A Necessary and Sufficient Condition for Having Independent TE and TM Modes in an Anisotropic Waveguide

TL;DR

This paper provides a definitive condition for the existence of independent TE and TM modes in anisotropic waveguides, advancing theoretical understanding and aiding waveguide design.

Contribution

It establishes a necessary and sufficient condition for independent TE and TM modes in anisotropic waveguides, a novel theoretical result in electromagnetic waveguide theory.

Findings

Derived a condition for independent TE and TM modes in anisotropic waveguides

Proved equality of propagation constants from different field stimulations for TE modes

Proved equality of propagation constants from different field stimulations for TM modes

Abstract

Whether there exist independent transverse electric (TE) and transverse magnetic (TM) modes in a metallic waveguide filled with an anisotropic medium is a fundamental question in electromagnetics waveguide theory, but so far no definitive answers have been published. This paper establishes a necessary and sufficient condition for having independent TE and TM modes in a waveguide filled with a homogeneous lossless anisotropic medium based on both waveguide theory in electromagnetics and basic knowledge in mathematics. Moreover, for the independent TE modes, we prove the propagation constants obtained from both the longitudinal scalar magnetic field stimulation and the transverse vector electric field stimulation are the same; for the independent TM modes, the propagation constants obtained from both the longitudinal scalar electric field stimulation and the transverse vector magnetic field stimulation are the same. This necessary and sufficient condition is a new theoretical result in electromagnetic waveguide theory, and is expected to be valuable for the design of waveguides filled with anisotropic media.