Wave propagation in a medium with position-dependent permittivity and permeability

The electromagnetic wave propagation in inhomogeneous media is studied. The wave equation in such a medium is obtained. By considering the permittivity as a positiondependent function (i.e, z-dependent) and the permeability as a constant (i.e, μ = kmμ0) the wave equation is determined. The wave function is reported exactly in a medium with smooth step dielectric constant, in terms of hypergeometric function. The asymptotic behaviors of the wave function are examined and the reflection and transmission coefficients are found in perfect agreement with the previous results. Moreover, a smooth double layer case is studied and the corresponding wave function is presented and plotted exactly in terms of Heun function. Besides, the asymptotic behavior of the wave function is appointed. It is noticeable that the result of this thesis published in an international journal.