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Twist-Controlled Second-Order Spatial Differentiation in a Three-Sheet Black Arsenic Stack
Wenhao Xu1, Shiyang Zhang1,2, Lan Xu1,2
1School of Physics and Chemistry, Hunan First Normal University, Changsha 410205, China.
Abstract:
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.
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