A STUDY ON THE EIGENMODES OF THE SQUARE AND CIRCULAR COAXIAL WAVEGUIDES BY FEM

FEM has been used to construct an eigen-equation for coaxial waveguides. Their cross sections have been square and circular shapes made with different dielectric constants. Krylov-Schur iteration method has been carried out to obtain the eigen-modes for these waveguides. The eigen-modes for each waveguides have been divided into two classes of TE and TM modes. These eigen-modes have been schematically represented with the spectra of transverse vector fields and their corresponding vector potential values. The spectra have shown the distribution of fields surrounding the interface between two dielectrics. Especially, the spectra have revealed the complicated distribution of field at the inner region of the dielectrics. As increased the distance from the center, the intensity of electromagnetic wave is decreased and arranged in the structured form. From these results, it could be identified that the eigen-modes seemed reflecting on the dielectric properties of coaxial waveguides. The eigen-property of the waveguide is a matter that must be considered firstly than others. Physically, this property may be revealed by the eigen-mode and eigen-value which is the most important thing characterizing the waveguide. These are directly related to the geometrical structure of waveguide and the distribution of dielectrics in its space. The eigen-properties for above mentioned waveguides have been investigated variously with theoretical and experimental methods. So far, for a long time, a lot of information about the eigen-mode have been accumulated and applied in the actual communication system. But in some case, the theoretical method could not explain the eigen-properties including the influence of the interface between the different dielectrics. In particular, the high order eigen-modes obtained through experiments have been shown a complicated form that cannot be theoretically analysis. This phenomenon has been appeared even more seriously from the coaxial waveguide of complicated structure. Generally, the numerical analysis has been applied to overcome this problem. Among others, FEM(Finite element method) has been well known as one of the most reliable method to resolve such a problem. Previously, we have studied on the eigen-modes of square waveguide made with two different dielectrics. The distribution of dielectrics was simply a step-like along the transvers direction of the waveguide. In there, the eign-pairs have been obtained and compared them with the theoretically calculated results (4). As an extension of this study, the similar calculation have applied to waveguides of the some more complicated structure. Waveguides were square and circular coaxial forms with the greater dielectric constant in the core region. In the course of FEM analysis, the cross section was divided into triangular mesh. The eigen-matrix equation was constructed using tangential edges and nodes of triangular element meshes. Tangential edges and nodes were used as calculating variables for transverse vector fields and their vector potential component respectively. The eigen-modes were obtained by using the Krylov-Schur iteration method (5). TE(Transverse Electric) and TM(Transverse magnetic) modes could be calculated by giving different boundary conditions on the surface of the waveguide. Each columns of the similarity transforming matrix have contained the eigen-modes of transverse vector field and its vector potential component simultaneously. As a result, among the eigen-modes,