  This paper theoretically proposes a multichannel functional metasurface
computer characterized by Generalized Sheet Transition Conditions (GSTCs) and
surface susceptibility tensors. The study explores a polarization- and
angle-multiplexed metasurfaces enabling multiple and independent parallel
analog spatial computations when illuminated by differently polarized incident
beams from different directions. The proposed synthesis overcomes substantial
restrictions imposed by previous designs such as large architectures arising
from 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 single
mathematical operation. The versatility of the design is demonstrated in a way
that an ultra-compact, integrable and planar metasurface-assisted platform can
execute a variety of optical signal processing operations such as spatial
differentiation and integration. It is demonstrated that a metasurface
featuring non-reciprocal property can be thought of as a new paradigm to break
the even symmetry of reflection and perform both even- and odd-symmetry
mathematical operations at normal incidences. Numerical simulations also
illustrate different aspects of multichannel edge detection scheme through
projecting multiple images on the metasurface from different directions. Such
appealing findings not only circumvent the major potential drawbacks of
previous designs but also may offer an efficient, easy-to-fabricate, and
flexible approach in wave-based signal processing, edge detection, image
contrast enhancement, hidden object detection, and equation solving without any
Fourier lens.
