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Updated: Jan 20, 2026

Protocol for Isolating the Mouse Circle of Willis
Published on: October 22, 2016
Nonreciprocal Willis Coupling in Zero-Index Moving Media.
Li Quan1, Dimitrios L Sounas1,2, Andrea Alù1,3,4,5
1Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA.
This study demonstrates extreme acoustic nonreciprocity using moving metamaterials with zero-index propagation. This breakthrough enables novel applications like one-way sound focusing lenses at modest speeds.
Area of Science:
- Acoustics
- Metamaterials
- Wave Propagation
Background:
- Mechanical motion breaks sound propagation symmetry, but achieving significant nonreciprocity usually requires high speeds.
- Zero-index acoustic metamaterials offer unique wave manipulation possibilities.
Purpose of the Study:
- To achieve extreme acoustic nonreciprocity and induced bianisotropy at modest motion speeds.
- To explore the use of asymmetric Willis coupling in metamaterials for directional sound control.
Main Methods:
- Combining moving media with zero-index acoustic propagation.
- Designing a metamaterial with an array of waveguides loaded by Helmholtz resonators.
- Utilizing asymmetric Willis coupling to create opposite refractive indices for bidirectional propagation.
Main Results:
- Demonstrated extreme acoustic nonreciprocity and induced bianisotropy at modest speeds.
- Achieved nonreciprocal positive-to-negative sound refraction.
- Metamaterial exhibits opposite signs of the refractive index for opposite propagation directions.
Conclusions:
- Moving zero-index acoustic metamaterials offer a pathway to extreme nonreciprocity and bianisotropy.
- The asymmetric Willis coupling is key to achieving directional control of sound.
- Proposed a novel nonreciprocal metamaterial lens with one-sided focusing capabilities.
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