Cutoff Wavenumbers of Multilayered Gyrotropic Circular Waveguides

Abstract

A coupled-field volume integral equation (CFVIE) method is developed for the calculation of the normalized cutoff wavenumbers of circular metallic walled waveguides having concentric continuously varying highly inhomogeneous gyrotropic (i.e., gyroelectric and gyromagnetic) infill. The normalized cutoff wavenumbers are obtained as the roots of a determinantal equation formed by solving the CFVIEs using the cylindrical Dini series expansion (CDSE) method where the unknown fields inside the waveguide are expanded by entire domain orthogonal Dini-type vectorial basis functions. To account for the electric boundary condition (BC) on waveguide's circular perfect electric conducting (PEC) surface, two modified 2-D tensorial Green's functions (GFs), expanded in cylindrical vector wave functions (CVWFs), are employed in the kernels of the CFVIEs. These modified 2-D tensorial GFs are constructed by enforcing, on their dyadic form, the satisfaction of the electric BC. The CDSE, along with the modified 2-D tensorial GFs, allow for the analytical integration of the volumetric-type integrals and the reduction of the CFVIEs to a set of algebraic equations. We exhaustively demonstrate the validity of the CFVIE-CDSE by a series of comparisons on the normalized cutoff wavenumbers: we first construct the solutions for obtaining the normalized cutoff wavenumbers in homogeneous gyrotropic waveguides by the separation of variables method (SVM), and second, we employ HFSS commercial software for two-layered isotropic and three-layered gyroelectric loaded waveguides. We characterize the type of modes, i.e., TE/TM or hybrid HE/EH, for each configuration presented, and discuss the efficiency of the CFVIE-CDSE method.