Recursive asymptotic stiffness matrix method for analysis of surface acoustic wave devices on layered piezoelectric media

Based on a simple second-order thin layer asymptotic expansion for the transfer matrix, an asymptotic solution for the stiffness matrix for a general anisotropic piezoelectric thin layer is obtained. The total stiffness matrix for thick layers or multilayers is calculated with arbitrary precision by subdividing them into thin sublayers and combining recursively the thin layer stiffness matrices. It is shown that this method converges to the exact solution and is computationally stable, efficient and easy to implement. A semispace substrate is substituted for by a finite thickness layer loaded by a perfectly matched attenuating layer. The effective permittivity and general Green’s functions for a layered system on a substrate are formulated in terms of stiffness and compliance matrices. The advantage of the method is that one does not need to compute the exact wave propagation solution for an anisotropic piezoelectric layer or semispace.