A Sufficient Condition of Having Independent TE and TM Modes in a Waveguide Filled with Homogenous Anisotropic Lossless Medium

TL;DR

This paper establishes a mathematical condition ensuring the independence of TE and TM modes in waveguides filled with homogeneous anisotropic lossless media, verified through numerical experiments, aiding microwave waveguide design.

Contribution

It introduces a sufficient condition for TE and TM mode independence in anisotropic waveguides using Abelian group theory, a novel theoretical approach in this context.

Findings

Proves nonzero cut-off wavenumbers are equal for TE modes from different stimulations.

Proves nonzero cut-off wavenumbers are equal for TM modes from different stimulations.

Numerical experiments verify the theoretical condition.

Abstract

Based on the idea of the Abelian group theory in mathematics,this paper finds a sufficient condition of having independent TE and TM modes in a waveguide filled with homogenous anisotropic lossless medium. For independent TE modes, we prove the nonzero cut-off wavenumbers obtained from longitudinal scalar magnetic field stimulation and transverse vector electric field stimulation are same in theory. For independent TM modes, we also prove the nonzero cut-off wavenumbers obtained from longitudinal scalar electric field stimulation and transverse vector magnetic field stimulation are same in theory. Finally we carry out several numerical experiments to verify the correctness of the condition given by us.We hope that this condition is useful for the designs of waveguide with homogenous anisotropic lossless medium in microwave engineering community.