Electromagnetic wave propagation through inhomogeneous material layers
arXiv:1303.3264 · doi:10.1080/09205071.2013.831741
Abstract
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $μ(\mathbf{r}) $ and permittivity $% ε(\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived and by virtue of some physical assumptions, including $μ$ and $ε$ as functions of $z,$ the equation has been simplified. Finally by introducing a smooth step dielectric variable we solve the wave equation in the corresponding medium which is in conform with the well known results. Exact double-layer solution in analytic form has been given in terms of the Heun functions.
8 pages, 2 figures, final version, accepted for publication in Journal of Electromagnetic Waves and Applications