On mathematical modeling of a triangular building block in the analysis of E-plane waveguide structures

A conventional approach to the analysis of a complex waveguide component consists of dividing the whole unit into buildings blocks and exploiting the method of generalized scattering matrices. The procedure works successfully if the blocks which arise after segmentation have simple shape and can be studied on the basis of effective numerical-analytical techniques. The set of such objects is clearly limited in number. A triangular region with the attached wave channels represents a key-configuration in the theory of guided waves. Potentially, it allows modeling rather complicated structures. However its boundaries have irregular geometry, which restricts the capabilities of efficient techniques to deal with it. In this paper, we consider an E-plane waveguide two-port, whose connecting cavity (result of segmentation) is bounded by arbitrary triangle. The analysis exploits the domain-product technique (DPT). The cavity field is specified in the form of a trigonometric-series expansion for a convexly polygonal region. This construction provides good convergence properties of the algorithm and allows carrying out analytically all mathematical procedures involved in the algebraization process.