  We use Maxwell's equations in a sourceless, inhomogeneous medium with
continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon
(\mathbf{r}) $ to study the wave propagation. The general form of the wave
equation is derived and by virtue of some physical assumptions, including $\mu
$ and $\epsilon $ 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.
