Omnidirectional total reflection for liquid surface waves propagating over a bottom with one-dimensional periodic undulations

We study theoretically the propagation of liquid surface waves over a bottom with one-dimensional (1D) periodic undulations. We find a general criterion for omnidirectional total reflection in such a system. Numerical simulations based on a transfer matrix method demonstrate unambiguously the existence of omnidirectional total reflection for liquid surface waves propagating over a bottom with 1D periodic undulations.