# Modes of an elliptical cylindrical resonant cavity -- analytical solution

## TL;DR

This paper derives an analytical solution for electromagnetic modes in an elliptic cylindrical resonant cavity, showing how ellipticity affects mode frequencies, Q-factor, and degeneracy splitting, with validation against numerical and experimental data.

## Contribution

It provides the first analytical solution for the Helmholtz equation in elliptic cylindrical cavities and analyzes the impact of ellipticity on mode characteristics.

## Key findings

- Analytical expressions for mode frequencies in elliptic cavities
- Ellipticity influences the Q-factor and mode splitting
- Excellent agreement with numerical and experimental results

## Abstract

An analytical solution of the Helmholtz equation for electromagnetic field distribution in a resonant cavity with elliptic cross-section is found. We compare the frequencies of the eigenmodes with numerical and experimental values for a metallic cavity and find an excellent matching. We focus our analysis on the microwave frequency region, and show how the ellipticity of the cavity (ratio of the minor and major axes length $b/a$) influences several mode frequencies and also the $Q$-factor of the cavity. By doing so, we demonstrate how the elliptic geometry splits the degeneracy of certain modes of the circular cylindric cavity.