Diffraction by Circular and Triangular Apertures as a Diagnostic Tool of Twisted Matter Waves

• URL: http://arxiv.org/abs/2510.00826v1
• Date: Wed, 01 Oct 2025 12:37:17 GMT
• Title: Diffraction by Circular and Triangular Apertures as a Diagnostic Tool of Twisted Matter Waves
• Authors: Maksim Maksimov, Nikita Borodin, Daria Kargina, Dmitry Naumov, Dmitry Karlovets,
• Abstract summary: Circular apertures preserve cylindrical symmetry and produce far-field profiles whose radii depend on $|ell|$ but are insensitive to its sign.<n> equilateral triangles break axial symmetry and yield structured patterns that encode both the magnitude and the sign of $ell$.<n>Our results establish triangular diffraction as a simple, passive, and robust method for reading out the OAM content of structured quantum beams.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study diffraction of twisted matter waves (electrons and light ions carrying orbital angular momentum $\ell/\hbar=0,\pm1,\pm2,\ldots$ by circular and triangular apertures. Within the scalar Kirchhoff-Fresnel framework, circular apertures preserve cylindrical symmetry and produce ringlike far-field profiles whose radii and widths depend on $|\ell|$ but are insensitive to its sign. In contrast, equilateral triangles break axial symmetry and yield structured patterns that encode both the magnitude and the sign of $\ell$. A transparent Fraunhofer mapping links detector coordinates to the Fourier plane, explaining the $(|\ell|+1)$-lobe rule and the sign-dependent rotation of the pattern. We validate these results for both ideal Bessel beams and localized Laguerre-Gaussian packets, and we cross-check them by split-step Fourier propagation of the time-dependent Schr"odinger equation. From these analyses we extract practical design rules (Fraunhofer distance, lattice pitch, detector sampling) relevant to OAM diagnostics with moderately relativistic electrons with $E_{\rm kin}\sim0.1$ to $5$ MeV and light ions with $E_{\rm kin}\sim0.1$ to $1$ MeV/u. Our results establish triangular diffraction as a simple, passive, and robust method for reading out the OAM content of structured quantum beams.

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