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Peer-reviewedCC BY 4.0Nanomaterials

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

  • Wenhao Xu1
  • Shiyang Zhang1,2
  • Lan Xu1,2
  1. 1School of Physics and Chemistry, Hunan First Normal University, Changsha 410205, China
  2. 2Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of the Ministry of Education, Hunan Normal University, Changsha 410081, China
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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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Cite

BibTeXRIS
BibTeX
@article{xu2026twistcontrolled,
  title = {{Twist-Controlled Second-Order Spatial Differentiation in a Three-Sheet Black Arsenic Stack}},
  author = {Wenhao Xu and Shiyang Zhang and Lan Xu},
  journal = {Nanomaterials},
  year = {2026},
  month = oct,
  doi = {10.3390/nano16201315},
  url = {https://www.mdpi.com/2079-4991/16/20/1315},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Twist-Controlled Second-Order Spatial Differentiation in a Three-Sheet Black Arsenic Stack
AU  - Wenhao Xu
AU  - Shiyang Zhang
AU  - Lan Xu
PY  - 2026
DA  - 2026/10/01
JO  - Nanomaterials
DO  - 10.3390/nano16201315
UR  - https://www.mdpi.com/2079-4991/16/20/1315
AB  - 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.
SN  - 2079-4991
ER  -