Properties and Numerical Solutions of Dispersion Curves in General Isotropic Waveguides

Abstract

Abstract-In this paper, some properties of dispersion curves in general isotropic piecewise homogeneous waveguides are rigorously derived. These properties are leveraged in a numerical implementation capable of determining the dispersion curves of such waveguides with cross-section materials that can be highly conductive (such as copper). In a numerical example, the influence of a lossy shielding conductor on the complex modes of a shielded dielectric image guide is investigated for the first time.

Analytic properties of dispersion curves for efficient eigenmode analysis of isotropic waveguides using a boundary element method

“…In an eigenmode analysis, we are interested in non-trivial solutions of the homogeneous time-harmonic Maxwell equations (e jωt convention) that have an e −jβz dependence. This leads to representation formulas for the fields that depend on the parameters ω, β ∈ C [1]. Imposing continuity of the tangential fields at the medium boundaries, and introducing the two-dimensional version M of the PMCHWT operator [7]-[9], leads to the following system for the tangential traces of the fields:…”

“…The following theorems discuss the analyticity of the determinant and the behavior of a dispersion curve as a function of frequency [1].…”

“…They predict all occuring wave phenomena, including crosstalk and signal losses. There is a large number of numerical techniques available for the eigenmode analysis of uniform waveguides [1], but we will only briefly discuss the two predominant methods.…”

Accurate 2.5‐D boundary element method for conductive media

“…This paper considers two-dimensional geometries with conductive material regions, which can be magnetic, illuminated by arbitrary three-dimensional sources, leading to a so-called 2.5-D boundary element method. Important applications of this class of problems are propagation in uniform waveguides with nonperfect conductors [Coluccini et al, 2013;Tong et al, 2005;Dobbelaere et al, 2013a], scattering problems [Murphy et al, 1991], and shielding problems [Dobbelaere et al, 2013b].…”