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This paper theoretically proposes a multichannel functional metasurfacecomputer characterized by Generalized Sheet Transition Conditions (GSTCs) andsurface susceptibility tensors. The study explores a polarization- andangle-multiplexed metasurfaces enabling multiple and independent parallelanalog spatial computations when illuminated by differently polarized incidentbeams from different directions. The proposed synthesis overcomes substantialrestrictions imposed by previous designs such as large architectures arisingfrom the need of additional subblocks, slow responses, and most importantly,supporting only the even reflection symmetry operations for normal incidences,working for a certain incident angle or polarization, and executing only singlemathematical operation. The versatility of the design is demonstrated in a waythat an ultra-compact, integrable and planar metasurface-assisted platform canexecute a variety of optical signal processing operations such as spatialdifferentiation and integration. It is demonstrated that a metasurfacefeaturing non-reciprocal property can be thought of as a new paradigm to breakthe even symmetry of reflection and perform both even- and odd-symmetrymathematical operations at normal incidences. Numerical simulations alsoillustrate different aspects of multichannel edge detection scheme throughprojecting multiple images on the metasurface from different directions. Suchappealing findings not only circumvent the major potential drawbacks ofprevious designs but also may offer an efficient, easy-to-fabricate, andflexible approach in wave-based signal processing, edge detection, imagecontrast enhancement, hidden object detection, and equation solving without anyFourier lens.

Generalized Optical Signal Processing Based on Multi-Operator Metasurfaces Synthesized by Susceptibility Tensors