Electromagnetic wave propagation through position dependent permeability and permittivity

We use Maxwell's equations in a source-less, non-uniform medium with position dependent, continuous permeability $\mu $ and permittivity $\epsilon $ 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 significantly 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 has been given in terms of the Heun's functions.