H- modes of rectangular dielectric waveguide

The rectangular dielectric waveguides (RDWs) have been considered and investigated for various practical applications in the series of works. They have been used as probes, in the structures of filters and planar integrated circuits, as elements of resonators, for measurements of dielectric material properties, and for other purpose. Different approximate and rigorous approaches have been applied to analyze the RDW and its discontinuities. There are: the decomposition on the cylindrical harmonics, the Marcatilipsilas approach, the transverse resonance method, the generalized telegraph equation method, the finite difference method, the mode matching method, the integral equation method and the variation approac. For numerical investigations of these approaches several numerical algorithms have been applied: the moment method, the Bubnov-Galerkin method, the collocations, the finite elements, the finite differences and some others. The dimensions of such approaches are very high when good accuracy is need. Therefore the precise determination of RDW mode parameters is actual. In this paper we introduce the simple relations and effective algorithm for accurate determinations of eigenmodes (eigenwaves) and complex H-waves for RDW. The approach is based on two-dimensional hyper-singular integral equation and iteration procedure for its solution which allow one to determine the mode parameters with very high accuracy and small computing resources. Instead of usually used infinite-dimensional functional banach spaces we seek the solution in the two-dimensional Euclidean numeric space with analytical field presentation.