  Analog computing has emerged as a promising candidate for real-time and
parallel continuous data processing. This paper presents a reciprocal way for
realizing asymmetric optical transfer functions (OTFs) in the reflection side
of the on-axis processing channels. It is rigorously demonstrated that the
presence of Cross-polarization Exciting Normal Polarizabilities (CPENP) of a
reciprocal metasurface circumvents the famous challenge of Green's function
approach in implementation of on-axis reflective optical signal processing
while providing dual computing channels under orthogonal polarizations.
Following a comprehensive theoretical discussion and as a proof of concept, an
all-dielectric optical metasurface is elaborately designed to exhibit the
desired surface polarizabilities, thereby reflecting the first derivative and
extracting the edges of images impinging from normal direction. The proposed
study offers a flexible design method for on-axis metasurface-based optical
signal processing and also, dramatically facilitates the experimental setup
required for ultrafast analog computation and image processing.
