Prediction of interface states in liquid surface waves with one-dimensional modulation

We theoretically studied the interface states of liquid surface waves propagating through the heterojunctions formed by a bottom with one-dimensional periodic undulations. Via considering the periodic structure as a homogeneous one, our systematic study shows that the signs of the effective depth and gravitational acceleration are opposite within the band gaps no matter the structure is symmetric or asymmetric. Those effective parameters can be used to predict the interface states which could amplify the amplitudes of liquid surface waves. These phenomena provide new opportunities to control the localization of water-wave energy.