Guided waves in layered cubic media: Convergence study of a polynomial expansion approach

A new numerical method to compute propagation constants and mode functions of a planar layered acoustic waveguide is described. The basic feature is the expansion of velocity and stress fields in each layer on different Legendre polynomial bases, which ensures an exponential convergence rate of the method. No transcendental equation has to be solved and also modes that have very close propagation constants (e.g., coupled Rayleigh waves) are computed with great accuracy. Convergence of the method is studied and a way to estimate and control the error on the solutions is discussed.