Modeling of a resonator with multilayered dielectric using the method of auxiliary sources and the expansion wave concept

A numerical technique is developed for the calculation of electromagnetic fields inside a cavity filled with multilayered dielectric. The primary field generated by the source is expressed in terms of the eigenmodes of the parallel plate waveguide. As in the original method of auxiliary sources, auxiliary sources and collocation points are introduced on the perimeter of the cavity on the side walls, where the boundary conditions are imposed. Each auxiliary source is a source of omni-directional radiation of the waveguide's eigenmode. An example involving two coaxial probes in the rectangular cavity is presented. I. INTRODUCTION The method of auxiliary sources (MAS) is a numerical technique that is used to solve two dimensional (2D) and three dimensional (3D) scattering problems. The MAS was introduced and developed by several researchers in the republic of Georgia @art of the former Sovi.et Union) (I-31. The solution of scattering problems can be reduced to surface integral equations. The main feature of the MAS consists of the elimination of the singularity, which exists in the surface integral equations, by shifting the position of the auxiliary source away from the position where the boundary conditions are imposed. This step simplifies considerably the construction of numerical solutions. In the original MAS (I-41, auxiliary sources are chosen to be either current filements for 2D problems or pairs of elementary dipoles for 3D problems. It is well known that the MAS can he used to determine the solution of so-called interior problems associated with cavities (eigenfields and eigenvalues). In this paper we consider a resonator filled with plane multilayered dielectric excited by an arbitrary primary source. Our approach is based on the combination of the expansion wave concept (EWC) (5) with the MAS. Any primary source located in a parallel plate waveguide filled with plane multilayered dielectric generates fields, which can be expressed in terms of eigenmodes of this waveguide. Now let's construct the cavity by introducing the side walls on the perimeter of the resonator. The eigenmodes satisfy explicitly the boundary conditions on the top and bonom plates of the'waveguide. Therefore we need to impose the boundary conditions only at the side walls of the resonator. We consider a resonator in which the side walls are perpendicular to the ground planes of the waveguide. In this case there is no coupling between different eigenmodes on the perimeter of the resonator. As a consequence we can solve the problem consecutively for each eigenmode. It is worth pointing out that for a homogeneously filled resonator the solution for the TEM eigenmode becomes identical to the original 2D problem because for 2D problems we can introduce two electric or magnetic ground plates perpendicular to the auxiliary source's filaments. These plates will not alter the solution. In our case the waveguide is filled with layered dielectric. Meanwhile the basic idea of the MAS can be still used. The difference with the original approach consists in the type of waves that are excited by the auxiliary sources. In our case each auxiliary source generates an eigenmode of the waveguide with an omni-directional radiation panem. The properties of these eigenmodes differ a little bit from the properties of cylindrical waves in free space but the problem remains quasi two dimensional because all field components of any eigenmode can be expressed in terms of a single fieid component. For each eigenmode the boundary conditions on the perimeter of the resonator can be satisfied using the MAS. In many cases the height of the parallel plate waveguide is small in tem of the wavelength and as a consequence the number of propagating eigenmodes becomes very small. In many practical situations it will be sufficient to take only one eigenmode into, consideration. One of the advantages of our approach is that we are able to consider different primary sources with a rather complex