light, and these values remain high (ηpeak ≥ 3.5% and ηavg ≥ 1%) even under broadband and arbitrarily polarized excitation. Experimental measurements validated the high efficiencies. 5. **Experimental Validation:** The numerical findings were successfully validated through experiments, confirming the broadband, high-NA, dual-polarization, and high-efficiency capabilities of the designed metasurface for edge detection. The experimental results are in excellent agreement with the numerical simulations. 6. **Quantitative Metrics:** Two new efficiency metrics, ηpeak and ηavg, were introduced to quantitatively assess edge detection performance and to compare experimental results to theoretical limits. 7. **Potential for Improvement:** The study suggests that further optimization of the metasurface's dispersion properties could lead to even larger operational bandwidths (simulations suggest a potential doubling of the bandwidth).

The results demonstrate a significant advancement in analog image processing using metasurfaces. The achievement of high efficiency, broadband operation, and dual-polarization capability without sacrificing NA or isotropy addresses a critical gap in the field. The proposed dispersion engineering approach offers a powerful design principle for optimizing multiple figures of merit simultaneously. The high efficiencies achieved, approaching the theoretical limits of an ideal k-space filter, highlight the potential for practical applications. While the current design focuses on edge detection, the underlying principles of dispersion engineering can be extended to other analog image processing tasks and more complex functionalities by introducing additional optical modes and tailoring their dispersion properties. The simplicity of the fabricated device, a single-layer silicon-on-glass structure, makes it amenable to mass manufacturing and commercialization. The experimental validation strongly supports the feasibility and practical relevance of the proposed approach.

This work presents a significant advancement in analog optical image processing by demonstrating a dispersion-engineered metasurface capable of high-efficiency, broadband, and polarization-independent edge detection. The experimental validation of the numerical design, achieving high NA and operational bandwidths, significantly advances the field of metasurface-based optical computing. Future work could explore extending this approach to more complex operations and integrating these metasurfaces into larger optical systems for practical applications.

While the demonstrated metasurface achieves high performance, there are some limitations. The current design's bandwidth, though significantly improved compared to previous works, could be further enhanced through additional design optimization. Slight intensity fluctuations in the input image, due to diffraction effects, result in weaker peaks in the output images, although these do not significantly hinder edge detection. Further refinement of the fabrication process could potentially mitigate these minor imperfections and further improve the overall signal-to-noise ratio.