Application of exterior calculus to waveguides
Rafael Ferraro
TL;DR
This paper demonstrates how exterior calculus can be effectively used to derive electromagnetic TM and TE modes in hollow cylindrical waveguides, simplifying the process of finding solutions and calculating transmitted power.
Contribution
It introduces a novel application of exterior calculus combined with Lorentz boosts to derive waveguide modes and power transmission in a straightforward manner.
Findings
Derived electromagnetic TM and TE modes using exterior calculus
Provided a method to calculate transmitted power in waveguides
Simplified the solution process for waveguide electromagnetic fields
Abstract
Exterior calculus is a powerful tool to search for solutions to the electromagnetic field equations, whose strength can be better appreciated when applied to work out non-trivial configurations. Here we show how to exploit this machinery to obtain the electromagnetic TM and TE modes in hollow cylindrical waveguides. The proper use of exterior calculus and Lorentz boosts will straightforwardly lead to such solutions and the respective power transmitted along the waveguide.
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