A Semianalytical Approach for a Nonconfocal Suspended Strip in an Elliptical Waveguide

Abstract

A problem of a nonconfocal suspended strip in an elliptical waveguide is analyzed by using a semianalytical approach, which is the so-called null-field boundary integral-equation method (BIEM). The null-field BIEM is proposed by introducing the idea of null field, degenerate kernels, and eigenfunction expansion to improve the conventional dual boundary-element method (BEM). A closed-form fundamental solution can be expressed in terms of the degenerate kernel containing the Mathieu and modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. By this way, the efficiency is promoted in three aspects: analytical boundary integral without numerical error, natural bases for boundary densities, and exact description of boundary geometry. Due to the semianalytical formulation, the null-field BIEM can fully capture the property of geometry and the error only occurs from the truncation of the number of the eigenfunction expansion terms in the real implementation. The present method is also a kind of meshless method since only boundary nodes are needed to construct influence matrices instead of using boundary elements. Both TE and TM cases are considered in this paper. To verify the validity of the present method, the dual BEM and finite-element method are also utilized to provide cutoff wavenumbers. Besides, the analytical solution of a confocal elliptical waveguide can be derived by using the present method. After comparing with published data, good agreement is made.