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

We theoretically study the interface states of liquid surface waves propagating over the heterojunctions formed by a bottom with one-dimensional periodic undulations. By 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 whether the structure is symmetric or not. 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.