Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities

Analog optical signal processing has dramatically transcended the speed and energy limitations accompanied with its digital microelectronic counterparts. Motivated by recent metasurface?s evolution, the angular scattering diversity of a reciprocal passive bianisotropic metasurface with normal polarization is utilized in this paper to design a multi-channel meta-computing surface, performing multiple advanced mathematical operations on input fields coming from different directions, simultaneously. Here, the employed ultra-thin bianisotropic metasurface computer is theoretically characterized based on generalized sheet transition conditions and susceptibility tensors. The operators of choice are deliberately dedicated to asymmetric integro-differential equations and image processing functions, like edge detection and blurring. To clarify the concept, we present several illustrative simulations whereby diverse wave-based mathematical functionalities have been simultaneously implemented without any additional Fourier lenses. The performance of the designed metasurface overcomes the nettlesome restrictions imposed by the previous analog computing proposals such as bulky profiles, asserting only single mathematical operation, and most importantly, supporting only the even-symmetric operations for normal incidences. Besides, the realization possibility of the proposed metasurface computer is conceptually investigated via picturing the angular scattering behavior of several candidate meta-atoms. This work opens a new route for designing ultra-thin devices executing parallel and accelerated optical signal/image processing.