Localized defect modes of water waves through two-dimensional periodic bottoms with point defects

In this Letter, the localized defect modes of water waves over two-dimensional periodic bottoms with a point defect are investigated by supercell calculations and plane-wave expansion method. Two kinds of defects are introduced, one is a radius defect created by changing radius of cylinder, and another is a depth defect created by changing its depth. The results indicate that both can create defect modes, and the amplitude distributions of the defect modes are well localized in the vicinity of the defects with various patterns. The influences of radius and depth of defect cylinder on the defect modes are investigated in detail.