Willis coupling, also known as pressure-velocity cross coupling, in acoustic materials has received much attention in the past years. This effect has been found useful in acoustic metasurface designs for wave redirection. We find that Willis coupling in phononic crystals also provides rich physics to manipulate waves. Here, we report the extreme asymmetric lateral sound beaming effect in a two-dimensional phononic crystal composed of Willis scatterers. By matching the second-order Bragg scattering with two leaky guided modes (a quadrupole resonance and a cross-coupling-induced dipole resonance), a normally incident wave is redirected towards the positive and negative directions orthogonal to the incident wave with different amounts of energy. Simulation and experimental results demonstrate the extraordinary asymmetric lateral beaming effect in the Willis medium. The results presented here may find applications in the design of tunable beam splitters and waveguides.

中文翻译：

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Willis 介质中的非对称横向声波

威利斯耦合，也称为压力-速度交叉耦合，在过去的几年里在声学材料中受到了很多关注。已经发现这种效应在用于波重定向的声学超表面设计中很有用。我们发现声子晶体中的威利斯耦合也提供了丰富的物理学来操纵波。在这里，我们报告了由威利斯散射体组成的二维声子晶体中的极端不对称横向声束效应。通过将二阶布拉格散射与两个泄漏导模（四极共振和交叉耦合引起的偶极共振）相匹配，法向入射波被重定向到与入射波正交的正负方向，具有不同的能量. 模拟和实验结果证明了威利斯介质中非凡的不对称横向光束效应。这里介绍的结果可能会在可调谐分束器和波导的设计中找到应用。