Perfect All-Angle Spatial Differentiators via Asymmetric Grazing-Angle Huygens' Metasurfaces

We present a perfect all-angle spatially deriving metasurface, overcoming numerical aperture and accuracy limitations of previous devices. While these were designed mainly via qualitative symmetry breaking and heuristic optimizations, we derive exact closed-form susceptibility conditions, highlighting the grazing-angle Huygens' condition as a crucial aspect of this functionality. We tailor proper physical inclusions, based on rigorous electromagnetic specifications beyond symmetry breaking, to validate this concept in simulation. Our excellent results herald a sound paradigm to engineer not only analog computers, but a myriad of novel nonlocal microwave and optical devices.