G. CAVIGLIA and A. MORRO
Electromagnetic waves in stratified media
Received: 7 April 1999
Mathematics Subject Classification: 78A40 - 78A25
Abstract: Time-harmonic wave propagation is considered in inhomogeneous, isotropic, electromagnetic solids. The particular case is then assumed that the material properties (permittivity and permeability) depend on a Cartesian coordinate only and the problem is shown to satisfy a system of linear, first-order, ordinary differential equations. A suitable change of unknown functions is performed by means of the eigenvectors of the coefficient matrix. The peculiar structure of the system of evolution equations results in a single equation for a suitable unknown variable thus providing finer approximations to the solution of a Cauchy problem with data at a surface. The recourse to properties of thermodynamic character allows a deeper understanding of the results. The coefficients of reflection and transmission are evaluated in closed form. As a check of consistency, in the thin-layer limit for a stratified slab, Fresnelís formulae for reflection and transmission are recovered.