Floquet waves and classical plane waves in an anisotropic periodically multilayered medium: Application to the validity domain of homogenization

Abstract

The aim of this paper is to better understand the correspondence between classical plane waves propagating in each layer of an anisotropic periodically multilayered medium and Floquet waves. The last are linear combinations of the classical plane waves. Their wave number is obtained from the eigenvalues of the transfer matrix of one cell of the medium. A Floquet polarization which varies with its position in the periodically multilayered medium has been defined. This allows one to define a Floquet wave displacement by analogy with the displacement of classical plane waves, and to check the equality of the two displacements at any interface separating two layers. The periodically multilayered medium is then an equivalent material, considered as homogeneous, and one can draw dispersion curves and slowness surfaces which are dispersive. In the low-frequency range, when the relation between the Floquet wave numbers and the frequency is linear, the multilayered medium can be homogenized; the Floquet polarization at different interfaces tends to a limit which is the polarization of the classical plane wave in the homogenized medium.