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arXiv · 2608.15499

Acoustic toroidal vortices with programmable links and knots

Shuai Liu·Xiang-Yuan Xu·Hao Ge·Yijie Shen·Yan-Feng Chen·Ming-Hui Lu
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Abstract

Toroidal vortices are three-dimensional torus-shaped wave structures characterized by phase circulation around a closed vortex line. Their toroidal geometry provides a natural foundation for constructing linked and knotted wave structures. Here we experimentally synthesize scalar acoustic toroidal vortices using a programmable circular phased array. Full spatiotemporal measurements directly resolve the toroidal envelope, the closed phase-singularity ring, the associated poloidal phase winding, and the free-space evolution of the wave packet. By introducing an independently controlled phase winding along the toroidal cycle, we realize scalar acoustic hopfions and directly reconstruct their three-dimensional equiphase fibers from the measured complex pressure field. Varying the poloidal and toroidal winding numbers controls the phase-fiber geometry, linking, and connectivity, yielding a Hopf link, a multicomponent torus link, and a trefoil knot. These results provide direct experimental access to the geometry, propagation dynamics, and phase-fiber topology of scalar toroidal wave fields, establishing a reconfigurable acoustic platform for linked and knotted wave structures.

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Shuai Liu, Xiang-Yuan Xu, Hao Ge, Yijie Shen, Yan-Feng Chen, Ming-Hui Lu. 2026-08-16. Acoustic toroidal vortices with programmable links and knots. https://arxiv.org/abs/2608.15499

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