Multifunctional Ultra‐Wide‐Angle Spatial Optical Analog Computing in the Terahertz Regime

ABSTRACT Optical analog spatial differentiation, as the core mathematical operation in optical computing, can realize real‐time edge detection in image processing and efficient feature extraction in data compression. Although analog spatial differential operations have been implemented in various optical systems, they still suffer from complex structural parameters dependency and a typically limited numerical aperture (NA) of smaller than 0.5. To date, achieving simultaneous first‐ and second‐order spatial differentiation with NA higher than 0.5 remains an unresolved challenge, even considering recent advances in metasurface‐based analog computing. Here, we propose a synergistic mechanism combining critical coupling and near‐far‐field multi‐wave superposition to simultaneously achieve ultra‐high‐NA analog spatial first‐ and second‐order differentiation. Operating in two orthogonal polarization modes, numerical simulations indicate that the maximum angle of incidence can reach 89.9°, corresponding to an NA approaching unity and yielding a spatial resolution limit of 1.27λ. Experimentally, the maximum incident angle achieved is 75°, corresponding to an NA of 0.966 and a spatial resolution limit of 1.3λ. We also propose the theoretical imaging resolution limit Δ(NA, λ) for edge detection. Our strategy significantly expands analog spatial computing to the non‐paraxial region, which is pivotal in the upcoming high‐speed communication, and can benefit future multifunctional terahertz imaging, computational analysis, medical diagnostics, and machine vision.