Modal Analysis of Gyrotropic Waveguides

Abstract: We report on the modal analysis of open gyrotropic waveguides (GWs). The GWs consist of a non-circular gyrotropic (i.e., gyroelectric and gyromagnetic) core and an infinitely extending isotropic cladding. To solve this problem, we develop two independent full-wave methods. The first technique is an extended integral equation (EIE) method, an extension of a previously developed EIE used to calculate the propagation constants in composite dielectric-isotropic waveguides. The second technique is a Chebyshev expansion method (CEM). In both implementations, the electric and magnetic fields in the gyrotropic core are expanded in superpotential-based cylindrical vector wave functions (SUPER-CVWFs), recently developed for the problem of oblique multiple scattering by gyrotropic cylinders. Both techniques allow us to calculate the propagation constants in the general case, without approximations. Various non-circular gyrotropic waveguides are considered. The EIE and CEM results are validated against a commercial finite element solver, and the accuracy and computational performance of both methods are benchmarked. A microwave application is presented where the complex propagation constants of ferrite rods are computed in the presence of an external magnetic flux density bias. Our work advances the theory of propagation in open waveguides, from dielectric/isotropic to gyrotropic ones, and enables the design of contemporary waveguiding structures.