Twist-Controlled Second-Order Spatial Differentiation in a Three-Sheet Black Arsenic Stack

We investigate transmission-mode second-order spatial differentiation in a stack of three twisted black-arsenic (b-As) conducting sheets separated by dielectric spacers. The symmetric twist provides a structural degree of freedom for controlling the normal-incidence Jones response and suppressing the zeroth-order helicity-converted background. Near the matching condition, the opposite-helicity transmission is dominated by a quadratic momentum-space response proportional to (kx±iky)2, giving conjugate phase windings with topological charges ℓ=±2. The corresponding complex operator combines Cartesian and mixed second-order derivatives and produces second-order beam shaping and two-dimensional edge enhancement. Full transfer-matrix calculations confirm the expected real-space operation for both Gaussian and image inputs within the demonstrated numerical aperture. These results show how crystallographic twist and multilayer interference can be used to engineer polarization-selective spatial operators in anisotropic two-dimensional multilayers without subwavelength patterning.