An accurate and efficient method for calculating surface waves in defective two–dimensional semi–infinite periodic structures

This study presents an efficient and accurate method for calculating surface waves in a defective two–dimensional (2D) semi–infinite periodic structure with semi–infinite length in two directions. Based on the attenuated propagation properties of surface waves and symplectic transfer matrices, we demonstrated that the eigenfrequencies of surface waves in a defective 2D semi–infinite periodic structure are the intersections of the eigenfrequencies within the bandgap of the corresponding defective 2D finite periodic structure composed of sufficient unit cells under different boundary conditions. The eigenfrequencies of a defective 2D finite periodic structure can be calculated efficiently and accurately by the method combining the 2^N algorithm and Wittrick–Williams algorithm. This method can also be used to efficiently and accurately calculate surface waves in an ideal 2D semi–infinite periodic structure. The accuracy and efficiency of the proposed method are demonstrated through serval numerical examples. In addition, the effects of boundary conditions and several different defects on surface wave propagation are investigated.