Electromagnetic wave propagation through inhomogeneous material layers

Abstract

We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability mu (r) and permittivity epsilon (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.