When sound interacts with geometrically asymmetric structures, it experiences coupling between pressure and particle velocity, known as Willis coupling. While in most instances this phenomenon is perturbative in nature, tailored asymmetries combined with resonances can largely enhance it, enabling exotic acoustic phenomena. In these systems, Willis coupling obeys reciprocity, imposing an even symmetry of the Willis coefficients with respect to time reversal and the impinging wave vector, which translates into stringent constraints on the overall scattering response. In this work, we introduce and experimentally observe a dual form of acoustic Willis coupling, arising in geometrically symmetric structures when time-reversal symmetry is broken, for which the pressure-velocity coupling is purely odd-symmetric. We derive the conditions to maximize this effect, we experimentally verify it in a symmetric subwavelength scatterer biased by angular momentum, and we demonstrate the opportunities for sound scattering enabled by odd Willis coupling. Our study opens directions for acoustic metamaterials, with direct implications for sound control, non-reciprocal scattering, wavefront shaping and signal routing, of broad interest also for nano-optics, photonics, elasto-dynamics, and mechanics.

当声音与几何非对称结构相互作用时，它会经历压力和粒子速度之间的耦合，即威利斯耦合。尽管在大多数情况下，这种现象本质上是微扰的，但量身定制的不对称性与共振相结合可以大大增强这种现象，从而产生奇异的声学现象。在这些系统中，威利斯耦合服从互易性，威利斯系数相对于时间反转和冲击波矢量具有均匀的对称性，这转化为对整体散射响应的严格约束。在这项工作中，我们引入并实验观察了声威利斯耦合的一种双重形式，这种形式出现在几何形状对称的结构中，而时间-逆向对称性破裂时，压力-速度耦合纯粹是奇对称的。我们推导了使这种效应最大化的条件，我们在由角动量偏置的对称亚波长散射体中进行了实验验证，并证明了奇威利斯耦合所带来的声音散射机会。我们的研究为声学超材料打开了方向，直接影响到声音控制，不可逆散射，波阵面整形和信号路由，纳米光学，光子学，弹性动力学和力学也引起了广泛关注。