Electromagnetic wave propagation through inhomogeneous material layers

Abstract We use Maxwell’s equations in a sourceless, inhomogeneous medium with continuous permeability and permittivity to study the wave propagation. The general form of the wave equation is derived and by virtue of some physical assumptions, including and as functions of 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.