A Maher

The existence of eigenvalue problems for the waveguide theory

In this paper, the existence of the eigenvalue problem for the waveguide theory is investigated. We used the Fourier transformation method for the solution of this problem. Also, we applied this problem to a dielectric waveguide. In this study, four theorems and two lemmas are obtained.MSC: 35A22, 35P10.

Plane electromagnetic wave scattering and diffraction in a stratified medium

The two-dimensional jump problem for the Helmholtz equation in a stratified medium is considered. Preliminary two auxiliary overdetermined Cauchy problems for a half-plane and for a strip in Sobolev classes of distributions of slow growth at infinity are solved and explicit representations of their solutions are given. It is shown that the jump problem in the case of a multilayered medium can be reduced to a set of equations for the Fourier transforms of the boundary distributions for each layer. This set of equations can be transformed to two equations only. The jump problem for the Helmholtz equation is equivalent to a scattering problem for a plane electromagnetic wave in a multilayered space. The diffraction problem for an electromagnetic plane wave at a finite set of metallic strips in a stratified space is considered. It is proved that this problem is equivalent to an integral equation with a logarithmic singularity in the kernel.