Nonreciprocal Linear Transmission of Sound in a Viscous Environment with Broken P Symmetry

Reciprocity is a fundamental property of the wave equation in a linear medium that originates from time-reversal symmetry, or T symmetry. For electromagnetic waves, reciprocity can be violated by an external magnetic field. It is much harder to realize nonreciprocity for acoustic waves. Here we report the first experimental observation of linear nonreciprocal transmission of ultrasound through a water-submerged phononic crystal consisting of asymmetric rods. Viscosity of water is the factor that breaks the T symmetry. Asymmetry, or broken P symmetry along the direction of sound propagation, is the second necessary factor for nonreciprocity. Experimental results are in agreement with numerical simulations based on the Navier-Stokes equation. Our study demonstrates that a medium with broken PT symmetry is acoustically nonreciprocal. The proposed passive nonreciprocal device is cheap, robust, and does not require an energy source.