Asymmetric lateral sound beaming in a Willis medium

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