**G. CAVIGLIA** and **A. MORRO**

*Electromagnetic waves in stratified media*

**Pages:** 77-92

**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, Fresnel’s formulae for reflection and transmission
are recovered.

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