A robust method for surface wave dispersion in anisotropic semi-infinite periodically layered structures with coating layers

Abstract

This study presents a robust method towards the computation of dispersion curves of surface waves in an anisotropic semi-infinite periodically layered structure (PLS) coated by a stack of layers. Using the properties of the symplectic transfer matrix to analyze the relationship between the eigenequations of surface waves in a semi-infinite PLS and of its corresponding finite PLS, the eigenfrequencies within the stopbands for surface waves in a semi-infinite PLS are solved by a finite PLS consisting of a sufficient number of unit cells. The eigenvalues of a finite PLS are calculated by combining the precise integration method with the Wittrick–Williams (W-W) algorithm, which makes the present method accurate, efficient and numerically stable. On this basis, using the concept of the eigenvalue count in the W-W algorithm, the eigenfrequencies of surface waves in a semi-infinite PLS coated by a stack of layers are accurately computed for any given wavenumber. Unlike most existing approaches that determine dispersion curves by directly seeking roots from the transcendental eigenequation, the present method takes full advantages of the eigenvalue count to find all eigenfrequencies without the possibility of any being missed. The method can be applicable for surface wave problems in an arbitrarily anisotropic semi-infinite PLS and does not restrict layer number, layer thickness and material properties.