Propagation in an anisotropic periodically multilayered medium

Abstract

An anisotropic multilayered medium is studied using the method of transfer matrices, developed by Thomson [J. Appl. Phys. 21, 89 (1950)] and Haskell [Bull. Seismol. Soc. Am. 43, 17 (1953)]. The propagation equations in each layer of the multilayered medium use the form developed by Rokhlin et al. [J. Acoust. Soc. Am. 79, 906–918 (1986); J. Appl. Phys. 59 (11), 3672–3677 (1986)]. Physical explanations are given, notably when a layer is made up of a monoclinic crystal system medium. The displacement amplitudes of the waves in one layer may be expressed as a function of those in another layer using a propagation matrix form, which is equivalent to relating the displacement stresses of a layer to those in another layer. An anisotropic periodically multilayered medium is then studied by using a propagation matrix that has particular properties: a determinant equal to one and eigenvalues corresponding to the propagation of the Floquet waves. An example of such a medium with the axis of symmetry of each layer perpendicular to the interfaces is then presented together with the associated reflection coefficients as a function of the frequency or of the incident angle.