Improved Finite-Element Formulation in Terms of the Magnetic Field Vector for Dielectric Waveguides

TLDR

The authors develop an improved finite‑element method for dielectric waveguides that formulates the problem in terms of all three magnetic‑field components, eliminating spurious solutions above the air line and enabling accurate surface‑wave analysis. The method applies to waveguides with perfect electric and magnetic conductors, incorporates boundary conditions even when the conductor normal is not aligned with coordinate axes, and exploits symmetry planes to reduce matrix size. This approach economizes memory and rigorously enforces boundary conditions, thereby eliminating spurious solutions.

Abstract

An improved finite-element method for the analysis of dielectric waveguides is formulated in terms of all three components of the magnetic field H. In this approach, the spurious, nonphysical solutions do not appear anywhere above the "air-line," and therefore the present formulation is very useful for the analysis of the surface-wave modes of dielectric waveguides. The application of this improved finite-element method to the dielectric waveguides with perfect electric and magnetic conductors is also discussed. In particular, the discussion is how to use the conditions on a boundary surface of a perfect electric or magnetic conductor whose normal direction is not coincident with the direction of a coordinate axis. Application of these boundary conditions for perfect conductors to the dielectric waveguides with planes of symmetry reduces the matrix size. The strength of this approach to boundary conditions is not just the economical use of computer memory but the elimination of spurious solutions through rigorous enforcement of boundary conditions as well.