An accurate and efficient method for calculating surface waves in one-dimensional ideal and defective semi-infinite periodic structures

Abstract

This study presents an efficient and accurate method for calculating surface waves in one-dimensional ideal and defective semi-infinite periodic structures. The eigenequations for the surface waves in an ideal semi-infinite periodic structure and those eigenequations for the finite periodic structure within the bandgap are derived using the symplectic matrix. Based on these two eigenequations and the properties of the symplectic matrix, we show that the eigenfrequencies of the surface waves in an ideal semi-infinite periodic structure can be obtained using the eigenfrequencies within the bandgap of a finite periodic structure with different boundary conditions. The eigenfrequencies of the finite periodic structure can be calculated efficiently and accurately by the method combining the \(2^{N}\) algorithm and Wittrick–Williams algorithm. The proposed method is also extended to solve the surface waves in defective semi-infinite periodic structures. The accuracy and efficiency of the proposed method are demonstrated using several numerical examples.